  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 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. Relating our fully
quantum calculation to a previous semi-classical approximation, we find that
the dynamics of the oscillator can be considered to a good approximation as
that of a particle tunneling in a classical double-well potential, despite the
fundamentally entangled nature of the joint system. We assess the prospects for
observation of oscillator tunneling in the context of nano- or micro-mechanical
experiments and find that it should be possible if suitably high coupling
strengths can be engineered.
