Hidden time-reversal symmetry, quantum detailed balance and exact solutions of driven-dissipative quantum systems

• URL: http://arxiv.org/abs/2011.02148v1
• Date: Wed, 4 Nov 2020 06:21:44 GMT
• Title: Hidden time-reversal symmetry, quantum detailed balance and exact solutions of driven-dissipative quantum systems
• Authors: David Roberts, Andrew Lingenfelter, Aashish Clerk
• Abstract summary: Driven-dissipative quantum systems generically do not satisfy simple notions of detailed balance based on the time symmetry of correlation functions. We show that such systems can nonetheless exhibit a hidden time-reversal symmetry which most directly manifests itself in a doubled version of the original system. This hidden time-reversal symmetry has a direct operational utility: it provides a general method for finding exact solutions of non-trivial steady states.
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• License: http://creativecommons.org/licenses/by-sa/4.0/
• Abstract: Driven-dissipative quantum systems generically do not satisfy simple notions of detailed balance based on the time symmetry of correlation functions. We show that such systems can nonetheless exhibit a hidden time-reversal symmetry which most directly manifests itself in a doubled version of the original system prepared in an appropriate entangled thermofield double state. This hidden time-reversal symmetry has a direct operational utility: it provides a general method for finding exact solutions of non-trivial steady states. Special cases of this approach include the coherent quantum absorber and complex-$P$ function methods from quantum optics. We also show that hidden TRS has observable consequences even in single-system experiments, and can be broken by the non-trivial combination of nonlinearity, thermal fluctuations, and driving. To illustrate our ideas, we analyze concrete examples of driven qubits and nonlinear cavities. These systems exhibit hidden time-reversal symmetry but not conventional detailed balance.

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