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Quantum Many-Body Physics in Open Systems : Measurement and Strong Correlations

蘆田, 祐人東京大学 DOI:10.15083/0002001840

2021.10.04

概要

This Thesis studies the fundamental aspects of many-body physics in quantum systems open to an external world. The last two decades have witnessed remarkable developments in studies of in- and out-of-equilibrium many-body physics of closed quantum systems, as mainly motivated by experimental advances in atomic, molecular and optical (AMO) physics. Meanwhile, recent developments have allowed one to measure and manipulate many-body systems at the single- quantum level, thus revolutionizing our approach to many-body physics. At such ultimate resolution, the measurement backaction, which is the fundamental effect acted by an external observer, becomes significant. Moreover, microscopic manipulation capabilities of many-body systems have realized quantum systems strongly correlated with an external environment. These remarkable advances thus point to a new arena of many-body physics that is open to an external world, in which interactions with an external observer or an environment play a major role. The research of this Thesis is devoted to addressing the question of how the ability to measure and manipulate single quanta can create a new frontier of many-body physics beyond the conventional paradigm of closed systems.

In the first part of this Thesis (Chapters 3-4), we study the influences of measurement backaction from an external observer on quantum critical phenomena and out-of-equilibrium many-body dynamics. In the second part of this Thesis (Chapters 5-6), we reveal in- and out-of- equilibrium physics of quantum systems strongly correlated with an external environment, where the entanglement between the system and the environment plays an essential role. In the following paragraphs, we provide the backgrounds and specific details about the results provided in each part of this Thesis.

The first part of this Thesis is devoted to elucidating how the influences of measurement backaction from an external observer trigger new types of many-body phenomena that have no analogues in closed systems. The time evolution of an isolated quantum system is described by a single Hermitian operator, i.e., the Hamiltonian. In contrast, under continuous observation, the dynamics becomes intrinsically nonunitary due to the measurement backaction and is characterized not only by the Hamiltonian but also by a measurement process. Recent revolutionary developments in AMO physics, especially realizations of the technique known as quantum gas microscopy, have enabled one to measure quantum many-body systems at the single-atom precision, where the measurement backaction is expected to be significant. Moreover, further developments of in-situ imaging techniques of quantum gases will allow one to perform a nondestructive, real-time monitoring of the many-body dynamics. The aim of the first part of this Thesis is to show how one can utilize these revolutionary techniques to reveal previously unexplored effects of measurements on many-body physics.

To achieve this aim, we focus on two fundamental aspects of many-body physics, namely, quantum critical phenomena and out-of-equilibrium dynamics. In Chapter 3, we analyze an effective non-Hermitian Hamiltonian that governs the nonunitary evolution under continuous observation and elucidate the influence of measurement backaction on quantum criticality. We first consider universal low-energy behavior of one-dimensional quantum many-body systems and identify two possible types of relevant non-Hermitian perturbations to them. We show how they significantly alter the underlying critical phenomena and phase transitions beyond the conventional paradigms of the Tomonaga-Luttinger liquid theory and the Berezinskii- Kosterlitz-Thouless transition. We then study the influence of measurement backaction on quantum phase transitions in higher dimensions by analyzing the superfluid-to-Mott insulator transition in the Bose-Hubbard model as a concrete example. In Chapter 4, we discuss out-of- equilibrium dynamics influenced by measurement backaction. Specifically, we present three theoretical frameworks to describe the dynamics of quantum many-body systems under continuous observation and apply them to particular models to elucidate the underlying physics. Firstly, we formulate a class of many-body dynamics conditioned on measurement outcomes, which we term as the full-counting dynamics, and address propagation of correlations and that of information through many-body systems under measurement backaction. We apply the formalism to an exactly solvable model and show that, by harnessing backaction due to observation of individual quanta, correlations can propagate beyond the Lieb-Robinson bound at the cost of the probabilistic nature of quantum measurement. Secondly, we formulate the thermalization and heating dynamics in generic many-body systems under measurements. Combining the eigenstate thermalization hypothesis with quantum measurement theory, we extend the framework of quantum thermalization to open many-body systems, where we consider couplings of quantum systems to generic Markovian environments permitted by quantum measurements and engineered dissipations. This gives yet another insight into why thermodynamics emerges so universally in our world. Finally, we formulate the diffusive dynamics under a minimally destructive spatial observation. We derive a diffusive stochastic time-evolution equation to describe the dynamics of indistinguishable particles by taking the limit of weak-spatial resolution and strong atom-light coupling. We apply the general theory to a minimal example of two-particle systems and demonstrate that the measurement backaction qualitatively alters the underlying dynamics depending on the distinguishability of particles.

The second part of this Thesis is devoted to revealing in- and out-of-equilibrium many-body physics in quantum systems that are strongly correlated with an external environment, where the entanglement between the system and the environment plays a central role. In such situations, the strong system-bath correlations invalidate the Born-Markov approximation. We thus need to explicitly take into account the degrees of freedom of the environment rather than eliminating them as done in the master-equation approach. We focus on quantum impurity as the most fundamental paradigm of such a strongly correlated open quantum system. Historically, the physics of quantum impurity has originally been studied in the context of solid-state materials. The two most fundamental concepts developed there are the Kondo-singlet state, which is the many-body bound state formed by a localized spin impurity and the fermionic environment, and the polaron, which is a quasiparticle excitation formed by a mobile impurity dressed by surrounding phonon excitations. A broad class of problems that correspond to quantum impurity correlated with an external environment have been at the forefront of many subfields in physics. For instance, they have proven crucial to understanding thermodynamic properties of strongly correlated solid-state materials, and decoherence and transport phenomena of nanodevices such as quantum dots and Nitrogen-vacancy center that are promising candidates for future quantum information technology. They also lie at the heart of powerful numerical methods such as the dynamical mean-field theory. The physics of a quantum impurity has recently attracted renewed interests owing to experimental developments of microscopic manipulation capabilities in ultracold gases, molecular electronics, carbon nanotubes, and nanodevices such as quantum dots. While equilibrium properties of a quantum impurity are well established, these new techniques motivate a surge of studies in an out-of- equilibrium regime which is still an area of active research with many open questions. The aim of the second part of this Thesis is to elucidate the role of strong correlations in the prototypical open quantum systems for both in- and out-of-equilibrium regimes.

To achieve this aim, we develop a versatile and efficient theoretical approach to solving generic quantum spin-impurity problems in and out of equilibrium and apply it to reveal previously unexplored types of nonequilibrium many-body dynamics in Chapter 5. A quantum impurity in a nonequilibrium regime has been previously analyzed by a number of theoretical approaches. In spite of the rich theoretical toolbox, analysis of the long-time dynamics remains very challenging. Previous approaches become increasingly costly at long times due to, for instance, artifacts of the logarithmic discretization in Wilson’s numerical renormalization group or large entanglement in the time-evolved state. Another difficulty is to extend the previous approaches to generic spin-impurity models beyond the simplest Kondo models. These major challenges motivate a study to develop a new theoretical approach to quantum impurity systems. To overcome the challenges, we introduce new canonical transformations that can completely decouple the impurity and the environmental degrees of freedom. We achieve this by employing the parity symmetry hidden in the total Hamiltonian of spin-impurity models. We combine the transformation with the fermionic Gaussian states and introduce a family of variational many- body wavefunctions that can efficiently encode strong impurity-environment correlations. We benchmark our approach by demonstrating its successful application to the anisotropic and two-lead Kondo models and also by comparing it to results obtained by other methods such as the matrix-product state ansatz and the Bethe ansatz. We apply our method to reveal new types of out-of-equilibrium many-body dynamics that are difficult to study in the previous approaches. We propose a possible experiment in ultracold gases to test the predicted spatiotemporal dynamics by using quantum gas microscopy. We also extend our approach to a bosonic environment and apply it to study the strongly correlated system of spinful Rydberg molecules, which has been realized in state-of-the-art experiments. In Chapter 6, we analyze out-of- equilibrium physics of yet another fundamental class of a quantum impurity, that is, a mobile spinless impurity known as polaron. As a concrete physical system, we study an impurity atom strongly interacting with a two-component Bose-Einstein condensate mimicking a synthetic magnetic environment. We show how the Ramsey interference technique acting on the environment can be used to directly measure novel out-of-equilibrium dynamics of magnetic polarons beyond the conventional paradigm of solid-state physics. We also discuss a concrete experimental realization in ultracold gases to test our theroetical results.

In summary, the results obtained in this Thesis should serve as pivotal roles in understanding many-body physics of quantum systems open to an external world, and are applicable to experimental systems in AMO physics, quantum information science and condensed matter physics.

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参考文献

[1] R. P. Feynman, There’s Plenty of Room at the Bottom (Caltech’s Engineering and Science Magazine, Pasadena, USA, 1960).

[2] W. S. Bakr, J. I. Gillen, A. Peng, S. Fölling, and M. Greiner, “A quantum gas microscope for detecting single atoms in a Hubbard-regime optical lattice,” Nature 462, 74–77 (2009).

[3] J. F. Sherson, C. Weitenberg, M. Endres, M. Cheneau, I. Bloch, and S. Kuhr, “Single-atom- resolved fluorescence imaging of an atomic Mott insulator,” Nature 467, 68–72 (2010).

[4] M. Miranda, R. Inoue, Y. Okuyama, A. Nakamoto, and M. Kozuma, “Site-resolved imaging of ytterbium atoms in a two-dimensional optical lattice,” Phys. Rev. A 91, 063414 (2015).

[5] L. W. Cheuk, M. A. Nichols, M. Okan, T. Gersdorf, V. V. Ramasesh, W. S. Bakr, T. Lompe, and M. W. Zwierlein, “Quantum-gas microscope for fermionic atoms,” Phys. Rev. Lett. 114, 193001 (2015).

[6] M. F. Parsons, F. Huber, A. Mazurenko, C. S. Chiu, W. Setiawan, K. Wooley-Brown, S. Blatt, and M. Greiner, “Site-resolved imaging of fermionic 6Li in an optical lattice,” Phys. Rev. Lett. 114, 213002 (2015).

[7] E. Haller, J. Hudson, A. Kelly, D. A. Cotta, P. Bruno, G. D. Bruce, and S. Kuhr, “Single-atom imaging of fermions in a quantum-gas microscope,” Nat. Phys. 11, 738–742 (2015).

[8] A. Omran, M. Boll, T. A. Hilker, K. Kleinlein, G. Salomon, I. Bloch, and C. Gross, “Microscopic observation of Pauli blocking in degenerate fermionic lattice gases,” Phys. Rev. Lett. 115, 263001 (2015).

[9] G. J. A. Edge, R. Anderson, D. Jervis, D. C. McKay, R. Day, S. Trotzky, and J. H. Thywissen, “Imaging and addressing of individual fermionic atoms in an optical lattice,” Phys. Rev. A 92, 063406 (2015).

[10] R. Yamamoto, J. Kobayashi, T. Kuno, K. Kato, and Y. Takahashi, “An ytterbium quantum gas microscope with narrow-line laser cooling,” New J. Phys. 18, 023016 (2016).

[11] A. Alberti, C. Robens, W. Alt, S. Brakhane, M. Karski, R. Reimann, A. Widera, and D. Meschede, “Super-resolution microscopy of single atoms in optical lattices,” New J. Phys. 18, 053010 (2016).

[12] K. D. Nelson, X. Li, and D. S. Weiss, “Imaging single atoms in a three-dimensional array,” Nat. Phys. 3, 556–560 (2007).

[13] T. Gericke, P. Wurtz, D. Reitz, T. Langen, and H. Ott, “High-resolution scanning electron microscopy of an ultracold quantum gas,” Nat. Phys. 4, 949–953 (2008).

[14] S. Hoﬀerberth, I. Lesanovsky, T. Schumm, V. Gritsev, E. Demler, and J. Schmiedmayer, “Probing quantum and thermal noise in an interacting many-body system,” Nat. Phys. 4, 489– 495 (2008).

[15] Z. Hadzibabic, P. Krüger, M. Cheneau, B. Battelier, and J. Dalibard, “Berezinskii-Kosterlitz- Thouless crossover in a trapped atomic gas,” Nature 441, 1118–1121 (2006).

[16] C.-L. Hung, X. Zhang, N. Gemelke, and C. Chin, “Observation of scale invariance and univer- sality in two-dimensional Bose gases,” Nature 470, 236–239 (2011).

[17] W. S. Bakr, A. Peng, M. E. Tai, R. Ma, J. Simon, J. I. Gillen, S. Fölling, L. Pollet, and M. Greiner, “Probing the superfluid to Mott insulator transition at the single-atom level,” Science 329, 547–550 (2010).

[18] C. Weitenberg, M. Endres, J. F. Sherson, M. Cheneau, P. Schauß, T. Fukuhara, I. Bloch, and S. Kuhr, “Single-spin addressing in an atomic Mott insulator,” Nature 471, 319–324 (2011).

[19] P. M. Preiss, R. Ma, M. E. Tai, A. Lukin, M. Rispoli, P. Zupancic, Y. Lahini, R. Islam, and M. Greiner, “Strongly correlated quantum walks in optical lattices,” Science 347, 1229–1233 (2015).

[20] M. Cheneau, P. Barmettler, D. Poletti, M. Endres, P. Schauss, T. Fukuhara, C. Gross, I. Bloch, C. Kollath, and S. Kuhr, “Light-cone-like spreading of correlations in a quantum many-body system,” Nature 481, 484–487 (2012).

[21] T. Langen, R. Geiger, M. Kuhnert, B. Rauer, and J. Schmiedmayer, “Local emergence of thermal correlations in an isolated quantum many-body system,” Nat. Phys. 9, 640–643 (2013).

[22] T. Fukuhara, S. Hild, J. Zeiher, P. Schauß, I. Bloch, M. Endres, and C. Gross, “Spatially resolved detection of a spin-entanglement wave in a Bose-Hubbard chain,” Phys. Rev. Lett. 115, 035302 (2015).

[23] T. Fukuhara, A. Kantian, M. Endres, M. Cheneau, P. Schauß, S. Hild, D. Bellem, U. Schollwöck, T. Giamarchi, C. Gross, I. Bloch, and S. Kuhr, “Quantum dynamics of a mobile spin impurity,” Nat. Phys. 9, 235–241 (2013).

[24] T. Fukuhara, P. Schausz, M. Endres, S. Hild, M. Cheneau, I. Bloch, and C. Gross, “Microscopic observation of magnon bound states and their dynamics,” Nature 502, 76–79 (2013).

[25] R. Islam, R. Ma, P. M. Preiss, M. E. Tai, A. Lukin, M. Rispoli, and M. Greiner, “Measuring entanglement entropy in a quantum many-body system,” Nature 528, 77–83 (2015).

[26] M. F. Parsons, A. Mazurenko, C. S. Chiu, G. Ji, D. Greif, and M. Greiner, “Site-resolved measurement of the spin-correlation function in the Fermi-Hubbard model,” Science 353, 1253–1256 (2016).

[27] M. Boll, T. A. Hilker, G. Salomon, A. Omran, J. Nespolo, L. Pollet, I. Bloch, and C. Gross, “Spin- and density-resolved microscopy of antiferromagnetic correlations in fermi-hubbard chains,” Science 353, 1257–1260 (2016).

[28] L. W. Cheuk, M. A. Nichols, K. R. Lawrence, M. Okan, H. Zhang, E. Khatami, N. Trivedi, T. Paiva, M. Rigol, and M. W. Zwierlein, “Observation of spatial charge and spin correlations in the 2D Fermi-Hubbard model,” Science 353, 1260–1264 (2016).

[29] A. Mazurenko, C. S. Chiu, G. Ji, M. F. Parsons, M. Kanász-Nagy, R. Schmidt, F. Grusdt, E. Demler, D. Greif, and M. Greiner, “A cold-atom Fermi-Hubbard antiferromagnet,” Nature 545, 462–466 (2017).

[30] P. Jurcevic, B. P. Lanyon, P. Hauke, C. Hempel, P. Zoller, R. Blatt, and C. F. Roos, “Quasiparticle engineering and entanglement propagation in a quantum many-body system,” Nature 511, 202– 205 (2014).

[31] P. Richerme, Z.-X. Gong, A. Lee, C. Senko, J. Smith, M. Moss-Feig, S. Michalakis, A. V. Gorshkov, and C. Monroe, “Non-local propagation of correlations in quantum systems with long-range interactions,” Nature 511, 198–201 (2014).

