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arXiv:0806.4167

Useful transformations: from ion-laser interactions to master equations

Raúl Juárez-Amaro, J. M. Vargas-Martínez, H. M. Moya-Cessa

Published Jun 25, 2008• 0 citations
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Abstract

We show set of transformations which allow to obtain analytic solutions in several quantum-optical problems. We start with the ion-laser (time dependent) interaction, continue with the problem of a slow atom interacting with a quantized field to end with a master equation that describes losses. In all cases it is shown that one may find useful transformations that simplify the problems.

DOI
10.48550/arxiv.0806.4167

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We show set of transformations which allow to obtain analytic solutions in several quantum-optical problems. We start with the ion-laser (time dependent) interaction, continue with the problem of a slow atom interacting with a quantized field to end with a master equation that describes losses. In all cases it is shown that one may find useful transformations that simplify the problems.
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The interaction of a propagating pulse of quantum radiation with a localized quantum system can be described by a cascaded master equation with a distinct initially populated input and a finally populated output field mode [Kiilerich and M\o{}lmer, Phys. Rev. Lett. 123, 123604 (2019)]. By transformation to an appropriate interaction picture, we break the cascaded nature of the master equation and recover an effective time-dependent interaction with a lossless single mode and a supplementary lossy mode. The former closely represents the traveling pulse, while the latter constitutes a non-Markovian component in the exchange of quanta between the scatterer and the quantized field. The transformed master equation offers important insights into the system dynamics, and it permits numerically efficient solutions.
The basic tool in quantum optics for the description of atomic systems interacting with coherent and incoherent radiation fields is the atomic density matrix governed by the master equation. In the present paper we apply standard condensed-matter nonequilibrium many-body methods to the problem of a two-level atom driven by an external laser field and relaxing by interaction with the radiation field. We recover the well-known dressed-atom picture and, in particular, we present an alternative derivation of the master equation for the atomic density matrix which allows simple generalizations.
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