Oscillator tunneling dynamics in the Rabi model

The familiar Rabi model, comprising a two-level system coupled to a quantum harmonic oscillator, continues to produce rich and surprising physics when the coupling strength becomes comparable to the individual subsystem frequencies. We construct approximate solutions for the eigenstates and energies in the regime in which the oscillator frequency is small compared to that of the two-level system and the coupling strength matches or exceeds the oscillator frequency. The resulting oscillator dynamics closely resembles that of a particle tunneling in a classical double-well potential. Relating our calculation to an earlier semiclassical approximation in which coupling to the two-level system creates an effective potential for the oscillator, we examine the extent to which this picture is valid. We find that, for certain parameter regimes, the interpretation of the oscillator dynamics in terms of tunneling holds to a good approximation despite the fundamentally entangled nature of the joint system. We assess the prospects for observation of oscillator tunneling in the context of nano- or micromechanical experiments and find that it should be possible if suitably high coupling strengths can be engineered.