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 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 d is F/2, the field makes the populations of the vibrational states different, thus lifting the states symmetry. If d differs from 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.