Zero-temperature phase-flip rate in a biased parametric oscillator

TL;DR

This paper investigates how an extra bias affects phase-flip rates in a biased parametric oscillator, revealing conditions for state localization and implications for nonreciprocal quantum systems.

Contribution

Develops a semiclassical method to analyze switching rates in biased parametric oscillators, showing how bias influences state localization and phase trajectory topology.

Findings

Switching rate can be minimized at certain bias parameters.

Bias induces state localization by altering phase trajectory topology.

Results enable potential implementation of nonreciprocal quantum Ising systems.

Abstract

A parametrically driven oscillator has two stable vibrational states at half the modulation frequency. The states have opposite phase and equal amplitudes. An extra drive at half the modulation frequency provides an effective bias that lifts the state symmetry. Quantum fluctuations lead to switching between the states, i.e., to phase-flip transitions. We develop a semiclassical approach that allows us to find the dependence of the switching rates on the amplitude of the bias and the parameters of the modulating field. We find that the rate of switching from a ''shallow'' state can become anomalously small at certain parameter values, leading to an efficient localization in this state. This is a consequence of the change of the topology of the oscillator phase trajectories. The results pave the way for implementing nonreciprocal quantum Ising systems based on parametric oscillators.