[32] N. Gemelke, X. Zhang, C.-L. Hung, and C. Chin, “In situ observation of incompressible Mott-insulating domains in ultracold atomic gases,” Nature 460, 995–998 (2009).

[33] Y. S. Patil, S. Chakram, L. M. Aycock, and M. Vengalattore, “Nondestructive imaging of an ultracold lattice gas,” Phys. Rev. A 90, 033422 (2014).

[34] Y. S. Patil, S. Chakram, and M. Vengalattore, “Measurement-induced localization of an ultracold lattice gas,” Phys. Rev. Lett. 115, 140402 (2015).

[35] P. M. Preiss, R. Ma, M. E. Tai, J. Simon, and M. Greiner, “Quantum gas microscopy with spin, atom-number, and multilayer readout,” Phys. Rev. A 91, 041602 (2015).

[36] Y. Ashida and M. Ueda, “Diﬀraction-unlimited position measurement of ultracold atoms in an optical lattice,” Phys. Rev. Lett. 115, 095301 (2015).

[37] Y. Ashida and M. Ueda, “Precise multi-emitter localization method for fast super-resolution imaging,” Opt. Lett. 41, 72–75 (2016).

[38] G. Mazzucchi, W. Kozlowski, S. F. Caballero-Benitez, T. J. Elliott, and I. B. Mekhov, “Quantum measurement-induced dynamics of many-body ultracold bosonic and fermionic systems in optical lattices,” Phys. Rev. A 93, 023632 (2016).

[39] P. B. Wigley, P. J. Everitt, K. S. Hardman, M. R. Hush, C. H. Wei, M. A. Sooriyabandara, P. Manju, J. D. Close, N. P. Robins, and C. C. N. Kuhn, “Non-destructive shadowgraph imaging of ultra-cold atoms,” Opt. Lett. 41, 4795–4798 (2016).

[40] J. Kondo, “Resistance minimum in dilute magnetic alloys,” Prog. Theor. Phys. 32, 37–49 (1964).

[41] L. Landau and S. Pekar, “Eﬀective mass of the polaron,” J. Exp. Theor. Phys 423, 71–74 (1948).

[42] K. Andres, J. E. Graebner, and H. R. Ott, “4 f -virtual-bound-state formation in Ceal3 at low temperatures,” Phys. Rev. Lett. 35, 1779–1782 (1975).

[43] A. C. Hewson, The Kondo problem to heavy fermions (Cambridge Univ. Press, Cambridge New York, 1997).

[44] H. v. Löhneysen, A. Rosch, M. Vojta, and P. Wölfle, “Fermi-liquid instabilities at magnetic quantum phase transitions,” Rev. Mod. Phys. 79, 1015 (2007).

[45] P. Gegenwart, Q. Si, and F. Steglich, “Quantum criticality in heavy-fermion metals,” Nat. Phys. 4, 186–197 (2008).

[46] Q. Si and F. Steglich, “Heavy fermions and quantum phase transitions,” Science 329, 1161–1166 (2010).

[47] A. J. Leggett, S. Chakravarty, A. T. Dorsey, M. P. A. Fisher, A. Garg, and W. Zwerger, “Dynamics of the dissipative two-state system,” Rev. Mod. Phys. 59, 1–85 (1987).

[48] D. Loss and D. P. DiVincenzo, “Quantum computation with quantum dots,” Phys. Rev. A 57, 120–126 (1998).

[49] W. Zhang, N. Konstantinidis, K. A. Al-Hassanieh, and V. V. Dobrovitski, “Modelling decoher- ence in quantum spin systems,” J. Phys. Cond. Matt. 19, 083202 (2007).

[50] L. Glazman and M. Raikh, “Resonant Kondo transparency of a barrier with quasilocal impurity states,” JETP Lett. 47, 452–455 (1988).

[51] T. K. Ng and P. A. Lee, “On-site coulomb repulsion and resonant tunneling,” Phys. Rev. Lett. 61, 1768 (1988).

[52] Y. Meir, N. S. Wingreen, and P. A. Lee, “Low-temperature transport through a quantum dot: The Anderson model out of equilibrium,” Phys. Rev. Lett. 70, 2601–2604 (1993).

[53] W. Liang, M. P. Shores, M. Bockrath, J. R. Long, and H. Park, “Kondo resonance in a single- molecule transistor,” Nature 417, 725–729 (2002).

[54] L. H. Yu and D. Natelson, “The Kondo eﬀect in C60 single-molecule transistors,” Nano Lett. 4, 79–83 (2004).

[55] D. Goldhaber-Gordon, J. Göres, M. A. Kastner, H. Shtrikman, D. Mahalu, and U. Meirav, “From the Kondo regime to the mixed-valence regime in a single-electron transistor,” Phys. Rev. Lett. 81, 5225–5228 (1998).

[56] S. M. Cronenwett, T. H. Oosterkamp, and L. P. Kouwenhoven, “A tunable Kondo eﬀect in quantum dots,” Science 281, 540–544 (1998).

[57] F. Simmel, R. H. Blick, J. P. Kotthaus, W. Wegscheider, and M. Bichler, “Anomalous Kondo eﬀect in a quantum dot at nonzero bias,” Phys. Rev. Lett. 83, 804–807 (1999).

[58] W. G. van der Wiel, S. D. Franceschi, T. Fujisawa, J. M. Elzerman, S. Tarucha, and L. P. Kouwenhoven, “The Kondo eﬀect in the unitary limit,” Science 289, 2105–2108 (2000).

[59] R. M. Potok, I. G. Rau, H. Shtrikman, Y. Oreg, and D. Goldhaber-Gordon, “Observation of the two-channel Kondo eﬀect,” Nature 446, 167–171 (2007).

[60] A. V. Kretinin, H. Shtrikman, D. Goldhaber-Gordon, M. Hanl, A. Weichselbaum, J. von Delft, T. Costi, and D. Mahalu, “Spin- 1 Kondo eﬀect in an InAs nanowire quantum dot: Unitary limit, conductance scaling, and Zeeman splitting,” Phys. Rev. B 84, 245316 (2011).

[61] A. V. Kretinin, H. Shtrikman, and D. Mahalu, “Universal line shape of the Kondo zero-bias anomaly in a quantum dot,” Phys. Rev. B 85, 201301 (2012).

[62] A. Georges, G. Kotliar, W. Krauth, and M. J. Rozenberg, “Dynamical mean-field theory of strongly correlated fermion systems and the limit of infinite dimensions,” Rev. Mod. Phys. 68, 13–125 (1996).

[63] A. Schirotzek, C.-H. Wu, A. Sommer, and M. W. Zwierlein, “Observation of fermi polarons in a tunable fermi liquid of ultracold atoms,” Phys. Rev. Lett. 102, 230402 (2009).

[64] S. Nascimbène, N. Navon, K. J. Jiang, L. Tarruell, M. Teichmann, J. McKeever, F. Chevy, and C. Salomon, “Collective oscillations of an imbalanced fermi gas: Axial compression modes and polaron eﬀective mass,” Phys. Rev. Lett. 103, 170402 (2009).

[65] M. Koschorreck, D. Pertot, E. Vogt, B. Frohlich, M. Feld, and M. Köhl, “Attractive and repulsive Fermi polarons in two dimensions,” Nature 485, 619–622 (2012).

[66] C. Kohstall, M. Zaccanti, M. Jag, A. Trenkwalder, P. Massignan, G. M. Bruun, F. Schreck, and R. Grimm, “Metastability and coherence of repulsive polarons in a strongly interacting Fermi mixture,” Nature 485, 615–618 (2012).

[67] F. Meinert, M. Knap, E. Kirilov, K. Jag-Lauber, M. B. Zvonarev, E. Demler, and H.-C. Nägerl, “Bloch oscillations in the absence of a lattice,” Science 356, 945–948 (2017).

[68] M.-G. Hu, M. J. Van de Graaﬀ, D. Kedar, J. P. Corson, E. A. Cornell, and D. S. Jin, “Bose polarons in the strongly interacting regime,” Phys. Rev. Lett. 117, 055301 (2016).

[69] N. B. Jørgensen, L. Wacker, K. T. Skalmstang, M. M. Parish, J. Levinsen, R. S. Christensen, G. M. Bruun, and J. J. Arlt, “Observation of attractive and repulsive polarons in a Bose-Einstein condensate,” Phys. Rev. Lett. 117, 055302 (2016).

[70] A. Makarovski, J. Liu, and G. Finkelstein, “Evolution of transport regimes in carbon nanotube quantum dots,” Phys. Rev. Lett. 99, 066801 (2007).

[71] S. J. Chorley, M. R. Galpin, F. W. Jayatilaka, C. G. Smith, D. E. Logan, and M. R. Buitelaar, “Tunable Kondo physics in a carbon nanotube double quantum dot,” Phys. Rev. Lett. 109, 156804 (2012).

[72] Z. Iftikhar, S. Jezouin, A. Anthore, U. Gennser, F. D. Parmentier, A. Cavanna, and F. Pierre, “Two-channel Kondo eﬀect and renormalization flow with macroscopic quantum charge states,” Nature 526, 233–236 (2015).

[73] T. L. Schmidt, P. Werner, L. Mühlbacher, and A. Komnik, “Transient dynamics of the Anderson impurity model out of equilibrium,” Phys. Rev. B 78, 235110 (2008).

[74] P. Werner, T. Oka, and A. J. Millis, “Diagrammatic Monte Carlo simulation of nonequilibrium systems,” Phys. Rev. B 79, 035320 (2009).

[75] M. Schiró and M. Fabrizio, “Real-time diagrammatic Monte Carlo for nonequilibrium quantum transport,” Phys. Rev. B 79, 153302 (2009).

[76] P. Werner, T. Oka, M. Eckstein, and A. J. Millis, “Weak-coupling quantum Monte Carlo cal- culations on the Keldysh contour: Theory and application to the current-voltage characteristics of the Anderson model,” Phys. Rev. B 81, 035108 (2010).

[77] G. Cohen, E. Gull, D. R. Reichman, A. J. Millis, and E. Rabani, “Numerically exact long- time magnetization dynamics at the nonequilibrium Kondo crossover of the Anderson impurity model,” Phys. Rev. B 87, 195108 (2013).

[78] P. Nordlander, M. Pustilnik, Y. Meir, N. S. Wingreen, and D. C. Langreth, “How long does it take for the Kondo eﬀect to develop?” Phys. Rev. Lett. 83, 808–811 (1999).

[79] A. Kaminski, Y. V. Nazarov, and L. I. Glazman, “Universality of the Kondo eﬀect in a quantum dot out of equilibrium,” Phys. Rev. B 62, 8154–8170 (2000).

[80] A. Hackl and S. Kehrein, “Real time evolution in quantum many-body systems with unitary perturbation theory,” Phys. Rev. B 78, 092303 (2008).

[81] M. Keil and H. Schoeller, “Real-time renormalization-group analysis of the dynamics of the spin-boson model,” Phys. Rev. B 63, 180302 (2001).

[82] M. Pletyukhov, D. Schuricht, and H. Schoeller, “Relaxation versus decoherence: Spin and current dynamics in the anisotropic Kondo model at finite bias and magnetic field,” Phys. Rev. Lett. 104, 106801 (2010).

[83] A. Hackl, D. Roosen, S. Kehrein, and W. Hofstetter, “Nonequilibrium spin dynamics in the ferromagnetic Kondo model,” Phys. Rev. Lett. 102, 196601 (2009).

[84] A. Hackl, M. Vojta, and S. Kehrein, “Nonequilibrium magnetization dynamics of ferromagnet- ically coupled Kondo spins,” Phys. Rev. B 80, 195117 (2009).

[85] C. Tomaras and S. Kehrein, “Scaling approach for the time-dependent Kondo model,” Europhys. Lett. 93, 47011 (2011).

[86] S. Bera, A. Nazir, A. W. Chin, H. U. Baranger, and S. Florens, “Generalized multipolaron expansion for the spin-boson model: Environmental entanglement and the biased two-state system,” Phys. Rev. B 90, 075110 (2014).

[87] S. Florens and I. Snyman, “Universal spatial correlations in the anisotropic Kondo screening cloud: Analytical insights and numerically exact results from a coherent state expansion,” Phys. Rev. B 92, 195106 (2015).

[88] Z. Blunden-Codd, S. Bera, B. Bruognolo, N.-O. Linden, A. W. Chin, J. von Delft, A. Nazir, and S. Florens, “Anatomy of quantum critical wave functions in dissipative impurity problems,” Phys. Rev. B 95, 085104 (2017).

[89] S. R. White and A. E. Feiguin, “Real-time evolution using the density matrix renormalization group,” Phys. Rev. Lett. 93, 076401 (2004).

[90] P. Schmitteckert, “Nonequilibrium electron transport using the density matrix renormalization group method,” Phys. Rev. B 70, 121302 (2004).

[91] K. A. Al-Hassanieh, A. E. Feiguin, J. A. Riera, C. A. Büsser, and E. Dagotto, “Adaptive time- dependent density-matrix renormalization-group technique for calculating the conductance of strongly correlated nanostructures,” Phys. Rev. B 73, 195304 (2006).

[92] L. G. G. V. Dias da Silva, F. Heidrich-Meisner, A. E. Feiguin, C. A. Büsser, G. B. Martins, E. V. Anda, and E. Dagotto, “Transport properties and Kondo correlations in nanostructures: Time-dependent dmrg method applied to quantum dots coupled to Wilson chains,” Phys. Rev. B 78, 195317 (2008).

[93] A. Weichselbaum, F. Verstraete, U. Schollwöck, J. I. Cirac, and J. von Delft, “Variational matrix-product-state approach to quantum impurity models,” Phys. Rev. B 80, 165117 (2009).

[94] F. Heidrich-Meisner, A. E. Feiguin, and E. Dagotto, “Real-time simulations of nonequilibrium transport in the single-impurity Anderson model,” Phys. Rev. B 79, 235336 (2009).

[95] F. Heidrich-Meisner, I. González, K. A. Al-Hassanieh, A. E. Feiguin, M. J. Rozenberg, and E. Dagotto, “Nonequilibrium electronic transport in a one-dimensional Mott insulator,” Phys. Rev. B 82, 205110 (2010).

[96] H. T. M. Nghiem and T. A. Costi, “Time evolution of the Kondo resonance in response to a quench,” Phys. Rev. Lett. 119, 156601 (2017).

[97] F. B. Anders and A. Schiller, “Real-time dynamics in quantum-impurity systems: A time- dependent numerical renormalization-group approach,” Phys. Rev. Lett. 95, 196801 (2005).

[98] F. B. Anders and A. Schiller, “Spin precession and real-time dynamics in the Kondo model: Time-dependent numerical renormalization-group study,” Phys. Rev. B 74, 245113 (2006).

[99] F. B. Anders, R. Bulla, and M. Vojta, “Equilibrium and nonequilibrium dynamics of the sub- ohmic spin-boson model,” Phys. Rev. Lett. 98, 210402 (2007).

[100] F. B. Anders, “Steady-state currents through nanodevices: A scattering-states numerical renormalization-group approach to open quantum systems,” Phys. Rev. Lett. 101, 066804 (2008).

[101] D. Roosen, M. R. Wegewijs, and W. Hofstetter, “Nonequilibrium dynamics of anisotropic large spins in the Kondo regime: Time-dependent numerical renormalization group analysis,” Phys. Rev. Lett. 100, 087201 (2008).

[102] J. Eckel, F. Heidrich-Meisner, S. G. Jakobs, M. Thorwart, M. Pletyukhov, and R. Egger, “Comparative study of theoretical methods for non-equilibrium quantum transport,” New J. Phys. 12, 043042 (2010).

[103] B. Lechtenberg and F. B. Anders, “Spatial and temporal propagation of Kondo correlations,” Phys. Rev. B 90, 045117 (2014).

[104] M. Nuss, M. Ganahl, E. Arrigoni, W. von der Linden, and H. G. Evertz, “Nonequilibrium spatiotemporal formation of the Kondo screening cloud on a lattice,” Phys. Rev. B 91, 085127 (2015).

[105] B. Dóra, M. A. Werner, and C. P. Moca, “Information scrambling at an impurity quantum critical point,” Phys. Rev. B 96, 155116 (2017).

