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.
Highlights
Time reversal is a basic symmetry that plays a crucial role in a vast variety of physical systems
We introduce a powerful, symmetry-based formulation of quantum detailed balance that goes beyond the simple definition in Ref. [2], and that directly enables an efficient way for finding nontrivial steady states
We introduce a new symmetry that can exist in driven-dissipative systems described by a Lindblad master equation: hidden time-reversal symmetry
Summary
Time reversal is a basic symmetry that plays a crucial role in a vast variety of physical systems. We show that the existence of hidden TRS directly yields a simple and direct method for analytically finding the steady-state density matrix of a Lindblad driven-dissipative quantum system This method is not limited to situations of weak driving, interactions, or dissipation. We explore in detail two classes of ubiquitous, experimentally accessible systems (see Table I): Rabidriven qubits subject to dissipation, and driven-dissipative nonlinear quantum cavities These systems exhibit, in general, no correlation-function time symmetry, and do not possess CQDB as defined in Ref. We wish to stress though that the basic notion of hidden TRS and connection to exact solutions we present is extremely general, going far beyond these simple examples We anticipate these ideas will have utility in the study of driven-dissipative many-body systems.
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