Hidden time-reversal symmetry, quantum detailed balance and exactly-solvable driven-dissipative quantum systems*

Driven-dissipative quantum systems generically do not satisfy simple notions of detailed balance based on microscopic reversibility. We show that such systems can nonetheless have one or more hidden time-reversal symmetries, a concept that we define in terms of correlation functions and thermofield double states. We demonstrate that the presence of hidden symmetry directly leads to an extremely efficient method for analytically solving for steady states of the dynamics, even if such states are non-trivial. This represents a generalization of the so-called coherent quantum absorber method [1, 2]. We discuss how hidden TRS is relevant to a variety of driven qubit and nonlinear cavity models, and how this symmetry has simple, experimentally-observable consequences. We also discuss how this symmetry underlies somewhat opaque exact solution techniques in quantum optics that are based on phase space methods (i.e. the complex-P representation).

[1] K. Stannigel, P. Rabl, and P. Zoller, New J. Phys. 14, 063014 (2012).
[2] D. Roberts and A. Clerk, Phys. Rev. X 10 021022 (2020)