[106] F. Lesage, H. Saleur, and S. Skorik, “Time correlations in 1D quantum impurity problems,” Phys. Rev. Lett. 76, 3388–3391 (1996).

[107] F. Lesage and H. Saleur, “Boundary interaction changing operators and dynamical correlations in quantum impurity problems,” Phys. Rev. Lett. 80, 4370–4373 (1998).

[108] A. Schiller and S. Hershfield, “Toulouse limit for the nonequilibrium Kondo impurity: Currents, noise spectra, and magnetic properties,” Phys. Rev. B 58, 14978–15010 (1998).

[109] D. Lobaskin and S. Kehrein, “Crossover from nonequilibrium to equilibrium behavior in the time-dependent Kondo model,” Phys. Rev. B 71, 193303 (2005).

[110] R. Vasseur, K. Trinh, S. Haas, and H. Saleur, “Crossover physics in the nonequilibrium dynamics of quenched quantum impurity systems,” Phys. Rev. Lett. 110, 240601 (2013).

[111] S. Ghosh, P. Ribeiro, and M. Haque, “Real-space structure of the impurity screening cloud in the resonant level model,” J. Stat. Mech. Theor. Exp. 2014, P04011 (2014).

[112] M. Medvedyeva, A. Hoﬀmann, and S. Kehrein, “Spatiotemporal buildup of the Kondo screening cloud,” Phys. Rev. B 88, 094306 (2013).

[113] C. J. Bolech and N. Shah, “Consistent bosonization-debosonization. ii. the two-lead Kondo problem and the fate of its nonequilibrium toulouse point,” Phys. Rev. B 93, 085441 (2016).

[114] A. Rosch, “Wilson chains are not thermal reservoirs,” Eur. Phys. J. B 85, 6 (2012).

[115] U. Schollwöck, “The density-matrix renormalization group in the age of matrix product states,” Ann. Phys. 326, 96 – 192 (2011).

[116] F. Verstraete, V. Murg, and J. I. Cirac, “Matrix product states, projected entangled pair states, and variational renormalization group methods for quantum spin systems,” Adv. Phys. 57, 143–224 (2008).

[117] N. Kawakami and A. Okiji, “Exact expression of the ground-state energy for the symmetric Anderson model,” Phys. Lett. A 86, 483 – 486 (1981).

[118] N. Andrei, K. Furuya, and J. H. Lowenstein, “Solution of the Kondo problem,” Rev. Mod. Phys. 55, 331–402 (1983).

[119] P. Schlottmann, “Some exact results for dilute mixed-valent and heavy-fermion systems,” Phys. Rep. 181, 1 – 119 (1989).

[120] V. Bendkowsky, B. Butscher, J. Nipper, J. P. Shaﬀer, R. Löw, and T. Pfau, “Observation of ultralong-range Rydberg molecules,” Nature 458, 1005–1008 (2009).

[121] A. Gaj, A. T. Krupp, J. B. Balewski, R. Löw, S. Hoﬀerberth, and T. Pfau, “From molecular spectra to a density shift in dense Rydberg gases,” Nat. Commun. 5, 4546 (2014).

[122] F. Böttcher, A. Gaj, K. M. Westphal, M. Schlagmüller, K. S. Kleinbach, R. Löw, T. C. Liebisch, T. Pfau, and S. Hoﬀerberth, “Observation of mixed singlet-triplet Rb2 Rydberg molecules,” Phys. Rev. A 93, 032512 (2016).

[123] Y. Ashida, S. Furukawa, and M. Ueda, “Parity-time-symmetric quantum critical phenomena,” Nat. Commun. 8, 15791 (2017).

[124] Y. Ashida, S. Furukawa, and M. Ueda, “Quantum critical behavior influenced by measurement backaction in ultracold gases,” Phys. Rev. A 94, 053615 (2016).

[125] Y. Ashida and M. Ueda, “Full-counting many-particle dynamics: Nonlocal and chiral propaga- tion of correlations,” Phys. Rev. Lett. 120, 185301 (2018).

[126] Y. Ashida, K. Saito, and M. Ueda, “Thermalization and heating dynamics in open generic many-body systems,” Phys. Rev. Lett. 121, 170402 (2018).

[127] Y. Ashida and M. Ueda, “Multiparticle quantum dynamics under real-time observation,” Phys. Rev. A 95, 022124 (2017).

[128] Y. Ashida, T. Shi, M. C. Bañuls, J. I. Cirac, and E. Demler, “Solving quantum impurity problems in and out of equilibrium with the variational approach,” Phys. Rev. Lett. 121, 026805 (2018).

[129] Y. Ashida, T. Shi, M. C. Bañuls, J. I. Cirac, and E. Demler, “Variational principle for quantum impurity systems in and out of equilibrium: Application to Kondo problems,” Phys. Rev. B 98, 024103 (2018).

[130] M. Kanász-Nagy, Y. Ashida, T. Shi, C. P. Moca, T. N. Ikeda, S. Fölling, J. I. Cirac, G. Zaránd, and E. A. Demler, “Exploring the anisotropic Kondo model in and out of equilibrium with alkaline-earth atoms,” Phys. Rev. B 97, 155156 (2018).

[131] Y. Ashida, T. Shi, R. Schmidt, J. I. Cirac, and E. Demler, “Efficient variational approach to bosonic quantum impurity systems and its application to Rydberg Kondo problems,” in preparation .

[132] Y. Ashida, R. Schmidt, L. Tarruell, and E. Demler, “Many-body interferometry of magnetic polaron dynamics,” Phys. Rev. B 97, 060302 (2018).

[133] H.-P. Breuer and F. Petruccione, The Theory of Open Quantum Systems (Oxford University Press, Oxford, England, 2002).

[134] M. Nielsen and I. L. Chuang, Quantum computation and quantum information (Cambridge University Press, Cambridge, England, 2010).

[135] H. Wiseman and G. Milburn, Quantum Measurement and Control (Cambridge University Press, Cambridge, England, 2010).

[136] K.-E. Hellwig and K. Kraus, “Operations and measurements. II,” Comm. Math. Phys. 16, 142–147 (1970).

[137] K. Kraus, “General state changes in quantum theory,” Ann. Phys. 64, 311–335 (1971).

[138] W. F. Stinespring, “Positive functions on C*-algebras,” Proc. Amer. Math. Soc. 6, 211–216 (1955).

[139] M. Ozawa, “Quantum measuring processes of continuous observables,” J. Math. Phys. 25, 79–87 (1984).

[140] N. Imoto, M. Ueda, and T. Ogawa, “Microscopic theory of the continuous measurement of photon number,” Phys. Rev. A 41, 4127–4130 (1990).

[141] M. Ueda, N. Imoto, H. Nagaoka, and T. Ogawa, “Continuous quantum-nondemolition mea- surement of photon number,” Phys. Rev. A 46, 2859–2869 (1992).

[142] S. Miyashita, H. Ezaki, and E. Hanamura, “Stochastic model of nonclassical light emission from a microcavity,” Phys. Rev. A 57, 2046–2055 (1998).

[143] M. Ueda, “Probability-density-functional description of quantum photodetection processes,” Quant. Opt. J. Euro. Opt. Soc. PB 1, 131 (1989).

[144] M. Ueda, “Nonequilibrium open-system theory for continuous photodetection processes: A probability-density-functional description,” Phys. Rev. A 41, 3875–3890 (1990).

[145] R. Dum, P. Zoller, and H. Ritsch, “Monte Carlo simulation of the atomic master equation for spontaneous emission,” Phys. Rev. A 45, 4879–4887 (1992).

[146] H. Carmichael, An Open System Approach to Quantum Optics (Springer, Berlin, 1993).

[147] J. Dalibard, Y. Castin, and K. Mølmer, “Wave-function approach to dissipative processes in quantum optics,” Phys. Rev. Lett. 68, 580–583 (1992).

[148] A. Barchielli and M. Gregoratti, “Quantum measurements in continuous time, non-Markovian evolutions and feedback,” Phil. Trans. R. Soc. A 370, 5364–5385 (2012).

[149] V. Gorini, A. Kossakowski, and E. C. G. Sudarshan, “Completely positive dynamical semigroups of n level systems,” J. Math. Phys. 17, 821–825 (1976).

[150] G. Lindblad, “On the generators of quantum dynamical semigroups,” Comm. Math. Phys. 48, 119–130 (1976).

[151] P. Würtz, T. Langen, T. Gericke, A. Koglbauer, and H. Ott, “Experimental demonstration of single-site addressability in a two-dimensional optical lattice,” Phys. Rev. Lett. 103, 080404 (2009).

[152] G. Barontini, R. Labouvie, F. Stubenrauch, A. Vogler, V. Guarrera, and H. Ott, “Controlling the dynamics of an open many-body quantum system with localized dissipation,” Phys. Rev. Lett. 110, 035302 (2013).

[153] R. Labouvie, B. Santra, S. Heun, and H. Ott, “Bistability in a driven-dissipative superfluid,” Phys. Rev. Lett. 116, 235302 (2016).

[154] R. El-Ganainy, K. G. Makris, M. Khajavikhan, Z. H. Musslimani, S. Rotter, and D. N. Christodoulides, “Non-Hermitian physics and PT symmetry,” Nat. Phys. 14, 11 (2018).

[155] H. Zhao and L. Feng, “Parity-time symmetric photonics,” Natl. Sci. Rev. 5, 183–199 (2018).

[156] A. J. Daley, “Quantum trajectories and open many-body quantum systems,” Adv. Phys. 63, 77–149 (2014).

[157] P. Kok, W. J. Munro, K. Nemoto, T. C. Ralph, J. P. Dowling, and G. J. Milburn, “Linear optical quantum computing with photonic qubits,” Rev. Mod. Phys. 79, 135–174 (2007).

[158] M. Endres, M. Cheneau, T. Fukuhara, C. Weitenberg, P. Schauß, C. Gross, L. Mazza, M. C. Bañuls, L. Pollet, I. Bloch, and S. Kuhr, “Observation of correlated particle-hole pairs and string order in low-dimensional Mott insulators,” Science 334, 200–203 (2011).

[159] Y. Yanay and E. J. Mueller, “Heating from continuous number density measurements in optical lattices,” Phys. Rev. A 90, 023611 (2014).

[160] J. Schachenmayer, L. Pollet, M. Troyer, and A. J. Daley, “Spontaneous emission and thermal- ization of cold bosons in optical lattices,” Phys. Rev. A 89, 011601 (2014).

[161] A. Mitra, S. Takei, Y. B. Kim, and A. J. Millis, “Nonequilibrium quantum criticality in open electronic systems,” Phys. Rev. Lett. 97, 236808 (2006).

[162] L. M. Sieberer, S. D. Huber, E. Altman, and S. Diehl, “Dynamical critical phenomena in driven-dissipative systems,” Phys. Rev. Lett. 110, 195301 (2013).

[163] U. C. Täuber and S. Diehl, “Perturbative field-theoretical renormalization group approach to driven-dissipative Bose-Einstein criticality,” Phys. Rev. X 4, 021010 (2014).

[164] I. Rotter, “A non-Hermitian Hamilton operator and the physics of open quantum systems,” J. Phys. A 42, 153001 (2009).

[165] C. Mahaux and H. A. Weidenmüller, Shell Model Approach to Nuclear Reactions (North Holland, Amsterdam, 1969).

[166] G. Binsch, “Unified theory of exchange eﬀects on nuclear magnetic resonance line shapes,” J. Am. Chem. Soc. 91, 1304–1309 (1969).

[167] C. H. Lewenkopf and H. A. Weidenmüller, “Stochastic versus semiclassical approach to quantum chaotic scattering,” Ann. Phys. 212, 53–83 (1991).

[168] J. Stein, H.-J. Stöckmann, and U. Stoﬀregen, “Microwave studies of billiard green functions and propagators,” Phys. Rev. Lett. 75, 53–56 (1995).

[169] Stöckmann, Quantum Chaos - An Introduction (Cambridge University Press, Cambridge, 1999).

[170] C. Dembowski, H.-D. Gräf, H. L. Harney, A. Heine, W. D. Heiss, H. Rehfeld, and A. Richter, “Experimental observation of the topological structure of exceptional points,” Phys. Rev. Lett. 86, 787–790 (2001).

[171] Y. Choi, S. Kang, S. Lim, W. Kim, J.-R. Kim, J.-H. Lee, and K. An, “Quasieigenstate coales- cence in an atom-cavity quantum composite,” Phys. Rev. Lett. 104, 153601 (2010).

[172] R. Stützle, M. C. Göbel, T. Hörner, E. Kierig, I. Mourachko, M. K. Oberthaler, M. A. Efremov, M. V. Fedorov, V. P. Yakovlev, K. A. H. van Leeuwen, and W. P. Schleich, “Observation of nonspreading wave packets in an imaginary potential,” Phys. Rev. Lett. 95, 110405 (2005).

[173] H. Cartarius, J. Main, and G. Wunner, “Exceptional points in atomic spectra,” Phys. Rev. Lett. 99, 173003 (2007).

[174] C. Brunel, B. Lounis, P. Tamarat, and M. Orrit, “Rabi resonances of a single molecule driven by RF and laser fields,” Phys. Rev. Lett. 81, 2679–2682 (1998).

[175] I. Rozhkov and E. Barkai, “Photon emission from a driven single-molecule source: A renor- malization group approach,” J. Chem. Phys. 123, 074703 (2005).

[176] T. Gao, E. Estrecho, K. Y. Bliokh, T. C. H. Liew, M. D. Fraser, S. Brodbeck, M. Kamp, C. Schneider, S. Hofling, Y. Yamamoto, F. Nori, Y. S. Kivshar, A. G. Truscott, R. G. Dall, and E. A. Ostrovskaya, “Observation of non-Hermitian degeneracies in a chaotic exciton-polariton billiard,” Nature 526, 554–558 (2015).

[177] B. Zhen, C. W. Hsu, Y. Igarashi, L. Lu, I. Kaminer, A. Pick, S.-L. Chua, J. D. Joannopoulos, and M. Soljacic, “Spawning rings of exceptional points out of Dirac cones,” Nature 525, 354–358 (2015).

[178] T. E. Lee and C.-K. Chan, “Heralded magnetism in non-Hermitian atomic systems,” Phys. Rev. X 4, 041001 (2014).

[179] W. Kozlowski, S. F. Caballero-Benitez, and I. B. Mekhov, “Non-Hermitian dynamics in the quantum Zeno limit,” Phys. Rev. A 94, 012123 (2016).

[180] G. Gamow, “Zur quantentheorie des atomkernes,” Z. Für Phys. 51, 204–212 (1928).

[181] H. Feshbach, C. E. Porter, and V. F. Weisskopf, “Model for nuclear reactions with neutrons,” Phys. Rev. 96, 448–464 (1954).

[182] M. S. Rudner and L. S. Levitov, “Topological transition in a non-Hermitian quantum walk,” Phys. Rev. Lett. 102, 065703 (2009).

[183] K. Kawabata, Y. Ashida, and M. Ueda, “Information retrieval and criticality in parity-time- symmetric systems,” Phys. Rev. Lett. 119, 190401 (2017).

[184] N. Hatano and D. R. Nelson, “Localization transitions in non-Hermitian quantum mechanics,” Phys. Rev. Lett. 77, 570–573 (1996).

[185] T. Fukui and N. Kawakami, “Breakdown of the Mott insulator: Exact solution of an asymmetric Hubbard model,” Phys. Rev. B 58, 16051–16056 (1998).

[186] T. Oka and H. Aoki, “Dielectric breakdown in a Mott insulator: Many-body Schwinger-Landau- Zener mechanism studied with a generalized Bethe ansatz,” Phys. Rev. B 81, 033103 (2010).

[187] H. Shen, B. Zhen, and L. Fu, “Topological band theory for non-Hermitian hamiltonians,” Phys. Rev. Lett. 120, 146402 (2018).

[188] T. Yoshida, R. Peters, and N. Kawakami, “Non-hermitian perspective of the band structure in heavy-fermion systems,” Phys. Rev. B 98, 035141 (2018).

[189] M. Esposito, U. Harbola, and S. Mukamel, “Nonequilibrium fluctuations, fluctuation theorems, and counting statistics in quantum systems,” Rev. Mod. Phys. 81, 1665–1702 (2009).

[190] J. Ren, P. Hänggi, and B. Li, “Berry-phase-induced heat pumping and its impact on the fluctuation theorem,” Phys. Rev. Lett. 104, 170601 (2010).

