Resonant symmetry lifting in a parametrically modulated oscillator

TL;DR

This paper investigates how a weak additional field influences switching rates and symmetry in a parametrically modulated oscillator with two vibrational states, revealing resonance effects and wave mixing phenomena.

Contribution

It introduces the concept of resonant symmetry lifting via a weak field and analyzes the frequency-dependent effects on switching activation energies in a parametrically modulated oscillator.

Findings

Weak field can significantly alter switching rates

Resonant peaks in activation energy change at specific frequencies

Wave mixing occurs when field frequency differs from half the modulation frequency

Abstract

We study a parametrically modulated oscillator that has two stable states of vibrations at half the modulation frequency $\omega_F$. Fluctuations of the oscillator lead to interstate switching. A comparatively weak additional field can strongly affect the switching rates, because it changes the switching activation energies. The change is linear in the field amplitude. When the additional field frequency $\omega_d$ is $\omega_F/2$, the field makes the populations of the vibrational states different thus lifting the states symmetry. If $\omega_d$ differs from $\omega_F/2$, the field modulates the state populations at the difference frequency, leading to fluctuation-mediated wave mixing. For an underdamped oscillator, the change of the activation energy displays characteristic resonant peaks as a function of frequency.