Rotating wave approximation: systematic expansion and application to coupled spin pairs

TL;DR

This paper introduces a systematic expansion method for the effective Liouvillian of periodically driven quantum systems, extending the rotating wave approximation to coupled spin pairs and identifying regimes where higher-order effects are significant.

Contribution

It develops a formalism that maps time-dependent Liouvillian dynamics to a time-independent problem and extends the RWA to coupled two-level systems, highlighting regimes where higher-order terms matter.

Findings

Lowest order matches the rotating wave approximation

Identifies parameter regimes where higher orders are important

Provides a tool for analyzing echo experiments in tunneling systems

Abstract

We propose a new treatment of the dynamics of a periodically time-dependent Liouvillian by mapping it onto a time-independent problem and give a systematic expansion for its effective Liouvillian. In the case of a two-level system, the lowest order contribution is equivalent to the well-known rotating wave approximation. We extend the formalism to a pair of coupled two-level systems. For this pair, we find two Rabi frequencies and we can give parameter regimes where the leading order of the expansion is suppressed and higher orders become important. These results might help to investigate the interaction of tunneling systems in mixed crystals by providing a tool for the analysis of echo experiments.