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.Comment: 16 pages, 11 figures; revised abstract; some text revisions; added two figures and combined others; added references. Submitted to Phys. Rev.
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