Emergent Finite Frequency Criticality of Driven-Dissipative Correlated Lattice Bosons

TL;DR

This paper introduces a new type of dynamical phase transition in driven-dissipative quantum lattice bosons, characterized by finite-frequency susceptibility divergence and non-stationary order parameters, relevant for non-equilibrium quantum systems.

Contribution

It reveals a novel class of non-equilibrium phase transitions with finite-frequency criticality and oscillating order parameters, expanding understanding beyond equilibrium static phase transitions.

Findings

Finite-frequency susceptibility divergence at criticality

Emergence of non-stationary, oscillating order parameters

Relevance to circuit QED arrays and non-equilibrium quantum phenomena

Abstract

Critical points and phase transitions are characterized by diverging susceptibilities, reflecting the tendency of the system toward spontaneous symmetry breaking. Equilibrium statistical mechanics bounds these instabilities to occur at zero frequency, giving rise to static order parameters. In this work we introduce a new class of dynamical transitions in a quantum many body system far from thermal equilibrium, characterized by a susceptibility diverging at a finite non-zero frequency, an emerging scale set by interactions and non-equilibrium effects. In the broken-symmetry phase the corresponding macroscopic order parameter becomes non-stationary and oscillates in time without damping, thus breaking continuous time-translational symmetry. Our results, obtained for a paradigmatic model of bosons interacting on lattice in prensence of drive and dissipation, are relevant for the upcoming generation of circuit QED arrays experiments and outline a generic framework to study time-domain instabilities in non-equilibrium quantum systems, including Floquet time crystals and quantum synchronization.