On the Dynamics of the Tavis-Cummings Model

• Published in: IEEE transactions on automatic control 2023-04, Vol.68 (4), p.2048-2063
• Main Authors: Dong, Zhiyuan, Zhang, Guofeng, Wu, Ai-Guo, Wu, Re-Bing
• Format: Article
• Language: English
• Subjects: Analytical models; Canonical forms; Cavity resonators; Couplings; Excitation; Indium tin oxide; Linear systems; Mathematical analysis; Mathematical models; Open quantum systems; quantum control; Quantum system; Systems theory; Tavis–Cummings model; two-level systems (TLSs); Vacuum systems
• ISSN: 0018-9286; 1558-2523
• DOI: 10.1109/TAC.2022.3169582

The purpose of this article 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 noninteracting 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 multiexcitation 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 multiexcitation case.