Phase-flip rates in a biased quantum parametric oscillator

Parametrically modulated oscillators are attracting much interest in different fields in particular in quantum information. The interest stems from the oscillators having two stable states with opposite phases, which can be used as Schrödinger cat states. A central problem is the rate of switching between the states. Switching may occur via tunnelling or via transitions over the effective barrier that separates the states in phase space. Overbarrier transitions result from the coupling to a thermal reservoir and are reminiscent of activated transitions over a potential barrier, except that they can come from quantum fluctuations and occur even for zero temperature.

A natural way to control parametrically excited vibrations is to break their symmetry. This can be accomplished by applying an extra drive at half the modulation frequency. We show that even a comparatively weak drive can change the rates of overbarrier transitions exponentially strongly. The rates become different for the two phase-states, and we find their dependence on the oscillator parameters. The rates also depend strongly on temperature. Remarkably, for zero temperature they can become equal to zero at certain parameter values. The results pave the way for implementing quantum Ising systems based on parametric oscillators, including nonreciprocal Ising systems.