  The existence of bistability in quantum optical systems remains a intensely
debated open question beyond the mean-field approximation. Quantum fluctuations
are finite-size corrections to the mean-field approximation used because the
full exact solution is unobtainable. Usually, quantum fluctuations destroy the
bistability present on the mean-field level. Here, by identifying and using
exact modulated semi-local dynamical symmetries in a certain quantum optical
models of driven-dissipative fermionic chains we exactly prove bistability in
precisely the quantum fluctuations. Surprisingly, rather than destroying
bistability, the quantum fluctuations themselves exhibit bistability, even
though it is absent on the mean-field level for our systems. Moreover, the
models studied acquire additional thermodynamic dynamical symmetries that imply
persistent periodic oscillations in the quantum fluctuations, constituting
pseudo-variants of boundary time crystals. Physically, these emergent operators
correspond to finite-frequency and finite-momentum semi-local Goldstone modes.
Our work therefore provides to the best of our knowledge the first example of a
provably bistable quantum optical system.
