Perturbative Expansion for Coherence Loss

Abstract

We construct a generally applicable short-time perturbative expansion for coherence loss. Successive terms of this expansion yield characteristic times for decorrelation processes involving successive powers of the Hamiltonian. The second order results are sufficient to precisely reproduce expressions for "decoherence times" obtained in the literature by much more involved and indirect methods. Examples illustrating the influence of initial conditions and the need to evaluate higher order terms are given in the context of the Jaynes-Cummings model. It is shown that, in this case, the short-time decoherence behavior can probe the importance of antiresonant contributions. [S0031-9007(96)00590-X] PACS numbers: 03.65.Db, 05.45.+bThe study of open quantum systems and/or subsystems has recently attracted the attention of physicists from very different areas: cosmology [1], condensed matter [2], quantum optics [3], particle physics [4], as well as of theorists working on the fundamentals of the quantum measurement process [5]. The problem can be stated very generally by considering several interacting subsystems and asking for the looks of the effective dynamics of one such subsystem. Generic, exact answers within the standard framework of quantum mechanics have been given before [6]. Recent experimental developments [7] as well as the analysis of models related to them [8] now indicate, however, that the specific knowledge of the (often very short) time scale for the onset of decoherence processes may be of considerable value. In order to meet such demand we develop here a short-time perturbative scheme to extract decorrelation time scales from the in general highly nonlinear effective dynamics of open quantum subsystems. Our results are generally applicable to situations in which the subsystem of interest appears as part of a larger, closed Hamiltonian system. They are based on a hierarchical analysis of the short-time dynamics of intersubsystem correlation processes which bears a strong resemblance in spirit to ordinary timedependent perturbation expansions.We consider the general case of a dynamically closed (i.e., autonomous) quantum system which is described as being composed of two interacting subsystems, so that the full Hamiltonian is written as a sum of three termsthe last of which represents the interaction between the subsystems, while H 0 describes their bare dynamics. Note that no a priori limitation is being imposed on the nature or complexity of the subsystems. In particular, all current models involving quantum systems coupled to dynamically implemented reservoirs (e.g., [9]) fit into the above characterization, the same being true all the way to 0031-9007͞96͞77(2)͞207(4)$10.00

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