Eur. Phys. J. B 9, 207-214 (1999)
https://doi.org/10.1007/s100510050758

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

¹ Institut für Theoretische Physik, Universität Heidelberg, Philosophenweg 19, 69120 Heidelberg, Germany
² Service de Physique de l'État Condensé, CEA Saclay, Orme des Merisiers, 91191 Gif-sur-Yvette Cedex, France

Received: 2 September 1998
Published online: 15 May 1999

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.