Exact solutions of many-body driven-dissipative systems using hidden time-reversal symmetry

Recent work has shown that the ability to analytically solve for the steady state of several  canonical quantum optics models (e.g. a driven-damped nonlinear bosonic mode [1]) is related to a surprising “hidden time reversal symmetry” [2].  These previous solutions were limited to systems with at most one or two modes.  Here, we show that the same approach can be used to derive analytic descriptions of truly many-body driven dissipative models, including variants of coherently driven Bose-Hubbard models subject to Markovian dissipation. These models were not previously known to be solvable. Our exact solutions let one transcend the limitations of standard approximation methods such as Gurtzwiller mean-field theory or semiclassical approximations, and reveal a wealth of new physical phenomena, including new subtle kinds of pairing correlations.  The models we describe are directly relevant to a number of experimental platforms, in particular realizations using superconducting circuits [3].

[1] Drummond, P., Walls, D., Quantum theory of optical bistability. I. Nonlinear polarisability model. J. Phys. A: Math. Gen. 13 725 (1980)

[2] Roberts, D., Lingenfelter, A., Clerk, A., Hidden Time-Reversal Symmetry, Quantum Detailed Balance and Exact Solutions of Driven-Dissipative Quantum Systems PRX Quantum 2, 020336 (2021)

[3] Ma, R., Saxberg, B., Owens, C. et al. A dissipatively stabilized Mott insulator of photons. Nature 566, 51–57 (2019).