[191] T. Sagawa and H. Hayakawa, “Geometrical expression of excess entropy production,” Phys. Rev. E 84, 051110 (2011).

[192] D. R. Nelson and N. M. Shnerb, “Non-Hermitian localization and population biology,” Phys. Rev. E 58, 1383–1403 (1998).

[193] A. Amir, N. Hatano, and D. R. Nelson, “Non-Hermitian localization in biological networks,” Phys. Rev. E 93, 042310 (2016).

[194] A. Murugan and S. Vaikuntanathan, “Topologically protected modes in non-equilibrium stochastic systems,” Nat. Commun. 8, 13881 (2017).

[195] T. McGrath, N. S. Jones, P. R. ten Wolde, and T. E. Ouldridge, “Biochemical machines for the interconversion of mutual information and work,” Phys. Rev. Lett. 118, 028101 (2017).

[196] M. E. Fisher, “Yang-Lee edge singularity and ϕ3 field theory,” Phys. Rev. Lett. 40, 1610–1613 (1978).

[197] C. M. Bender and S. Boettcher, “Real spectra in non-Hermitian hamiltonians having PT sym- metry,” Phys. Rev. Lett. 80, 5243–5246 (1998).

[198] T. Kato, Perturbation Theory for Linear Operators (Springer, New York, 1966).

[199] A. Mostafazadeh, “Spectral singularities of complex scattering potentials and infinite reflection and transmission coefficients at real energies,” Phys. Rev. Lett. 102, 220402 (2009).

[200] C. M. Bender, M. V. Berry, and A. Mandilara, “Generalized PT symmetry and real spectra,” J. Phys. A 35, L467 (2002).

[201] K. G. Makris, R. El-Ganainy, D. N. Christodoulides, and Z. H. Musslimani, “Beam dynamics in symmetric optical lattices,” Phys. Rev. Lett. 100, 103904 (2008).

[202] A. Regensburger, C. Bersch, M.-A. Miri, G. Onishchukov, D. N. Christodoulides, and U. Peschel, “Parity-time synthetic photonic lattices,” Nature 488, 167–171 (2012).

[203] L. Feng, Y.-L. Xu, W. S. Fegadolli, M.-H. Lu, J. E. B. Oliveira, V. R. Almeida, Y.-F. Chen, and A. Scherer, “Experimental demonstration of a unidirectional reflectionless parity-time metamaterial at optical frequencies,” Nat. Mater. 12, 108–113 (2013).

[204] B. Peng, S. K. Özdemir, F. Lei, F. Monifi, M. Gianfreda, G. L. Long, S. Fan, F. Nori, C. M. Bender, and L. Yang, “Parity-time-symmetric whispering-gallery microcavities,” Nat. Phys. 10, 394–398 (2014).

[205] N. M. Chtchelkatchev, A. A. Golubov, T. I. Baturina, and V. M. Vinokur, “Stimulation of the fluctuation superconductivity by PT symmetry,” Phys. Rev. Lett. 109, 150405 (2012).

[206] P. Peng, W. Cao, C. Shen, W. Qu, W. Jianming, L. Jiang, and Y. Xiao, “Anti-parity-time symmetry with flying atoms,” Nat. Phys. 12, 1139–1145 (2016).

[207] H. Jing, S. K. Özdemir, X.-Y. Lü, J. Zhang, L. Yang, and F. Nori, “ -symmetric phonon laser,” Phys. Rev. Lett. 113, 053604 (2014).

[208] L. D. Landau, “On the theory of the fermi liquid,” Sov. Phys. JETP 35, 70–74 (1959).

[209] F. D. M. Haldane, “Eﬀective harmonic-fluid approach to low-energy properties of one- dimensional quantum fluids,” Phys. Rev. Lett. 47, 1840–1843 (1981).

[210] E. Bour, “Théorie de la déformation des surfaces,” J. École Impériale Polytech 19, 1 (1862).

[211] M. J. Ablowitz and P. A. Clarkson, Solitons, Nonlinear Evolution Equations and Inverse Scattering (Cambridge University Press, Cambridge, England, 1991).

[212] V. L. Berezinskii, “Destruction of long-range order in one-dimensional and two-dimensional systems having a continuous symmetry group I. classical systems,” Sov. Phys. JETP 32, 493–500 (1971).

[213] V. L. Berezinskii, “Destruction of long-range order in one-dimensional and two-dimensional systems possessing a continuous symmetry group II. quantum systems,” Sov. Phys. JETP 34, 610–616 (1972).

[214] J. M. Kosterlitz and D. J. Thouless, “Ordering, metastability and phase transitions in two- dimensional systems,” J. Phys. C 6, 1181–1203 (1973).

[215] T. Giamarchi, Quantum Physics in One Dimension (Oxford University Press, Oxford, 2004).

[216] D. J. Amit, Y. Y. Goldschmidt, and S. Grinstein, “Renormalisation group analysis of the phase transition in the 2D Coulomb gas, Sine-Gordon theory and XY-model,” J. Phys. A 13, 585 (1980).

[217] R. S. Kaushal and Parthasarathi, “Quantum mechanics of complex hamiltonian systems in one dimension,” J. Phys. A 35, 8743 (2002).

[218] A. Jannussis, G. Brodimas, S. Baskoutas, and A. Leodaris, “Non-Hermitian harmonic oscillator with discrete complex or real spectrum for non-unitary squeeze operators,” J. Phys. A 36, 2507 (2003).

[219] S. Furukawa and Y. B. Kim, “Entanglement entropy between two coupled Tomonaga-Luttinger liquids,” Phys. Rev. B 83, 085112 (2011).

[220] A. Polkovnikov, E. Altman, and E. Demler, “Interference between independent fluctuating condensates,” Proc. Natl. Acad. Sci. USA 103, 6125–6129 (2006).

[221] H. F. Song, S. Rachel, and K. Le Hur, “General relation between entanglement and fluctuations in one dimension,” Phys. Rev. B 82, 012405 (2010).

[222] N. Syassen, D. M. Bauer, M. Lettner, T. Volz, D. Dietze, J. J. García-Ripoll, J. I. Cirac, G. Rempe, and S. Dürr, “Strong dissipation inhibits losses and induces correlations in cold molecular gases,” Science 320, 1329–1331 (2008).

[223] J. J. Garcia-Ripoll, S. Dürr, N. Syassen, D. M. Bauer, M. Lettner, G. Rempe, and J. I. Cirac, “Dissipation-induced hard-core boson gas in an optical lattice,” New J. Phys. 11, 013053 (2009).

[224] M. A. Cazalilla, R. Citro, T. Giamarchi, E. Orignac, and M. Rigol, “One dimensional bosons: From condensed matter systems to ultracold gases,” Rev. Mod. Phys. 83, 1405–1466 (2011).

[225] H. P. Büchler, G. Blatter, and W. Zwerger, “Commensurate-incommensurate transition of cold atoms in an optical lattice,” Phys. Rev. Lett. 90, 130401 (2003).

[226] M. A. Cazalilla, “Bosonizing one-dimensional cold atomic gases,” J. Phys. B 37, S1 (2004).

[227] A. Beige, D. Braun, B. Tregenna, and P. L. Knight, “Quantum computing using dissipation to remain in a decoherence-free subspace,” Phys. Rev. Lett. 85, 1762–1765 (2000).

[228] P. Facchi and S. Pascazio, “Quantum Zeno subspaces,” Phys. Rev. Lett. 89, 080401 (2002).

[229] M. P. A. Fisher, P. B. Weichman, G. Grinstein, and D. S. Fisher, “Boson localization and the superfluid-insulator transition,” Phys. Rev. B 40, 546–570 (1989).

[230] A. Mostafazadeh, “Pseudo-Hermiticity versus PT symmetry: The necessary condition for the reality of the spectrum of a non-Hermitian hamiltonian,” J. Math. Phys. 43, 205–214 (2002).

[231] C. M. Bender, H. F. Jones, and R. J. Rivers, “Dual PT-symmetric quantum field theories,” Phys. Lett. B 625, 333 – 340 (2005).

[232] A. B. Zamolodchikov, “Irreversibility of the flux of the renormalization group in a 2-d field theory,” JETP Lett. 43, 730–732 (1986).

[233] N. Seiberg, “Notes on quantum Liouville theory and quantum gravity,” Prog. Theor. Phys. Supp. 102, 319–349 (1990).

[234] Y. Ikhlef, J. L. Jacobsen, and H. Saleur, “Three-point functions in c 1 Liouville theory and conformal loop ensembles,” Phys. Rev. Lett. 116, 130601 (2016).

[235] O. A. Castro-Alvaredo, B. Doyon, and F. Ravanini, “Irreversibility of the renormalization group flow in non-unitary quantum field theory,” J. Phys. A 50, 424002 (2017).

[236] J. A. S. Lourenco, R. L. Eneias, and R. G. Pereira, “Kondo eﬀect in a -symmetric non- Hermitian hamiltonian,” Phys. Rev. B 98, 085126 (2018).

[237] M. Nakagawa, N. Kawakami, and M. Ueda, “Non-hermitian kondo eﬀect in ultracold alkaline- earth atoms,” Phys. Rev. Lett. 121, 203001 (2018).

[238] I. Aﬄeck and A. W. W. Ludwig, “Universal noninteger “ground-state degeneracy” in critical quantum systems,” Phys. Rev. Lett. 67, 161–164 (1991).

[239] K. Nomura, “Correlation functions of the 2D sine-Gordon model,” J. Phys. A 28, 5451 (1995).

[240] A. Kitazawa, K. Nomura, and K. Okamoto, “Phase diagram of s = 1 bond-alternating XXZ chains,” Phys. Rev. Lett. 76, 4038–4041 (1996).

[241] W. D. Heiss and W.-H. Steeb, “Avoided level crossings and riemann sheet structure,” J. Math. Phys. 32, 3003–3007 (1991).

[242] G. Vidal, “Classical simulation of infinite-size quantum lattice systems in one spatial dimen- sion,” Phys. Rev. Lett. 98, 070201 (2007).

[243] C. M. Bender, B. K. Berntson, D. Parker, and E. Samuel, “Observation of PT phase transition in a simple mechanical system,” Am. J. Phys. 81, 173–179 (2013).

[244] C. Wetterich, “Average action and the renormalization group equations,” Nucl. Phys. B 352, 529 (1991).

[245] C. Wetterich, “Exact evolution equation for the eﬀective potential,” Phys. Lett. B 301, 90 (1993).

[246] I. Nándori, “Functional renormalization group with a compactly supported smooth regulator function,” J. High Energy Phys. 2013, 150 (2013).

[247] N. Defenu, V. Bacsó, I. G. Márián, I. Nándori, and A. Trombettoni, “Criticality of models interpolating between the sine- and the sinh-Gordon Lagrangians,” arXiv:1706.01444 (2017).

[248] E. H. Lieb and W. Liniger, “Exact analysis of an interacting Bose gas. i. the general solution and the ground state,” Phys. Rev. 130, 1605–1616 (1963).

[249] M. K. Oberthaler, R. Abfalterer, S. Bernet, C. Keller, J. Schmiedmayer, and A. Zeilinger, “Dynamical diﬀraction of atomic matter waves by crystals of light,” Phys. Rev. A 60, 456–472 (1999).

[250] A. Turlapov, A. Tonyushkin, and T. Sleator, “Optical mask for laser-cooled atoms,” Phys. Rev. A 68, 023408 (2003).

[251] K. S. Johnson, J. H. Thywissen, N. H. Dekker, K. K. Berggren, A. P. Chu, R. Younkin, and M. Prentiss, “Localization of metastable atom beams with optical standing waves: Nanolithog- raphy at the Heisenberg limit,” Science 280, 1583–1586 (1998).

[252] D. Sarchi, I. Carusotto, M. Wouters, and V. Savona, “Coherent dynamics and parametric instabilities of microcavity polaritons in double-well systems,” Phys. Rev. B 77, 125324 (2008).

[253] I. Carusotto and C. Ciuti, “Spontaneous microcavity-polariton coherence across the parametric threshold: Quantum Monte Carlo studies,” Phys. Rev. B 72, 125335 (2005).

[254] M. Wouters and I. Carusotto, “Absence of long-range coherence in the parametric emission of photonic wires,” Phys. Rev. B 74, 245316 (2006).

[255] V. N. Gladilin, K. Ji, and M. Wouters, “Spatial coherence of weakly interacting one-dimensional nonequilibrium bosonic quantum fluids,” Phys. Rev. A 90, 023615 (2014).

[256] S. Trotzky, Y.-A. Chen, A. Flesch, I. P. McCulloch, U. Schollwöck, J. Eisert, and I. Bloch, “Probing the relaxation towards equilibrium in an isolated strongly correlated one-dimensional Bose gas,” Nat. Phys. 8, 325–330 (2012).

[257] D. Jaksch, C. Bruder, J. I. Cirac, C. W. Gardiner, and P. Zoller, “Cold bosonic atoms in optical lattices,” Phys. Rev. Lett. 81, 3108–3111 (1998).

[258] M. Greiner, O. Mandel, T. Esslinger, T. W. Hänsch, and I. Bloch, “Quantum phase transition from a superfluid to a Mott insulator in a gas of ultracold atoms,” Nature 415, 39–44 (2002).

[259] S. Sachdev, Quantum Phase Transitions (Cambridge University Press, Cambridge, England, 2001).

[260] A. J. Daley, J. M. Taylor, S. Diehl, M. Baranov, and P. Zoller, “Atomic three-body loss as a dynamical three-body interaction,” Phys. Rev. Lett. 102, 040402 (2009).

[261] B. Zhu, B. Gadway, M. Foss-Feig, J. Schachenmayer, M. L. Wall, K. R. A. Hazzard, B. Yan, S. A. Moses, J. P. Covey, D. S. Jin, J. Ye, M. Holland, and A. M. Rey, “Suppressing the loss of ultracold molecules via the continuous quantum Zeno eﬀect,” Phys. Rev. Lett. 112, 070404 (2014).

[262] B. Yan, S. A. Moses, B. Gadway, J. P. Covey, K. R. Hazzard, A. M. Rey, D. S. Jin, and J. Ye, “Observation of dipolar spin-exchange interactions with lattice-confined polar molecules,” Nature 501, 521–525 (2013).

[263] J. K. Freericks and H. Monien, “Strong-coupling expansions for the pure and disordered Bose- Hubbard model,” Phys. Rev. B 53, 2691–2700 (1996).

[264] C. Lacroix, P. Mendels, and F. Mila, eds., Introduction to Frustrated Magnetism: Materials, Experiments, Theory (Springer, Heidelberg, 2011).

[265] T. Tomita, S. Nakajima, I. Danshita, Y. Takasu, and Y. Takahashi, “Observation of the Mott insulator to superfluid crossover of a driven-dissipative Bose-Hubbard system,” Sci. Adv. 3, e1701513 (2017).

[266] H. Pichler, A. J. Daley, and P. Zoller, “Nonequilibrium dynamics of bosonic atoms in optical lattices: Decoherence of many-body states due to spontaneous emission,” Phys. Rev. A 82, 063605 (2010).

[267] I. Bloch, J. Dalibard, and S. Nascimbène, “Quantum simulations with ultracold quantum gases,” Nat. Phys. 8, 267–276 (2012).

[268] T. E. Lee, H. Häﬀner, and M. C. Cross, “Collective quantum jumps of Rydberg atoms,” Phys. Rev. Lett. 108, 023602 (2012).

[269] F. Brennecke, R. Mottl, K. Baumann, R. Landig, T. Donner, and T. Esslinger, “Real-time observation of fluctuations at the driven-dissipative Dicke phase transition,” Proc. Natl. Aca. Sci. USA 110, 11763–11767 (2013).

[270] M. Endres, T. Fukuhara, D. Pekker, M. Cheneau, P. Schauß, C. Gross, E. Demler, S. Kuhr, and I. Bloch, “The Higgs amplitude mode at the two-dimensional superfluid/Mott insulator transition,” Nature 487, 454–458 (2012).

[271] S. Uetake, R. Murakami, J. M. Doyle, and Y. Takahashi, “Spin-dependent collision of ultracold metastable atoms,” Phys. Rev. A 86, 032712 (2012).

