  Recent experiments on quantum behavior in microfabricated solid-state systems
suggest tantalizing connections to quantum optics. Several of these experiments
address the prototypical problem of cavity quantum electrodynamics: a two-level
system coupled to a quantum harmonic oscillator. Such devices may allow the
exploration of parameter regimes outside the near-resonance and weak-coupling
assumptions of the ubiquitous rotating-wave approximation (RWA), necessitating
other theoretical approaches. One such approach is an adiabatic approximation
in the limit that the oscillator frequency is much larger than the
characteristic frequency of the two-level system. A derivation of the
approximation is presented and the time evolution of the two-level-system
occupation probability is calculated using both thermal- and coherent-state
initial conditions for the oscillator. Closed-form evaluation of the time
evolution in the weak-coupling limit provides insight into the differences
between the thermal- and coherent-state models. Finally, potential experimental
observations in solid-state systems, particularly the Cooper-pair
box--nanomechanical resonator system, are discussed and found to be promising.
