Exact bistability and time pseudo-crystallization of driven-dissipative fermionic lattices

TL;DR

This paper proves that quantum fluctuations in driven-dissipative fermionic lattices can exhibit bistability and persistent oscillations, challenging the traditional view that fluctuations destroy mean-field bistability.

Contribution

It introduces exact dynamical symmetries that demonstrate bistability and pseudo-time-crystal behavior in quantum optical models, providing the first provably bistable quantum optical system.

Findings

Quantum fluctuations can exhibit bistability.

Emergence of persistent periodic oscillations in quantum fluctuations.

Identification of semi-local dynamical symmetries in fermionic chains.

Abstract

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.