[272] S. Trotzky, L. Pollet, F. Gerbier, I. Schnorrberger, U. Bloch, N. V. Prokofev, B. Svistunov, and M. Troyer, “Suppression of the critical temperature for superfluidity near the mott transition,” Nat. Phys. 6, 998–1004 (2010).

[273] K. V. Kheruntsyan, D. M. Gangardt, P. D. Drummond, and G. V. Shlyapnikov, “Finite- temperature correlations and density profiles of an inhomogeneous interacting one-dimensional Bose gas,” Phys. Rev. A 71, 053615 (2005).

[274] J. L. Cardy, “Conformal invariance and the Yang-Lee edge singularity in two dimensions,” Phys. Rev. Lett. 54, 1354–1356 (1985).

[275] V. Pasquier and H. Saleur, “Common structures between finite systems and conformal field theories through quantum groups,” Nucl. Phys. B 330, 521–556 (1990).

[276] K. Kawabata, Y. Ashida, H. Katsura, and M. Ueda, “Parity-time-symmetric topological super- conductor,” Phys. Rev. B 98, 085116 (2018).

[277] Z. Gong, Y. Ashida, K. Kawabata, K. Takasan, S. Higashikawa, and M. Ueda, “Topological phases of non-Hermitian systems,” Phys. Rev. X 8, 031079 (2018).

[278] K. Kawabata, S. Higashikawa, Z. Gong, Y. Ashida, and M. Ueda, arXiv:1804.04676 .

[279] D. Poletti, J.-S. Bernier, A. Georges, and C. Kollath, “Interaction-induced impeding of deco- herence and anomalous diﬀusion,” Phys. Rev. Lett. 109, 045302 (2012).

[280] D. Poletti, P. Barmettler, A. Georges, and C. Kollath, “Emergence of glasslike dynamics for dissipative and strongly interacting bosons,” Phys. Rev. Lett. 111, 195301 (2013).

[281] B. Rauer, P. Grišins, I. E. Mazets, T. Schweigler, W. Rohringer, R. Geiger, T. Langen, and J. Schmiedmayer, “Cooling of a one-dimensional Bose gas,” Phys. Rev. Lett. 116, 030402 (2016).

[282] H. P. Lüschen, P. Bordia, S. S. Hodgman, M. Schreiber, S. Sarkar, A. J. Daley, M. H. Fischer, E. Altman, I. Bloch, and U. Schneider, “Signatures of many-body localization in a controlled open quantum system,” Phys. Rev. X 7, 011034 (2017).

[283] J. Li, A. K. Harter, J. Liu, L. de Melo, Y. N. Joglekar, and L. Luo, “Observation of parity-time symmetry breaking transitions in a dissipative Floquet system of ultracold atoms,” arXiv:1608.05061 .

[284] L. S. Levitov, H. Lee, and G. B. Lesovik, “Electron counting statistics and coherent states of electric current,” J. Math. Phys. 37, 4845–4866 (1996).

[285] W. Belzig and Y. V. Nazarov, “Full counting statistics of electron transfer between supercon- ductors,” Phys. Rev. Lett. 87, 197006 (2001).

[286] K. Saito and Y. Utsumi, “Symmetry in full counting statistics, fluctuation theorem, and relations among nonlinear transport coefficients in the presence of a magnetic field,” Phys. Rev. B 78, 115429 (2008).

[287] W. Lu, Z. Ji, L. Pfeiﬀer, K. W. West, and A. J. Rimberg, “Real-time detection of electron tunneling in a quantum dot,” Nature 423, 422–425 (2003).

[288] T. Fujisawa, T. Hayashi, Y. Hirayama, H. D. Cheong, and Y. H. Jeong, “Electron counting of single-electron tunneling current,” Appl. Phys. Lett. 84, 2343–2345 (2004).

[289] J. Bylander, T. Duty, and P. Delsing, “Current measurement by real-time counting of single electrons,” Nature 434, 361–364 (2005).

[290] S. Gustavsson, R. Leturcq, B. Simovič, R. Schleser, T. Ihn, P. Studerus, K. Ensslin, D. C. Driscoll, and A. C. Gossard, “Counting statistics of single electron transport in a quantum dot,” Phys. Rev. Lett. 96, 076605 (2006).

[291] M. D. Eisaman, J. Fan, A. Migdall, and S. V. Polyakov, “Invited review article: Single-photon sources and detectors,” Rev. Sci. Instrum. 82, 071101 (2011).

[292] E. Altman, E. Demler, and M. D. Lukin, “Probing many-body states of ultracold atoms via noise correlations,” Phys. Rev. A 70, 013603 (2004).

[293] I. Klich and L. Levitov, “Quantum noise as an entanglement meter,” Phys. Rev. Lett. 102, 100502 (2009).

[294] E. H. Lieb and D. W. Robinson, “The finite group velocity of quantum spin systems,” Comm. Math. Phys. 28, 251–257 (1972).

[295] I. Bloch, J. Dalibard, and W. Zwerger, “Many-body physics with ultracold gases,” Rev. Mod. Phys. 80, 885–964 (2008).

[296] D. Poulin, “Lieb-Robinson bound and locality for general Markovian quantum dynamics,” Phys. Rev. Lett. 104, 190401 (2010).

[297] M. Kliesch, C. Gogolin, and J. Eisert, “Lieb-Robinson bounds and the simulation of time- evolution of local observables in lattice systems,” in “Many-Electron Approaches in Physics, Chemistry and Mathematics,” (Springer, Cham, 2014), pp. 301–318.

[298] P. Calabrese and J. Cardy, “Evolution of entanglement entropy in one-dimensional systems,” J. Stat. Mech. (2005), P04010.

[299] P. Calabrese and J. Cardy, “Time dependence of correlation functions following a quantum quench,” Phys. Rev. Lett. 96, 136801 (2006).

[300] C. Kollath, A. M. Läuchli, and E. Altman, “Quench dynamics and nonequilibrium phase diagram of the Bose-Hubbard model,” Phys. Rev. Lett. 98, 180601 (2007).

[301] M. Collura, P. Calabrese, and F. H. L. Essler, “Quantum quench within the gapless phase of the spin 1 Heisenberg XXZ spin chain,” Phys. Rev. B 92, 125131 (2015).

[302] H. Kim and D. A. Huse, “Ballistic spreading of entanglement in a diﬀusive nonintegrable system,” Phys. Rev. Lett. 111, 127205 (2013).

[303] M. Kormos, M. Collura, G. Takács, and P. Calabrese, “Real-time confinement following a quantum quench to a non-integrable model,” Nat. Phys. 13, 246–249 (2017).

[304] M. Fagotti and P. Calabrese, “Evolution of entanglement entropy following a quantum quench: Analytic results for the XY chain in a transverse magnetic field,” Phys. Rev. A 78, 010306 (2008).

[305] V. Eisler and I. Peschel, “Entanglement in a periodic quench,” Ann. Phys. 17, 410–423 (2008).

[306] R. Geiger, T. Langen, I. E. Mazets, and J. Schmiedmayer, “Local relaxation and light-cone-like propagation of correlations in a trapped one-dimensional Bose gas,” New J. Phys. 16, 053034 (2014).

[307] S. Bravyi, M. B. Hastings, and F. Verstraete, “Lieb-Robinson bounds and the generation of correlations and topological quantum order,” Phys. Rev. Lett. 97, 050401 (2006).

[308] J.-S. Bernier, R. Tan, L. Bonnes, C. Guo, D. Poletti, and C. Kollath, “Light-cone and diﬀusive propagation of correlations in a many-body dissipative system,” Phys. Rev. Lett. 120, 020401 (2018).

[309] N. Gisin, “A simple nonlinear dissipative quantum evolution equation,” J. Phys. A 14, 2259 (1981).

[310] D. C. Brody and E.-M. Graefe, “Mixed-state evolution in the presence of gain and loss,” Phys. Rev. Lett. 109, 230405 (2012).

[311] C. E. Ruter, K. G. Makris, R. El-Ganainy, D. N. Christodoulides, M. Segev, and D. Kip, “Observation of parity-time symmetry in optics,” Nat. Phys. 6, 192–195 (2010).

[312] V. V. Konotop, J. Yang, and D. A. Zezyulin, “Nonlinear waves in -symmetric systems,” Rev. Mod. Phys. 88, 035002 (2016).

[313] W. Heiss and H. Harney, “The chirality of exceptional points,” Eur. Phys. J. D 17, 149–151 (2001).

[314] S. Longhi, “Bloch oscillations in complex crystals with PT symmetry,” Phys. Rev. Lett. 103, 123601 (2009).

[315] S. Longhi, “Spectral singularities and bragg scattering in complex crystals,” Phys. Rev. A 81, 022102 (2010).

[316] Z. Lin, H. Ramezani, T. Eichelkraut, T. Kottos, H. Cao, and D. N. Christodoulides, “Unidirec- tional invisibility induced by -symmetric periodic structures,” Phys. Rev. Lett. 106, 213901 (2011).

[317] D. D. Scott and Y. N. Joglekar, “ -symmetry breaking and ubiquitous maximal chirality in a -symmetric ring,” Phys. Rev. A 85, 062105 (2012).

[318] J. Wiersig, “Chiral and nonorthogonal eigenstate pairs in open quantum systems with weak backscattering between counterpropagating traveling waves,” Phys. Rev. A 89, 012119 (2014).

[319] I. Peschel, “Calculation of reduced density matrices from correlation functions,” J. Phys. A 36, L205 (2003).

[320] S. Popescu, A. J. Short, and A. Winter, “Entanglement and the foundations of statistical mechanics,” Nat. Phys. 2, 754–758 (2006).

[321] S. Goldstein, J. L. Lebowitz, R. Tumulka, and N. Zanghì, “Canonical typicality,” Phys. Rev. Lett. 96, 050403 (2006).

[322] S. R. Manmana, S. Wessel, R. M. Noack, and A. Muramatsu, “Strongly correlated fermions after a quantum quench,” Phys. Rev. Lett. 98, 210405 (2007).

[323] P. Reimann, “Foundation of statistical mechanics under experimentally realistic conditions,” Phys. Rev. Lett. 101, 190403 (2008).

[324] M. Cramer, A. Flesch, I. P. McCulloch, U. Schollwöck, and J. Eisert, “Exploring local quantum many-body relaxation by atoms in optical superlattices,” Phys. Rev. Lett. 101, 063001 (2008).

[325] M. C. Bañuls, J. I. Cirac, and M. B. Hastings, “Strong and weak thermalization of infinite nonintegrable quantum systems,” Phys. Rev. Lett. 106, 050405 (2011).

[326] A. J. Short and T. C. Farrelly, “Quantum equilibration in finite time,” New J. Phys. 14, 013063 (2012).

[327] C. Gogolin and J. Eisert, “Equilibration, thermalisation, and the emergence of statistical me- chanics in closed quantum systems,” Rep. Prog. Phys. 79, 056001 (2016).

[328] T. Mori, T. N. Ikeda, E. Kaminishi, and M. Ueda, “Thermalization and prethermalization in isolated quantum systems: a theoretical overview,” J. Phys. B 51, 112001 (2018).

[329] D. A. Abanin, W. De Roeck, and F. Huveneers, “Exponentially slow heating in periodically driven many-body systems,” Phys. Rev. Lett. 115, 256803 (2015).

[330] T. Kuwahara, T. Mori, and K. Saito, “Floquet-Magnus theory and generic transient dynamics in periodically driven many-body quantum systems,” Ann. Phys. 367, 96 – 124 (2016).

[331] M. Rigol, V. Dunjko, and M. Olshanii, “Thermalization and its mechanism for generic isolated quantum systems,” Nature 452, 854–858 (2008).

[332] M. Rigol, “Breakdown of thermalization in finite one-dimensional systems,” Phys. Rev. Lett. 103, 100403 (2009).

[333] G. Biroli, C. Kollath, and A. M. Läuchli, “Eﬀect of rare fluctuations on the thermalization of isolated quantum systems,” Phys. Rev. Lett. 105, 250401 (2010).

[334] R. Steinigeweg, J. Herbrych, and P. Prelovšek, “Eigenstate thermalization within isolated spin- chain systems,” Phys. Rev. E 87, 012118 (2013).

[335] R. Steinigeweg, A. Khodja, H. Niemeyer, C. Gogolin, and J. Gemmer, “Pushing the limits of the eigenstate thermalization hypothesis towards mesoscopic quantum systems,” Phys. Rev. Lett. 112, 130403 (2014).

[336] H. Kim, T. N. Ikeda, and D. A. Huse, “Testing whether all eigenstates obey the eigenstate thermalization hypothesis,” Phys. Rev. E 90, 052105 (2014).

[337] W. Beugeling, R. Moessner, and M. Haque, “Finite-size scaling of eigenstate thermalization,” Phys. Rev. E 89, 042112 (2014).

[338] A. Khodja, R. Steinigeweg, and J. Gemmer, “Relevance of the eigenstate thermalization hy- pothesis for thermal relaxation,” Phys. Rev. E 91, 012120 (2015).

[339] L. D’Alessio, Y. Kafri, A. Polkovnikov, and M. Rigol, “From quantum chaos and eigenstate thermalization to statistical mechanics and thermodynamics,” Adv. Phys. 65, 239–362 (2016).

[340] J. R. Garrison and T. Grover, “Does a single eigenstate encode the full hamiltonian?” Phys. Rev. X 8, 021026 (2018).

[341] T. Yoshizawa, E. Iyoda, and T. Sagawa, “Numerical large deviation analysis of the eigenstate thermalization hypothesis,” Phys. Rev. Lett. 120, 200604 (2018).

[342] J. v. Neumann, Z. Phys. 57, 30–70 (1929).

[343] E. T. Jaynes, “Information theory and statistical mechanics,” Phys. Rev. 106, 620–630 (1957).

[344] M. V. Berry, “Regular and irregular semiclassical wavefunctions,” J. Phys. A 10, 2083 (1977).

[345] A. Peres, “Ergodicity and mixing in quantum theory. i,” Phys. Rev. A 30, 504–508 (1984).

[346] R. V. Jensen and R. Shankar, “Statistical behavior in deterministic quantum systems with few degrees of freedom,” Phys. Rev. Lett. 54, 1879–1882 (1985).

[347] M. Srednicki, “Chaos and quantum thermalization,” Phys. Rev. E 50, 888–901 (1994).

[348] J. M. Deutsch, “Quantum statistical mechanics in a closed system,” Phys. Rev. A 43, 2046–2049 (1991).

[349] H. Tasaki, “From quantum dynamics to the canonical distribution: General picture and a rigorous example,” Phys. Rev. Lett. 80, 1373–1376 (1998).

[350] E. B. Davies, “Markovian master equations,” Comm. Math. Phys. 39, 91–110 (1974).

[351] H. Spohn and J. L. Lebowitz, “Irreversible thermodynamics for quantum systems weakly coupled to thermal reservoirs,” Adv. Chem. Phys. pp. 109–142 (1978).

[352] R. Alicki, “The quantum open system as a model of the heat engine,” J. Phys. A 12, L103 (1979).

[353] A. O. Caldeira and A. J. Leggett, “Path integral approach to quantum Brownian motion,” Physica A 121, 587 – 616 (1983).

[354] U. Weiss, Quantum Dissipative Systems (World Scientific, Singapore, 1999).

[355] T. Kinoshita, T. Wenger, and D. S. Weiss, “A quantum Newton’s cradle,” Nature 440, 900–903 (2006).

[356] M. Gring, M. Kuhnert, T. Langen, T. Kitagawa, B. Rauer, M. Schreitl, I. Mazets, D. A. Smith, E. Demler, and J. Schmiedmayer, “Relaxation and prethermalization in an isolated quantum system,” Science 337, 1318–1322 (2012).

[357] A. M. Kaufman, M. E. Tai, A. Lukin, M. Rispoli, R. Schittko, P. M. Preiss, and M. Greiner, “Quantum thermalization through entanglement in an isolated many-body system,” Science 353, 794–800 (2016).

[358] Y. Tang, W. Kao, K.-Y. Li, S. Seo, K. Mallayya, M. Rigol, S. Gopalakrishnan, and B. L. Lev, “Thermalization near integrability in a dipolar quantum Newton’s cradle,” Phys. Rev. X 8, 021030 (2018).

[359] M. Rigol, V. Dunjko, V. Yurovsky, and M. Olshanii, “Relaxation in a completely integrable many-body quantum system: An ab initio study of the dynamics of the highly excited states of 1d lattice hard-core bosons,” Phys. Rev. Lett. 98, 050405 (2007).

