Resonant-force induced symmetry breaking in a quantum parametric oscillator

TL;DR

This paper investigates how an external force can induce symmetry breaking in a quantum parametric oscillator, significantly affecting state transition rates due to quantum fluctuations and thermal bath interactions.

Contribution

It introduces a detailed analysis of symmetry breaking caused by external forces in quantum oscillators, including the effect on transition rates near bifurcation points.

Findings

Force causes exponential change in switching rates between vibrational states.

Quantum fluctuations and thermal bath interactions amplify the symmetry-breaking effect.

Analysis includes limiting cases and prebifurcation regime.

Abstract

A parametrically modulated oscillator has two opposite-phase vibrational states at half the modulation frequency. An extra force at the vibration frequency breaks the symmetry of the states. The effect can be extremely strong due to the interplay between the force and the quantum fluctuations resulting from the coupling of the oscillator to a thermal bath. The force changes the rates of the fluctuation-induced walk over the quantum states of the oscillator. If the number of the states is large, the effect accumulates to an exponentially large factor in the rate of switching between the vibrational states. We find the factor and analyze it in the limiting cases including the prebifurcation regime where the system is close but not too close to the bifurcation point.