Hidden Time-Reversal Symmetry, Quantum Detailed Balance, and Exact Solutions of Open Quantum Systems

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 apply our methods to quantum many-body systems, and discover an exact solution to several new models, including a kind of many-body parametric oscillator model, as well as the infinite-range limit of the dissipative transverse-field Ising model.