[360] P. Calabrese, F. H. L. Essler, and M. Fagotti, “Quantum quench in the transverse-field Ising chain,” Phys. Rev. Lett. 106, 227203 (2011).

[361] M. Fagotti and F. H. L. Essler, “Reduced density matrix after a quantum quench,” Phys. Rev. B 87, 245107 (2013).

[362] S. Sotiriadis and P. Calabrese, “Validity of the gge for quantum quenches from interacting to noninteracting models,” J. Stat. Mech. 2014, P07024 (2014).

[363] F. H. L. Essler and M. Fagotti, “Quench dynamics and relaxation in isolated integrable quantum spin chains,” J. Stat. Mech. 2016, 064002 (2016).

[364] L. Vidmar and M. Rigol, “Generalized Gibbs ensemble in integrable lattice models,” J. Stat. Mech. 2016, 064007 (2016).

[365] F. Lange, Z. Lenarcic, and A. Rosch, “Pumping approximately integrable systems,” Nat. Com- mun. 8, 15767 (2017).

[366] R. Nandkishore and D. A. Huse, “Many-body localization and thermalization in quantum statistical mechanics,” Ann. Rev. Cond. Matt. Phys. 6, 15–38 (2015).

[367] R. Vasseur and J. E. Moore, “Nonequilibrium quantum dynamics and transport: from integra- bility to many-body localization,” J. Stat. Mech. 2016, 064010 (2016).

[368] J. P. Garrahan and I. Lesanovsky, “Thermodynamics of quantum jump trajectories,” Phys. Rev. Lett. 104, 160601 (2010).

[369] T. E. Lee, F. Reiter, and N. Moiseyev, “Entanglement and spin squeezing in non-Hermitian phase transitions,” Phys. Rev. Lett. 113, 250401 (2014).

[370] M. D. Lee and J. Ruostekoski, “Classical stochastic measurement trajectories: Bosonic atomic gases in an optical cavity and quantum measurement backaction,” Phys. Rev. A 90, 023628 (2014).

[371] M. K. Pedersen, J. J. W. H. Sørensen, M. C. Tichy, and J. F. Sherson, “Many-body state engineering using measurements and fixed unitary dynamics,” New J. Phys. 16, 113038 (2014).

[372] T. J. Elliott, W. Kozlowski, S. F. Caballero-Benitez, and I. B. Mekhov, “Multipartite entangled spatial modes of ultracold atoms generated and controlled by quantum measurement,” Phys. Rev. Lett. 114, 113604 (2015).

[373] A. C. J. Wade, J. F. Sherson, and K. Mølmer, “Squeezing and entanglement of density oscilla- tions in a Bose-Einstein condensate,” Phys. Rev. Lett. 115, 060401 (2015).

[374] S. Dhar, S. Dasgupta, A. Dhar, and D. Sen, “Detection of a quantum particle on a lattice under repeated projective measurements,” Phys. Rev. A 91, 062115 (2015).

[375] S. Dhar and S. Dasgupta, “Measurement-induced phase transition in a quantum spin system,” Phys. Rev. A 93, 050103 (2016).

[376] M. Schemmer, A. Johnson, R. Photopoulos, and I. Bouchoule, “Monte Carlo wave-function description of losses in a one-dimensional Bose gas and cooling to the ground state by quantum feedback,” Phys. Rev. A 95, 043641 (2017).

[377] M. Mehboudi, A. Lampo, C. Charalambous, L. A. Correa, M. A. Garcia-March, and M. Lewen- stein, “Using polarons for sub-nK quantum non-demolition thermometry in a Bose-Einstein condensate,” arXiv:1806.07198 .

[378] L. Buﬀoni, A. Solfanelli, P. Verrucchi, A. Cuccoli, and M. Campisi, “Quantum Measurement Cooling,” arXiv:1806.07814 .

[379] J. J. Soerensen, M. Dalgaard, A. H. Kiilerich, K. Moelmer, and J. Sherson, “Quantum control with measurements and quantum Zeno dynamics,” arXiv:1806.07793 .

[380] B. Kraus, H. P. Büchler, S. Diehl, A. Kantian, A. Micheli, and P. Zoller, “Preparation of entangled states by quantum Markov processes,” Phys. Rev. A 78, 042307 (2008).

[381] S. Diehl, A. Micheli, A. Kantian, B. Kraus, H. P. Büchler, and P. Zoller, “Quantum states and phases in driven open quantum systems with cold atoms,” Nat. Phys. 4, 878–883 (2008).

[382] F. Verstraete, M. M. Wolf, and J. I. Cirac, “Quantum computation and quantum-state engineering driven by dissipation,” Nat. Phys. 5, 633–636 (2009).

[383] W. Yi, S. Diehl, A. J. Daley, and P. Zoller, “Driven-dissipative many-body pairing states for cold fermionic atoms in an optical lattice,” New J. Phys. 14, 055002 (2012).

[384] C. Joshi, J. Larson, and T. P. Spiller, “Quantum state engineering in hybrid open quantum systems,” Phys. Rev. A 93, 043818 (2016).

[385] J. Marino and A. Silva, “Relaxation, prethermalization, and diﬀusion in a noisy quantum Ising chain,” Phys. Rev. B 86, 060408 (2012).

[386] H. Pichler, J. Schachenmayer, A. J. Daley, and P. Zoller, “Heating dynamics of bosonic atoms in a noisy optical lattice,” Phys. Rev. A 87, 033606 (2013).

[387] A. Chenu, M. Beau, J. Cao, and A. del Campo, “Quantum simulation of generic many-body open system dynamics using classical noise,” Phys. Rev. Lett. 118, 140403 (2017).

[388] L. Banchi, D. Burgarth, and M. J. Kastoryano, “Driven quantum dynamics: Will it blend?” Phys. Rev. X 7, 041015 (2017).

[389] P. Hayden, S. Nezami, X.-L. Qi, N. Thomas, M. Walter, and Z. Yang, “Holographic duality from random tensor networks,” J. High Energy Phys. 2016, 9 (2016).

[390] A. Nahum, J. Ruhman, S. Vijay, and J. Haah, “Quantum entanglement growth under random unitary dynamics,” Phys. Rev. X 7, 031016 (2017).

[391] A. Nahum, S. Vijay, and J. Haah, “Operator spreading in random unitary circuits,” Phys. Rev. X 8, 021014 (2018).

[392] C. W. von Keyserlingk, T. Rakovszky, F. Pollmann, and S. L. Sondhi, “Operator hydrodynamics, otocs, and entanglement growth in systems without conservation laws,” Phys. Rev. X 8, 021013 (2018).

[393] C. Sünderhauf, D. Pérez-Garcia, D. A. Huse, N. Schuch, and J. I. Cirac, “Localisation with random time-periodic quantum circuits,” arXiv:1805.08487 .

[394] M. Knap, “Entanglement production and information scrambling in a noisy spin system,” arXiv:1806.04686 .

[395] S. Hernández-Santana, A. Riera, K. V. Hovhannisyan, M. Perarnau-Llobet, L. Tagliacozzo, and A. Acin, “Locality of temperature in spin chains,” New J. Phys. 17, 085007 (2015).

[396] M. Kliesch, C. Gogolin, M. J. Kastoryano, A. Riera, and J. Eisert, “Locality of temperature,” Phys. Rev. X 4, 031019 (2014).

[397] L. F. Santos, A. Polkovnikov, and M. Rigol, “Entropy of isolated quantum systems after a quench,” Phys. Rev. Lett. 107, 040601 (2011).

[398] A. Polkovnikov, “Microscopic diagonal entropy and its connection to basic thermodynamic relations,” Ann. Phys. 326, 486 – 499 (2011).

[399] T. N. Ikeda, N. Sakumichi, A. Polkovnikov, and M. Ueda, “The second law of thermodynamics under unitary evolution and external operations,” Ann. Phys. 354, 338 – 352 (2015).

[400] W. Thirring, Quantum Mathematical Physics (Springer-Verlag, Berlin, 2002).

[401] C. Neuenhahn and F. Marquardt, “Thermalization of interacting fermions and delocalization in fock space,” Phys. Rev. E 85, 060101 (2012).

[402] T. Mori, “Weak eigenstate thermalization with large deviation bound,” arXiv:1609.09776 .

[403] H. M. Wiseman and G. J. Milburn, “Quantum theory of optical feedback via homodyne detec- tion,” Phys. Rev. Lett. 70, 548–551 (1993).

[404] C. Sayrin, I. Dotsenko, X. Zhou, B. Peaudecerf, T. Rybarczyk, S. Gleyzes, P. Rouchon, M. Mir- rahimi, H. Amini, M. Brune, J.-M. Raimond, and S. Haroche, “Real-time quantum feedback prepares and stabilizes photon number states,” Nature 477, 73–77 (2011).

[405] C. M. Caves and G. J. Milburn, “Quantum-mechanical model for continuous position measure- ments,” Phys. Rev. A 36, 5543–5555 (1987).

[406] L. Diósi, “Continuous quantum measurement and its formalism,” Phys. Lett. A 129, 419 – 423 (1988).

[407] L. Diósi, “Localized solution of a simple nonlinear quantum langevin equation,” Phys. Lett. A 132, 233 – 236 (1988).

[408] V. P. Belavkin and P. Staszewski, “Nondemolition observation of a free quantum particle,” Phys. Rev. A 45, 1347–1356 (1992).

[409] M. J. Gagen, H. M. Wiseman, and G. J. Milburn, “Continuous position measurements and the quantum Zeno eﬀect,” Phys. Rev. A 48, 132–142 (1993).

[410] A. Bassi, K. Lochan, S. Satin, T. P. Singh, and H. Ulbricht, “Models of wave-function collapse, underlying theories, and experimental tests,” Rev. Mod. Phys. 85, 471–527 (2013).

[411] S. Keßler, A. Holzner, I. P. McCulloch, J. von Delft, and F. Marquardt, “Stroboscopic observa- tion of quantum many-body dynamics,” Phys. Rev. A 85, 011605 (2012).

[412] M. Gullans, T. G. Tiecke, D. E. Chang, J. Feist, J. D. Thompson, J. I. Cirac, P. Zoller, and M. D. Lukin, “Nanoplasmonic lattices for ultracold atoms,” Phys. Rev. Lett. 109, 235309 (2012).

[413] O. Romero-Isart, C. Navau, A. Sanchez, P. Zoller, and J. I. Cirac, “Superconducting vortex lattices for ultracold atoms,” Phys. Rev. Lett. 111, 145304 (2013).

[414] A. González-Tudela, C.-L. Hung, D. E. Chang, I. J. Cirac, and J. H. Kimble, “Subwavelength vacuum lattices and atom–atom interactions in two-dimensional photonic crystals,” Nat. Photon. 9, 320–325 (2015).

[415] S. Nascimbene, N. Goldman, N. R. Cooper, and J. Dalibard, “Dynamic optical lattices of subwavelength spacing for ultracold atoms,” Phys. Rev. Lett. 115, 140401 (2015).

[416] L. Diósi, “Models for universal reduction of macroscopic quantum fluctuations,” Phys. Rev. A 40, 1165–1174 (1989).

[417] P. Schauß, J. Zeiher, T. Fukuhara, S. Hild, M. Cheneau, T. Macri, T. Pohl, I. Bloch, and C. Gross, “Crystallization in Ising quantum magnets,” Science 347, 1455–1458 (2015).

[418] J. S. Douglas and K. Burnett, “Quantum imaging of spin states in optical lattices,” Phys. Rev. A 82, 033434 (2010).

[419] G. C. Ghirardi, A. Rimini, and T. Weber, “Unified dynamics for microscopic and macroscopic systems,” Phys. Rev. D 34, 470–491 (1986).

[420] G. C. Ghirardi, P. Pearle, and A. Rimini, “Markov processes in hilbert space and continuous spontaneous localization of systems of identical particles,” Phys. Rev. A 42, 78–89 (1990).

[421] Y. Lahini, M. Verbin, S. D. Huber, Y. Bromberg, R. Pugatch, and Y. Silberberg, “Quantum walk of two interacting bosons,” Phys. Rev. A 86, 011603 (2012).

[422] M. Grifoni and P. Hänggi, “Driven quantum tunneling,” Phys. Rep. 304, 229 – 354 (1998).

[423] E. Schwarzer and H. Haken, “The moments of the coupled coherent and incoherent motion of excitons,” Phys. Lett. A 42, 317 – 318 (1972).

[424] T. A. Brun, H. A. Carteret, and A. Ambainis, “Quantum to classical transition for random walks,” Phys. Rev. Lett. 91, 130602 (2003).

[425] S. Hoyer, M. Sarovar, and K. B. Whaley, “Limits of quantum speedup in photosynthetic light harvesting,” New J. Phys. 12, 065041 (2010).

[426] A. Schreiber, K. N. Cassemiro, V. Potoček, A. Gábris, I. Jex, and C. Silberhorn, “Decoherence and disorder in quantum walks: From ballistic spread to localization,” Phys. Rev. Lett. 106, 180403 (2011).

[427] K. Jacobs and D. A. Steck, “A straightforward introduction to continuous quantum measure- ment,” Contemp. Phys. 47, 279–303 (2006).

[428] J. Eschner, G. Morigi, F. Schmidt-Kaler, and R. Blatt, “Laser cooling of trapped ions,” J. Opt. Soc. Am. B 20, 1003–1015 (2003).

[429] C. Weitenberg, P. Schauß, T. Fukuhara, M. Cheneau, M. Endres, I. Bloch, and S. Kuhr, “Coherent light scattering from a two-dimensional mott insulator,” Phys. Rev. Lett. 106, 215301 (2011).

[430] E. Iyoda, K. Kaneko, and T. Sagawa, “Fluctuation theorem for many-body pure quantum states,” Phys. Rev. Lett. 119, 100601 (2017).

[431] J. Z. Imbrie, “Diagonalization and many-body localization for a disordered quantum spin chain,” Phys. Rev. Lett. 117, 027201 (2016).

[432] D. Nagy, G. Kónya, G. Szirmai, and P. Domokos, “Dicke-model phase transition in the quantum motion of a Bose-Einstein condensate in an optical cavity,” Phys. Rev. Lett. 104, 130401 (2010).

[433] Y. Vasin, Y. Ryzhov, and V. M. Vinokur, Sci. Rep. 5, 18600 (2015).

[434] P. Anderson, “A poor man’s derivation of scaling laws for the Kondo problem,” J. Phys. C 3, 2436 (1970).

[435] K. G. Wilson, “The renormalization group: Critical phenomena and the Kondo problem,” Rev. Mod. Phys. 47, 773–840 (1975).

[436] R. Bulla, N.-H. Tong, and M. Vojta, “Numerical renormalization group for bosonic systems and application to the sub-ohmic spin-boson model,” Phys. Rev. Lett. 91, 170601 (2003).

[437] L. Borda, “Kondo screening cloud in a one-dimensional wire: Numerical renormalization group study,” Phys. Rev. B 75, 041307 (2007).

[438] R. Bulla, T. A. Costi, and T. Pruschke, “Numerical renormalization group method for quantum impurity systems,” Rev. Mod. Phys. 80, 395–450 (2008).

[439] H. Saberi, A. Weichselbaum, and J. von Delft, “Matrix-product-state comparison of the numeri- cal renormalization group and the variational formulation of the density-matrix renormalization group,” Phys. Rev. B 78, 035124 (2008).

[440] L. Borda, M. Garst, and J. Kroha, “Kondo cloud and spin-spin correlations around a partially screened magnetic impurity,” Phys. Rev. B 79, 100408 (2009).

[441] C. A. Büsser, G. B. Martins, L. Costa Ribeiro, E. Vernek, E. V. Anda, and E. Dagotto, “Numerical analysis of the spatial range of the Kondo eﬀect,” Phys. Rev. B 81, 045111 (2010).

[442] L. Riegger, N. Darkwah Oppong, M. Höfer, D. R. Fernandes, I. Bloch, and S. Fölling, “Localized magnetic moments with tunable spin exchange in a gas of ultracold fermions,” Phys. Rev. Lett. 120, 143601 (2018).

