On the Dynamics of the Tavis-Cummings Model

• URL: http://arxiv.org/abs/2110.14174v2
• Date: Mon, 9 May 2022 05:27:03 GMT
• Title: On the Dynamics of the Tavis-Cummings Model
• Authors: Zhiyuan Dong, Guofeng Zhang, Ai-Guo Wu, and Re-Bing Wu
• Abstract summary: This paper presents a comprehensive study of the Tavis-Cummings model from a system-theoretic perspective. A typical form of the Tavis-Cummings model is composed of an ensemble of non-interacting two-level systems. The passivity of this linear system is related to the vacuum Rabi mode splitting phenomenon.
• Score: 1.951894384472803
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: The purpose of this paper is to present a comprehensive study of the Tavis-Cummings model from a system-theoretic perspective. A typical form of the Tavis-Cummings model is composed of an ensemble of non-interacting two-level systems (TLSs) that are collectively coupled to a common cavity resonator. The associated quantum linear passive system is proposed, whose canonical form reveals typical features of the Tavis-Cummings model, including $\sqrt{N}$- scaling, dark states, bright states, single-excitation superradiant and subradiant states. The passivity of this linear system is related to the vacuum Rabi mode splitting phenomenon in Tavis-Cummings systems. On the basis of the linear model, an analytic form is presented for the steady-state output state of the Tavis-Cummings model driven by a single-photon state. Master equations are used to study the excitation properties of the Tavis-Cummings model in the multi-excitation scenario. Finally, in terms of the transition matrix for a linear time-varying system, a computational framework is proposed for calculating the state of the Tavis-Cummings model, which is applicable to the multi-excitation case.

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