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Communications in Theoretical Physics

Dynamics of Jaynes–Cummings Model in the Absence of Rotating-Wave Approximation

Fan Yun-Xia, Tao Liu, Feng Mang, Kelin Wang

Published May 1, 2007• 4 citations
Publisher

Abstract

The Jaynes-Cummings model (JCM) is studied in the absence of the rotating-wave approximation (RWA) by a coherent-state expansion technique. In comparison with the previous paper in which the coherent-state expansion was performed only to the third order, we carry out in this paper a complete expansion to demonstrate exactly the dynamics of the JCM without the RWA. Our study gives a systematic method to solve the non-RWA problem, which would be useful in various physical systems, e.g., in a system with an ultracold trapped ion experiencing the running waves of lasers.

DOI
10.1088/0253-6102/47/5/004

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The Jaynes-Cummings model (JCM) is studied in the absence of the rotating-wave approximation (RWA) by a coherent-state expansion technique. In comparison with the previous paper in which the coherent-state expansion was performed only to the third order, we carry out in this paper a complete expansion to demonstrate exactly the dynamics of the JCM without the RWA. Our study gives a systematic method to solve the non-RWA problem, which would be useful in various physical systems, e.g., in a system with an ultracold trapped ion experiencing the running waves of lasers.
Jaynes-Cummings 模型(JCM ) 被一种协调状态的扩大技术当 therotating 波浪近似(RWA ) 不在时学习。与协调状态的扩大仅仅在被执行到第三份订单的以前的纸比较，我们在这篇论文的供打包的酒菜没有 theRWA，确切表明 JCM 的动力学的完全的扩大。我们的学习给一个系统的方法解决 non-RWA 问题，它将在各种各样的 physicai 系统是有用的，例如，在有 uitracold 的一个系统，套住的离子经历跑激光飘动。
In this paper we define, in the context of dynamical algebras, a set of operators that are suitable for studying any relevant quantity related to the two-level Jaynes–Cummings model (JCM). We study the usual JCM with and without the rotating wave approximation (RWA), and then we add the presence of an external field. In this last case we find that in the strong driving regime there are significant differences between the results obtained with the RWA and without it. This holds even for the case in which the usual requirements for applying the RWA without an external driving are fulfilled.
This report presents an approach to the exact solutions of the time-dependent Jaynes-Cummings (J-C) model without the rotating wave approximation (RWA). It is shown that there is a squeezing-operator unitary transformation for relating the J-C model without RWA and the one with RWA. Thus by using an appropriate squeezing unitary transformation, the time-dependent J-C model without RWA can be transformed into the one with RWA that has been exactly solved previously, and based on this one can readily obtain the exact solutions of the time-dependent Jaynes-Cummings (J-C) model without RWA. The approach presented here also shows that we can treat these two kinds of time-dependent J-C models (both with and without RWA) in a unified way.