(a) Top panel: Sketch of the modulation (dotted line) and the additive extra force (red solid line). Lower panel: Sketch of the vibrating coordinate for the two vibrational states of the oscillator for no extra force (dotted line), the vibrations with the phase close to the phase of the extra force (light blue line), and the vibrations in the counterphase with the force (dark blue line). (b) The cross-section of the scaled Hamiltonian function of the oscillator in the rotating frame g(Q, P) as a function of the quadrature Q for P = 0. For no extra force g(Q, P) is symmetric, g(Q, P) = g(−Q, −P) (dotted line). The extra force breaks the symmetry, making one well of g(Q, P) deeper and the other well shallower (magenta line).

Resonant-force-induced symmetry breaking in a quantum parametric oscillator

A parametrically modulated oscillator has two opposite-phase vibrational states at half the modulation frequency. An extra force at the vibration frequency breaks the symmetry of the states. The effect can be extremely strong due to the interplay between the force and the quantum fluctuations resulting from the coupling of the oscillator to a thermal bath. The force changes the rates of the fluctuation-induced walk over the quantum states of the oscillator. If the number of the states is large, then the effect accumulates to an exponentially large factor in the rate of switching between the vibrational states. We find the factor and analyze it in the limiting cases, including the prebifurcation regime where the system is close but not too close to the bifurcation point.

D. K. J. Boneß, W. Belzig and M. I. Dykman
Phys. Rev. Res. 6, 033240 (2024)