Resonant symmetry lifting in a parametrically modulated oscillator.

We study a parametrically modulated oscillator that has two stable states of vibration 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.