Interaction-induced time-symmetry breaking in driven quantum oscillators

TL;DR

This paper investigates how weak interactions in driven quantum oscillators can lead to spontaneous breaking of time-translation symmetry, revealing quantum phase transitions and connections to spin systems and Brownian particles.

Contribution

It introduces a comprehensive analysis of interaction-induced time-symmetry breaking in driven quantum oscillators, including quantum phase transitions and mappings to spin and Brownian particle models.

Findings

Weak coupling causes oscillators to exhibit many-body states with broken time-translation symmetry.

The stationary state can be mapped onto an Ising model with an effective temperature proportional to .

Near bifurcation points, the system maps onto coupled overdamped Brownian particles.

Abstract

We study parametrically driven quantum oscillators and show that, even for weak coupling between the oscillators, they can exhibit various many-body states with broken time-translation symmetry. In the quantum-coherent regime, the symmetry breaking occurs via a nonequilibrium quantum phase transition. For dissipative oscillators, the main effect of the weak coupling is to make the switching rate of an oscillator between its period-2 states dependent on the states of other oscillators. This allows mapping the oscillators onto a system of coupled spins. Away from the bifurcation parameter values where the period-2 states emerge, the stationary state corresponds to having a microscopic current in the spin system, in the presence of disorder. In the vicinity of the bifurcation point or for identical oscillators, the stationary state can be mapped on that of the Ising model with an effective temperature $\propto \hbar$, for low temperature. Closer to the bifurcation point the coupling can not be considered weak and the system maps onto coupled overdamped Brownian particles performing quantum diffusion in a potential landscape.