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We investigate a resonantly modulated harmonic mode, dispersively coupled toa nonequilibrium few-level quantum system. We focus on the regime where therelaxation rate of the system greatly exceeds that of the mode, and develop aquantum adiabatic approach for analyzing the dynamics. Semiclassically, thedispersive coupling leads to a mutual tuning of the mode and system into andout of resonance with their modulating fields, leading to multistability. Inthe important case where the system has two energy levels and is excited nearresonance, the compound system can have up to three metastable states.Nonadiabatic quantum fluctuations associated with spontaneous transitions inthe few-level system lead to switching between the metastable states. Weprovide parameter estimates for currently available systems.

Vibration multistability and quantum switching for dispersive coupling