Dynamics of a two-level system strongly coupled to a high-frequency quantum oscillator

TL;DR

This paper explores the dynamics of a two-level quantum system strongly coupled to a high-frequency oscillator, using an adiabatic approximation to analyze behavior beyond the weak-coupling regime, with implications for solid-state quantum experiments.

Contribution

It introduces a derivation of an adiabatic approximation for a two-level system coupled to a high-frequency oscillator and analyzes its time evolution under different initial conditions.

Findings

Adiabatic approximation effectively describes the system dynamics.

Differences observed between thermal and coherent initial states.

Potential for experimental observation in solid-state systems.

Abstract

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.