Interaction-induced time-symmetry breaking in driven dissipative quantum systems

Periodically driven systems have discrete time-translation symmetry. This symmetry is broken if the expectation values of physical observables oscillate with a period which is a multiple of the period of the drive. In classical dissipative systems this effect is well-known for a parametric oscillator that will oscillate at half the drive frequency. In a quantum parametric oscillator, fluctuations lead to switching between the period-2 states and can wash out the period doubling on a comparatively short time scale. We consider an array of weakly-coupled quantum oscillators which are driven at a frequency close to twice or three times the oscillator eigenfrequency and can exhibit period doubling or period tripling, respectively. We determine the rate of interstate switching of each oscillator as a function of the coupling to the other oscillators. In the case of period doubling, the dynamics can be mapped onto a Ising spin-1/2 system. For the period-two state, disregarding spatial fluctuations, we show that the rate of switching for the whole ensemble is exponentially small in its size. For period tripling, the situation turns out to be more delicate. We also study spatially nonuniform states and explore possible experimental realizations.