Nonequilibrium quantum many-body physics in ultracold atoms subject to dissipation

概要

about open quantum systems and non-Hermitian (NH) quantum systems, which naturally appear
in atomic, molecular, and optical (AMO) systems coupled to Markovian environments. Sec. 1.3
is devoted to the explanation of analytical and numerical methods which are beneficial to analyze
open quantum systems. In Sec. 1.4, we review the basics of quantum many-body phenomena,
which is helpful to understand our results in the subsequent chapters.
In Chap. 2, we demonstrate how fermionic superfluidity in ultracold atoms is affected by inelastic collisions. This chapter gives a generalized property of fermionic superfluids without dissipation
discussed in Sec. 1.4.1. Our approach is based on the generalization of the standard BardeenCooper-Schrieffer (BCS) theory to a situation in which fermions interact with each other via a
complex-valued attraction. As a result, we find that non-Hermiticity leads to unique reentrant
quantum phase transitions in superfluids.
In Chap. 3, we theoretically investigate nonequilibrium dynamics followed by a sudden switch-on
of two-particle loss due to inelastic collisions between atoms. Based on closed-time-contour (CTC)
path integrals discussed in Sec. 1.3.1, we formulate a dissipative BCS theory that fully incorporates
a change in particle number, which is included via quantum jump terms in the Lindblad equation.
As an experimentally relevant model, we propose introducing a particle loss in one of two coupled
superfluids, and find a nonequilibrium phase transition characterized by the vanishing dc Josephson
current.
In Chap. 4, we study a unidirectional particle transport in nonequilibrium steady states (NESSs)
of one-dimensional (1D) open fermionic systems subject to homogeneous dissipation, based on
the time-dependent generalized Gibbs ensemble (tGGE) approach discussed in Sec. 1.3.2. We
demonstrate both reciprocal and nonreciprocal dissipation can be used to induce nonreciprocal
transport in NESSs.
In Chap. 5, we study the NH XXZ spin chain by starting from an experimentally relevant twocomponent Bose-Hubbard model with two-body loss and applying a quantum trajectory method
to the Lindblad master equation. We derive correlation functions by using the effective field
theory, and obtain the energy spectrum in a finite system consistent with the finite-size scaling
formula generalized to NH Tomonaga-Luttinger (TL) liquids. Based on the NH density-matrix
renormalization group (DMRG) algorithm discussed in Sec. 1.3.3, we also report the numerical
demonstration of the analytically obtained results for the NH XXZ spin chain.
Finally, in Chap. 6, we conclude this thesis. ...