Resonant symmetry lifting in a parametrically modulated oscillator

Abstract

We study a parametrically modulated oscillator that has two stable states of vibrations at half the modulation frequency $ω_F$. 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 $ω_d$ is $ω_F/2$, the field makes the populations of the vibrational states different thus lifting the states symmetry. If $ω_d$ differs from $ω_F/2$, 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.