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Acknowledgements

We are grateful to M. Devoret for valuable discussions. This work was supported by Japan Society for the Promotion of Science (JSPS) Grants-in-Aid for Scientific Research (KAKENHI) (No. JP19H01831 and JP19K03693),

Japan Science and Technology Agency (JST) Precursory Research for Embryonic Science and Technology

(PRESTO) (Grant No. JPMJPR1767), JST Core Research for Evolutionary Science and Technology (CREST)

(Grant No. JPMJCR1775), and MEXT Quantum Leap Flagship Program (MEXT Q-LEAP) Grant Number

JPMXS0120319794.

Author contributions

F.Y. conceived the main idea of the paper. F.Y., S.A., and M.B. constructed equations of the paper. F.Y., S.A., T.F.,

and M.B. conducted numerical calculations. F.Y. wrote the manuscript with feedback from all authors. F.Y. and

K.S. supervised the project.

Competing interests The authors declare no competing interests.

Additional information

Supplementary Information The online version contains supplementary material available at https://​doi.​org/​

10.​1038/​s41598-​022-​10203-1.

Correspondence and requests for materials should be addressed to F.Y.

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