Dynamics of a two-level system coupled to a quantum oscillator: Transformed rotating-wave approximation

TL;DR

This paper introduces the transformed rotating-wave approximation, an analytical method for studying two-level systems coupled to quantum oscillators, effectively accounting for counter-rotating terms and matching numerical results in certain regimes.

Contribution

The paper presents a simplified analytical approach that includes counter-rotating effects while maintaining mathematical simplicity, extending the rotating-wave approximation.

Findings

Accurately calculates energy levels and quantum dynamics.

Shows good agreement with exact numerical results for weak and intermediate coupling.

Provides a versatile method applicable to more complex systems.

Abstract

For studying the dynamics of a two-level system coupled to a quantum oscillator we have presented an analytical approach, the transformed rotating-wave approximation, which takes into account the effect of the counter-rotating terms but still keeps the simple mathematical structure of the ordinary rotating-wave approximation. We have calculated the energy levels of ground and lower-lying excited states, as well as the time-dependent quantum dynamics. It is obvious that the approach is quite simple and can be easily extended to more complicated situation. Besides, the results are compared with the numerically exact ones to show that for weak and intermediate coupling and moderate detuning our analytic calculations are quantitatively in good agreement with the exact ones.