[443] S. De Franceschi, R. Hanson, W. G. van der Wiel, J. M. Elzerman, J. J. Wijpkema, T. Fujisawa, S. Tarucha, and L. P. Kouwenhoven, “Out-of-equilibrium Kondo eﬀect in a mesoscopic device,” Phys. Rev. Lett. 89, 156801 (2002).

[444] H. E. Türeci, M. Hanl, M. Claassen, A. Weichselbaum, T. Hecht, B. Braunecker, A. Govorov, L. Glazman, A. Imamoglu, and J. von Delft, “Many-body dynamics of exciton creation in a quantum dot by optical absorption: A quantum quench towards Kondo correlations,” Phys. Rev. Lett. 106, 107402 (2011).

[445] C. Latta, F. Haupt, M. Hanl, A. Weichselbaum, M. Claassen, W. Wuester, P. Fallahi, S. Faelt, L. Glazman, J. von Delft, H. E. Türeci, and A. Imamoglu, “Quantum quench of Kondo correlations in optical absorption,” Nature 474, 627–630 (2011).

[446] M. M. Desjardins, J. J. Viennot, M. C. Dartiailh, L. E. Bruhat, M. R. Delbecq, M. Lee, M.-S. Choi, A. Cotter, and T. Kontos, “Observation of the frozen charge of a Kondo resonance,” Nature 545, 71–74 (2017).

[447] A. J. Leggett, “Bose-Einstein condensation in the alkali gases: Some fundamental concepts,” Rev. Mod. Phys. 73, 307–356 (2001).

[448] S. Tomonaga, “On the eﬀect of the field reactions on the interaction of mesotrons and nuclear particles. III,” Prog. Theor. Phys. 2, 6–24 (1947).

[449] T. D. Lee, F. E. Low, and D. Pines, “The motion of slow electrons in a polar crystal,” Phys. Rev. 90, 297–302 (1953).

[450] J. T. Devreese and A. S. Alexandrov, “Fröhlich polaron and bipolaron: recent developments,” Rep. Prog. Phys. 72, 066501 (2009).

[451] J. T. Devreese, “Fröhlich polarons. lecture course including detailed theoretical derivations,” arXiv:1012.4576 (2010).

[452] A. S. Alexandrov, Polarons in advanced materials (Canopus Pub., 2007).

[453] R. P. Feynman, “Slow electrons in a polar crystal,” Phys. Rev. 97, 660–665 (1955).

[454] J. Bardeen, G. Baym, and D. Pines, “Eﬀective interaction of He 3 atoms in dilute solutions of He 3 in He 4 at low temperatures,” Phys. Rev. 156, 207 (1967).

[455] P. Nagy, “The polaron and squeezed states,” J. Phys. Cond. Matt. 2, 10573 (1990).

[456] W.-M. Zhang, D. H. Feng, and R. Gilmore, “Coherent states: Theory and some applications,” Rev. Mod. Phys. 62, 867–927 (1990).

[457] T. Altanhan and B. S. Kandemir, “A squeezed state approach for the large polarons,” J. Phys. Cond. Matt. 5, 6729 (1993).

[458] J. Tempere, W. Casteels, M. K. Oberthaler, S. Knoop, E. Timmermans, and J. T. Devreese, “Feynman path-integral treatment of the BEC-impurity polaron,” Phys. Rev. B 80, 184504 (2009).

[459] A. Novikov and M. Ovchinnikov, “Variational approach to the ground state of an impurity in a Bose-Einstein condensate,” J. Phys. B 43, 105301 (2010).

[460] W. Casteels, T. Van Cauteren, J. Tempere, and J. T. Devreese, “Strong coupling treatment of the polaronic system consisting of an impurity in a condensate,” Laser Phys. 21, 1480–1485 (2011).

[461] W. Casteels, J. Tempere, and J. T. Devreese, “Many-polaron description of impurities in a Bose-Einstein condensate in the weak-coupling regime,” Phys. Rev. A 84, 063612 (2011).

[462] S. P. Rath and R. Schmidt, “Field-theoretical study of the Bose polaron,” Phys. Rev. A 88, 053632 (2013).

[463] J. Vlietinck, J. Ryckebusch, and K. Van Houcke, “Quasiparticle properties of an impurity in a Fermi gas,” Phys. Rev. B 87, 1–11 (2013).

[464] J. Vlietinck, W. Casteels, K. Van Houcke, J. Tempere, J. Ryckebusch, and J. T. Devreese, “Diagrammatic Monte Carlo study of the acoustic and the BEC polaron,” New J. Phys. p. 9 (2014).

[465] W. Li and S. Das Sarma, “Variational study of polarons in Bose-Einstein condensates,” Phys. Rev. A 90, 013618 (2014).

[466] F. Grusdt, Y. E. Shchadilova, a. N. Rubtsov, and E. Demler, “Renormalization group approach to the Fröhlich polaron model: application to impurity-BEC problem,” Sci. Rep. 5, 12124 (2015).

[467] Y. E. Shchadilova, F. Grusdt, A. N. Rubtsov, and E. Demler, “Polaronic mass renormalization of impurities in Bose-Einstein condensates: Correlated Gaussian-wave-function approach,” Phys. Rev. A 93, 043606 (2016).

[468] Y. E. Shchadilova, R. Schmidt, F. Grusdt, and E. Demler, “Quantum dynamics of ultracold Bose polarons,” Phys. Rev. Lett. 117, 113002 (2016).

[469] R. M. Konik, H. Saleur, and A. Ludwig, “Transport in quantum dots from the integrability of the Anderson model,” Phys. Rev. B 66, 125304 (2002).

[470] J. Schliemann, A. Khaetskii, and D. Loss, “Electron spin dynamics in quantum dots and related nanostructures due to hyperfine interaction with nuclei,” J. Phys. Condens. Matter 15, R1809 (2003).

[471] G. Zaránd and J. von Delft, “Analytical calculation of the finite-size crossover spectrum of the anisotropic two-channel Kondo model,” Phys. Rev. B 61, 6918–6933 (2000).

[472] P. Sala, T. Shi, S. Kühn, M. C. Bañuls, E. Demler, and J. I. Cirac, “Variational study of U(1) and SU(2) lattice gauge theories with Gaussian states in 1+1 dimensions,” arXiv:1805.05190 (2018).

[473] C. Weedbrook, S. Pirandola, R. García-Patrón, N. J. Cerf, T. C. Ralph, J. H. Shapiro, and S. Lloyd, “Gaussian quantum information,” Rev. Mod. Phys. 84, 621–669 (2012).

[474] J. Mitroy, S. Bubin, W. Horiuchi, Y. Suzuki, L. Adamowicz, W. Cencek, K. Szalewicz, J. Ko- masa, D. Blume, and K. Varga, “Theory and application of explicitly correlated Gaussians,” Rev. Mod. Phys. 85, 693–749 (2013).

[475] C. V. Kraus and J. I. Cirac, “Generalized Hartree-Fock theory for interacting fermions in lattices: numerical methods,” New J. Phys. 12, 113004 (2010).

[476] R. Jackiw and A. Kerman, “Time-dependent variational principle and the eﬀective action,” Phys. Lett. A 71, 1–5 (1979).

[477] P. Kramer, “A review of the time-dependent variational principle,” J. Phys. Conf. Ser. 99, 012009 (2008).

[478] T. Shi, E. Demler, and J. I. Cirac, “Variational study of fermionic and bosonic systems with non-Gaussian states: Theory and applications,” Ann. Phys. 390, 245–302 (2018).

[479] K. B. Petersen and M. S. Petersen, “The matrix cookbook,” Version 20051003 (2006).

[480] P. B. Weigmann, JETP Lett. 31, 364 (1980).

[481] N. Andrei, “Diagonalization of the Kondo hamiltonian,” Phys. Rev. Lett. 45, 379–382 (1980).

[482] N. Andrei and J. H. Lowenstein, “Scales and scaling in the Kondo model,” Phys. Rev. Lett. 46, 356–360 (1981).

[483] K. Yosida, “Bound state due to the s − d exchange interaction,” Phys. Rev. 147, 223–227 (1966).

[484] C. M. Varma and Y. Yafet, “Magnetic susceptibility of mixed-valence rare-earth compounds,” Phys. Rev. B 13, 2950–2954 (1976).

[485] G. Bergmann and L. Zhang, “Compact approximate solution to the Kondo problem,” Phys. Rev. B 76, 064401 (2007).

[486] C. Yang and A. E. Feiguin, “Unveiling the internal entanglement structure of the Kondo singlet,” Phys. Rev. B 95, 115106 (2017).

[487] S. R. White, “Density matrix formulation for quantum renormalization groups,” Phys. Rev. Lett. 69, 2863–2866 (1992).

[488] F. Verstraete, D. Porras, and J. I. Cirac, “Density matrix renormalization group and periodic boundary conditions: A quantum information perspective,” Phys. Rev. Lett. 93, 227205 (2004).

[489] G. Vidal, “Efficient classical simulation of slightly entangled quantum computations,” Phys. Rev. Lett. 91, 147902 (2003).

[490] G. Vidal, “Efficient simulation of one-dimensional quantum many-body systems,” Phys. Rev. Lett. 93, 040502 (2004).

[491] A. J. Daley, C. Kollath, U. Schollwöck, and G. Vidal, “Time-dependent density-matrix renormalization-group using adaptive eﬀective Hilbert spaces,” J. Stat. Mech. Theor. Exp. 2004, P04005 (2004).

[492] B. Pirvu, V. Murg, J. I. Cirac, and F. Verstraete, “Matrix product operator representations,” New J. Phys. 12, 025012 (2010).

[493] H. F. Trotter, “On the product of semi-groups of operators,” Proc. Amer. Math. Soc. 10, 545–551 (1959).

[494] M. Suzuki, “Decomposition formulas of exponential operators and lie exponentials with some applications to quantum mechanics and statistical physics,” J. Math. Phys. 26, 601–612 (1985).

[495] F. Verstraete, J. J. García-Ripoll, and J. I. Cirac, “Matrix product density operators: Simulation of finite-temperature and dissipative systems,” Phys. Rev. Lett. 93, 207204 (2004).

[496] A. Holzner, I. P. McCulloch, U. Schollwöck, J. von Delft, and F. Heidrich-Meisner, “Kondo screening cloud in the single-impurity Anderson model: A density matrix renormalization group study,” Phys. Rev. B 80, 205114 (2009).

[497] H. Ishii, “Spin correlation in dilute magnetic alloys,” J. Low Temp. Phys. 32, 457–467 (1978).

[498] V. Barzykin and I. Aﬄeck, “Screening cloud in the k-channel Kondo model: Perturbative and large-k results,” Phys. Rev. B 57, 432–448 (1998).

[499] T. Hand, J. Kroha, and H. Monien, “Spin correlations and finite-size eﬀects in the one- dimensional Kondo box,” Phys. Rev. Lett. 97, 136604 (2006).

[500] D. N. Basov, R. D. Averitt, D. van der Marel, M. Dressel, and K. Haule, “Electrodynamics of correlated electron materials,” Rev. Mod. Phys. 83, 471–541 (2011).

[501] A. Rosch, J. Kroha, and P. Wölfle, “Kondo eﬀect in quantum dots at high voltage: Universality and scaling,” Phys. Rev. Lett. 87, 156802 (2001).

[502] A. C. Hewson, J. Bauer, and A. Oguri, “Non-equilibrium diﬀerential conductance through a quantum dot in a magnetic field,” J. Phys. Cond. Matt. 17, 5413 (2005).

[503] E. Sela and J. Malecki, “Nonequilibrium conductance of asymmetric nanodevices in the Kondo regime,” Phys. Rev. B 80, 233103 (2009).

[504] C. Mora, P. Vitushinsky, X. Leyronas, A. A. Clerk, and K. Le Hur, “Theory of nonequilibrium transport in the SU n Kondo regime,” Phys. Rev. B 80, 155322 (2009).

[505] C. Mora, C. P. Moca, J. von Delft, and G. Zaránd, “Fermi-liquid theory for the single-impurity Anderson model,” Phys. Rev. B 92, 075120 (2015).

[506] M. Filippone, C. P. Moca, J. von Delft, and C. Mora, “At which magnetic field, exactly, does the Kondo resonance begin to split? A fermi liquid description of the low-energy properties of the Anderson model,” Phys. Rev. B 95, 165404 (2017).

[507] A. Oguri and A. C. Hewson, “Higher-order fermi-liquid corrections for an Anderson impurity away from half filling,” Phys. Rev. Lett. 120, 126802 (2018).

[508] A. Oguri and A. C. Hewson, “Higher-order fermi-liquid corrections for an Anderson impurity away from half filling : Equilibrium properties,” Phys. Rev. B 97, 045406 (2018).

[509] N. Shah and C. J. Bolech, “Consistent bosonization-debosonization. I. A resolution of the nonequilibrium transport puzzle,” Phys. Rev. B 93, 085440 (2016).

[510] R. Schmidt, H. R. Sadeghpour, and E. Demler, “Mesoscopic Rydberg impurity in an atomic quantum gas,” Phys. Rev. Lett. 116, 105302 (2016).

[511] E. Fermi, “Sopra lo spostamento per pressione delle righe elevate delle serie spettrali,” II Nuovo Cimento 11, 157 (1934).

[512] A. Khaetskii, D. Loss, and L. Glazman, “Electron spin evolution induced by interaction with nuclei in a quantum dot,” Phys. Rev. B 67, 195329 (2003).

[513] M. Bortz and J. Stolze, “Exact dynamics in the inhomogeneous central-spin model,” Phys. Rev. B 76, 014304 (2007).

[514] W. A. Coish and D. Loss, “Hyperfine interaction in a quantum dot: Non-markovian electron spin dynamics,” Phys. Rev. B 70, 195340 (2004).

[515] R. Hanson, V. V. Dobrovitski, A. E. Feiguin, O. Gywat, and D. D. Awschalom, “Coherent dynamics of a single spin interacting with an adjustable spin bath,” Science 320, 352–355 (2008).

[516] W. M. Witzel, M. S. Carroll, A. Morello, L. Cywiński, and S. Das Sarma, “Electron spin decoherence in isotope-enriched silicon,” Phys. Rev. Lett. 105, 187602 (2010).

[517] A. M. Tyryshkin, S. Tojo, J. J. L. Morton, H. Riemann, N. V. Abrosimov, P. Becker, H.-J. Pohl, T. Schenkel, M. L. W. Thewalt, K. M. Itoh et al., “Electron spin coherence exceeding seconds in high-purity silicon,” Nat. Mater. 11, 143 (2012).

[518] A. Recati, P. O. Fedichev, W. Zwerger, J. von Delft, and P. Zoller, “Atomic quantum dots coupled to a reservoir of a superfluid Bose-Einstein condensate,” Phys. Rev. Lett. 94, 040404 (2005).

[519] D. Pekker, M. Babadi, R. Sensarma, N. Zinner, L. Pollet, M. W. Zwierlein, and E. Demler, “Competition between pairing and ferromagnetic instabilities in ultracold fermi gases near feshbach resonances,” Phys. Rev. Lett. 106, 050402 (2011).

[520] J. Bauer, C. Salomon, and E. Demler, “Realizing a Kondo-correlated state with ultracold atoms,” Phys. Rev. Lett. 111, 215304 (2013).

[521] Y. Nishida, “SU(3) orbital Kondo eﬀect with ultracold atoms,” Phys. Rev. Lett. 111, 135301 (2013).

[522] Y. Nishida, “Transport measurement of the orbital Kondo eﬀect with ultracold atoms,” Phys. Rev. A 93, 011606 (2016).

[523] M. Nakagawa and N. Kawakami, “Laser-induced Kondo eﬀect in ultracold alkaline-earth fermions,” Phys. Rev. Lett. 115, 165303 (2015).

[524] R. Zhang, Y. Cheng, H. Zhai, and P. Zhang, “Orbital feshbach resonance in alkali-earth atoms,” Phys. Rev. Lett. 115, 135301 (2015).

[525] R. Zhang, D. Zhang, Y. Cheng, W. Chen, P. Zhang, and H. Zhai, “Kondo eﬀect in alkaline- earth-metal atomic gases with confinement-induced resonances,” Phys. Rev. A 93, 043601 (2016).

[526] E. Miranda, V. Dobrosavljevic, and G. Kotliar, “Kondo disorder: a possible route towards non-fermi-liquid behaviour,” J. Phys. Cond. Matt. 8, 9871 (1996).

