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 ${\omega }_F$. 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.

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