[527] H. Tsunetsugu, M. Sigrist, and K. Ueda, “The ground-state phase diagram of the one- dimensional Kondo lattice model,” Rev. Mod. Phys. 69, 809–864 (1997).

[528] Z.-q. Bao and F. Zhang, “Topological majorana two-channel Kondo eﬀect,” Phys. Rev. Lett. 119, 187701 (2017).

[529] K. S. Kleinbach, F. Meinert, F. Engel, W. J. Kwon, R. Löw, T. Pfau, and G. Raithel, “Photoasso- ciation of trilobite Rydberg molecules via resonant spin-orbit coupling,” Phys. Rev. Lett. 118, 223001 (2017).

[530] F. Camargo, R. Schmidt, J. D. Whalen, R. Ding, G. Woehl, Jr., S. Yoshida, J. Burgdörfer, F. B. Dunning, H. R. Sadeghpour, E. Demler, and T. C. Killian, “Creation of Rydberg Polarons in a Bose Gas,” arXiv:1706.03717 (2017).

[531] F. Romeo and R. Citro, “Adiabatic pumping in a double quantum dot structure with strong spin-orbit interaction,” Phys. Rev. B 80, 165311 (2009).

[532] R. Citro, F. Romeo, and N. Andrei, “Electrically controlled pumping of spin currents in topological insulators,” Phys. Rev. B 84, 161301 (2011).

[533] M. Diez, A. M. R. V. L. Monteiro, G. Mattoni, E. Cobanera, T. Hyart, E. Mulazimoglu, N. Bovenzi, C. W. J. Beenakker, and A. D. Caviglia, “Giant negative magnetoresistance driven by spin-orbit coupling at the LaAlO3 SrTiO3 interface,” Phys. Rev. Lett. 115, 016803 (2015).

[534] Y. Peng, Y. Vinkler-Aviv, P. W. Brouwer, L. I. Glazman, and F. von Oppen, “Parity anomaly and spin transmutation in quantum spin Hall Josephson junctions,” Phys. Rev. Lett. 117, 267001 (2016).

[535] D. B. Gutman, Y. Gefen, and A. D. Mirlin, “Bosonization of one-dimensional fermions out of equilibrium,” Phys. Rev. B 81, 085436 (2010).

[536] D. B. Gutman, Y. Gefen, and A. D. Mirlin, “Full counting statistics of a Luttinger liquid conductor,” Phys. Rev. Lett. 105, 256802 (2010).

[537] Y. V. Nazarov and D. A. Bagrets, “Circuit theory for full counting statistics in multiterminal circuits,” Phys. Rev. Lett. 88, 196801 (2002).

[538] J. Maldacena, S. H. Shenker, and D. Stanford, “A bound on chaos,” J. High Energy Phys. 2016, 106 (2016).

[539] J. Cui, J. I. Cirac, and M. C. Bañuls, “Variational matrix product operators for the steady state of dissipative quantum systems,” Phys. Rev. Lett. 114, 220601 (2015).

[540] H. Weimer, “Variational principle for steady states of dissipative quantum many-body systems,” Phys. Rev. Lett. 114, 040402 (2015).

[541] T. A. Costi, “Kondo eﬀect in a magnetic field and the magnetoresistivity of Kondo alloys,” Phys. Rev. Lett. 85, 1504–1507 (2000).

[542] R. Bulla, T. A. Costi, and D. Vollhardt, “Finite-temperature numerical renormalization group study of the Mott transition,” Phys. Rev. B 64, 045103 (2001).

[543] P.-H. Chou, L.-J. Zhai, C.-H. Chung, C.-Y. Mou, and T.-K. Lee, “Emergence of a fermionic finite-temperature critical point in a Kondo lattice,” Phys. Rev. Lett. 116, 177002 (2016).

[544] G. Mahan, Many-Particle Physics (Kluwer Academic/Plenum Publishers, New York, 2000).

[545] T. Jungwirth, J. Sinova, J. Mašek, J. Kučera, and A. H. MacDonald, “Theory of ferromagnetic (III,Mn)V semiconductors,” Rev. Mod. Phys. 78, 809–864 (2006).

[546] P. Majumdar and P. B. Littlewood, “Dependence of magnetoresistivity on charge-carrier density in metallic ferromagnets and doped magnetic semiconductors,” Nature 395, 479–481 (1998).

[547] E. K. H. Salje, A. S. Alexandrov, and W. Y. Liang, eds., Polarons and Bipolarons in High Temperature Superconductors and Related Materials (Cambridge University Press, Cambridge, 2005).

[548] J. M. De Teresa, M. R. Ibarra, P. A. Algarabel, C. Ritter, C. Marquina, J. Blasco, J. Garcia, A. del Moral, and Z. Arnold, “Evidence for magnetic polarons in the magnetoresistive perovskites,” Nature 386, 256–259 (1997).

[549] Y. Zhang, W. Ong, I. Arakelyan, and J. E. Thomas, “Polaron-to-polaron transitions in the radio-frequency spectrum of a quasi-two-dimensional fermi gas,” Phys. Rev. Lett. 108, 235302 (2012).

[550] C.-H. Wu, J. W. Park, P. Ahmadi, S. Will, and M. W. Zwierlein, “Ultracold fermionic feshbach molecules of 23Na40K,” Phys. Rev. Lett. 109, 085301 (2012).

[551] M. Cetina, M. Jag, R. S. Lous, J. T. M. Walraven, R. Grimm, R. S. Christensen, and G. M. Bruun, “Decoherence of impurities in a fermi sea of ultracold atoms,” Phys. Rev. Lett. 115, 135302 (2015).

[552] M. Cetina, M. Jag, R. S. Lous, I. Fritsche, J. T. M. Walraven, R. Grimm, J. Levinsen, M. M. Parish, R. Schmidt, M. Knap, and E. Demler, “Ultrafast many-body interferometry of impurities coupled to a fermi sea,” Science 354, 96–99 (2016).

[553] M. M. Parish and J. Levinsen, “Quantum dynamics of impurities coupled to a fermi sea,” Phys. Rev. B 94, 184303 (2016).

[554] R. Schmidt, M. Knap, D. A. Ivanov, J.-S. You, M. Cetina, and E. Demler, “Universal many-body response of heavy impurities coupled to a fermi sea: a review of recent progress,” Rep. Prog. Phys. 81, 024401 (2018).

[555] L. Mathey, D. W. Wang, W. Hofstetter, M. D. Lukin, and E. Demler, “Luttinger liquid of polarons in one-dimensional boson-fermion mixtures,” Phys. Rev. Lett. 93, 120404 (2004).

[556] S. Palzer, C. Zipkes, C. Sias, and M. Köhl, “Quantum Transport through a Tonks-Girardeau Gas,” Phys. Rev. Lett. 103, 150601 (2009).

[557] F. M. Cucchietti and E. Timmermans, “Strong-coupling polarons in dilute gas Bose-Einstein condensates,” Phys. Rev. Lett. 96, 210401 (2006).

[558] A. Klein, M. Bruderer, S. R. Clark, and D. Jaksch, “Dynamics, dephasing and clustering of impurity atoms in Bose-Einstein condensates,” New J. Phys. 9, 411 (2007).

[559] W. Casteels, J. Tempere, and J. T. Devreese, “Many-polaron description of impurities in a Bose-Einstein condensate in the weak-coupling regime,” Phys. Rev. A 84, 063612 (2011).

[560] N. Spethmann, F. Kindermann, S. John, C. Weber, D. Meschede, and A. Widera, “Dynamics of single neutral impurity atoms immersed in an ultracold gas,” Phys. Rev. Lett. 109, 235301 (2012).

[561] W. Casteels, J. Tempere, and J. T. Devreese, “Bipolarons and multipolarons consisting of impurity atoms in a Bose-Einstein condensate,” Phys. Rev. A 88, 013613 (2013).

[562] R. S. Christensen, J. Levinsen, and G. M. Bruun, “Quasiparticle properties of a mobile impurity in a Bose-Einstein condensate,” Phys. Rev. Lett. 115, 160401 (2015).

[563] L. A. P. Ardila and S. Giorgini, “Impurity in a Bose-Einstein condensate: Study of the attractive and repulsive branch using quantum Monte Carlo methods,” Phys. Rev. A 92, 033612 (2015).

[564] L. A. P. Ardila and S. Giorgini, “Bose polaron problem: Eﬀect of mass imbalance on binding energy,” Phys. Rev. A 94, 063640 (2016).

[565] J. Levinsen, M. M. Parish, and G. M. Bruun, “Impurity in a Bose-Einstein condensate and the Efimov eﬀect,” Phys. Rev. Lett. 115, 125302 (2015).

[566] R. Schmidt and M. Lemeshko, “Rotation of quantum impurities in the presence of a many-body environment,” Phys. Rev. Lett. 114, 203001 (2015).

[567] A. G. Volosniev, H.-W. Hammer, and N. T. Zinner, “Real-time dynamics of an impurity in an ideal Bose gas in a trap,” Phys. Rev. A 92, 023623 (2015).

[568] R. Schmidt and M. Lemeshko, “Deformation of a quantum many-particle system by a rotating impurity,” Phys. Rev. X 6, 011012 (2016).

[569] F. F. Bellotti, T. Frederico, M. T. Yamashita, D. V. Fedorov, A. S. Jensen, and N. T. Zinner, “Three-body bound states of two bosonic impurities immersed in a fermi sea in 2d,” New J. Phys. 18, 043023 (2016).

[570] B. Midya, M. Tomza, R. Schmidt, and M. Lemeshko, “Rotation of cold molecular ions inside a Bose-Einstein condensate,” Phys. Rev. A 94, 041601 (2016).

[571] X. Cui and H. Zhai, “Stability of a fully magnetized ferromagnetic state in repulsively interacting ultracold fermi gases,” Phys. Rev. A 81, 041602 (2010).

[572] R. Schmidt and T. Enss, “Excitation spectra and rf response near the polaron-to-molecule transition from the functional renormalization group,” 83, 063620 (2011).

[573] P. Massignan and G. M. Bruun, “Repulsive polarons and itinerant ferromagnetism in strongly polarized fermi gases,” Eur. Phys. J. D 65, 83–89 (2011).

[574] R. Schmidt, T. Enss, V. Pietilä, and E. Demler, “Fermi polarons in two dimensions,” Phys. Rev. A 85, 021602 (2012).

[575] C. J. M. Mathy, M. B. Zvonarev, and E. Demler, “Quantum flutter of supersonic particles in one-dimensional quantum liquids,” Nat. Phys. 8, 881–886 (2012).

[576] P. Massignan, M. Zaccanti, and G. M. Bruun, “Polarons, dressed molecules and itinerant ferromagnetism in ultracold fermi gases,” Rep. Prog. Phys. 77, 034401 (2014).

[577] W. Yi and X. Cui, “Polarons in ultracold fermi superfluids,” Phys. Rev. A 92, 013620 (2015).

[578] W. Ong, C. Cheng, I. Arakelyan, and J. E. Thomas, “Spin-imbalanced quasi-two-dimensional fermi gases,” Phys. Rev. Lett. 114, 110403 (2015).

[579] M. Knap, A. Kantian, T. Giamarchi, I. Bloch, M. D. Lukin, and E. Demler, “Probing real-space and time-resolved correlation functions with many-body ramsey interferometry,” Phys. Rev. Lett. 111, 147205 (2013).

[580] F. Scazza, G. Valtolina, P. Massignan, A. Recati, A. Amico, A. Burchianti, C. Fort, M. Inguscio, M. Zaccanti, and G. Roati, “Repulsive fermi polarons in a resonant mixture of ultracold 6Li atoms,” Phys. Rev. Lett. 118, 083602 (2017).

[581] P. G. de Gennes, “Eﬀects of double exchange in magnetic crystals,” Phys. Rev. 118, 141–154 (1960).

[582] G. Valtolina, F. Scazza, A. Amico, A. Burchianti, A. Recati, T. Enss, M. Inguscio, M. Zaccanti, and G. Roati, “Exploring the ferromagnetic behaviour of a repulsive fermi gas through spin dynamics,” Nat. Phys. 13, 704–709 (2017).

[583] A. V. Gorshkov, M. Hermele, V. Gurarie, C. Xu, P. S. Julienne, J. Ye, P. Zoller, E. Demler, M. D. Lukin, and A. M. Rey, “Two-orbital SU(N) magnetism with ultracold alkaline-earth atoms,” Nat. Phys. 6, 289–295 (2010).

[584] G. E. Marti, A. MacRae, R. Olf, S. Lourette, F. Fang, and D. M. Stamper-Kurn, “Coherent magnon optics in a ferromagnetic spinor Bose-Einstein condensate,” Phys. Rev. Lett. 113, 155302 (2014).

[585] J. Zeiher, R. Van Bijnen, P. Schauß, S. Hild, J.-y. Choi, T. Pohl, I. Bloch, and C. Gross, “Many- body interferometry of a Rydberg-dressed spin lattice,” Nat. Phys. 12, 1095–1099 (2016).

[586] D. Petrosyan, “Dipolar exchange induced transparency with Rydberg atoms,” New J. Phys. 19, 033001 (2017).

[587] E. G. M. van Kempen, S. J. J. M. F. Kokkelmans, D. J. Heinzen, and B. J. Verhaar, “Interisotope determination of ultracold rubidium interactions from three high-precision experiments,” Phys. Rev. Lett. 88, 093201 (2002).

[588] C. Samuelis, E. Tiesinga, T. Laue, M. Elbs, H. Knöckel, and E. Tiemann, “Cold atomic collisions studied by molecular spectroscopy,” Phys. Rev. A 63, 012710 (2000).

[589] H. Fröhlich, “Electrons in lattice fields,” Adv. Phys. 3, 325–361 (1954).

[590] S. Aubry, “Breathers in nonlinear lattices: Existence, linear stability and quantization,” Physica D 103, 201 – 250 (1997).

[591] C. D’Errico, M. Zaccanti, M. Fattori, G. Roati, M. Inguscio, G. Modugno, and A. Simoni, “Feshbach resonances in ultracold 39 k,” New J. Phys. 9, 223 (2007).

[592] F. Fang, R. Olf, S. Wu, H. Kadau, and D. M. Stamper-Kurn, “Condensing magnons in a degenerate ferromagnetic spinor Bose gas,” Phys. Rev. Lett. 116, 095301 (2016).

[593] R. J. Fletcher, R. Lopes, J. Man, N. Navon, R. P. Smith, M. W. Zwierlein, and Z. Hadzibabic, “Two- and three-body contacts in the unitary Bose gas,” Science 355, 377–380 (2017).

[594] L. Tanzi, C. R. Cabrera, J. Sanz, P. Cheiney, M. Tomza, and L. Tarruell, “Feshbach resonances in potassium Bose-Bose mixtures,” arXiv:1810.12453 (2018).

[595] D. M. Stamper-Kurn and M. Ueda, “Spinor Bose gases: Symmetries, magnetism, and quantum dynamics,” Rev. Mod. Phys. 85, 1191–1244 (2013).

[596] P. Naidon, “Two impurities in a Bose-Einstein condensate: From Yukawa to Efimov attracted polarons,” J. Phys. Soc. Jpn. 87, 043002 (2018).

[597] P. Facchi and S. Pascazio, “Quantum Zeno dynamics: mathematical and physical aspects,” J. Phys. A 41, 493001 (2008).

[598] F. Reiter and A. S. Sørensen, “Eﬀective operator formalism for open quantum systems,” Phys. Rev. A 85, 032111 (2012).

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Quantum Many-Body Physics in Open Systems : Measurement and Strong Correlations

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Functional Renormalization Group Study on Kitaev Quantum Spin Liquid

Shortcuts to Adiabaticity Applied to Many-Body Systems

Quantum Thermodynamics with Measurement Processes

Stochastic description and quantum aspects of curvature perturbations in the inflationary universe

軟粒子の存在を考慮した摂動的場の量子論における散乱問題の定式化と赤外三角関係

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Quantum Many-Body Physics in Open Systems : Measurement and Strong Correlations

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関連論文

Functional Renormalization Group Study on Kitaev Quantum Spin Liquid

Shortcuts to Adiabaticity Applied to Many-Body Systems

Quantum Thermodynamics with Measurement Processes

Stochastic description and quantum aspects of curvature perturbations in the inflationary universe

軟粒子の存在を考慮した摂動的場の量子論における散乱問題の定式化と赤外三角関係

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