On the Dynamics of the Tavis-Cummings Model

Zhiyuan Dong, Guofeng Zhang, Ai Guo Wu, Re Bing Wu

Research output: Journal article publicationJournal articleAcademic researchpeer-review

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 <formula><tex>$\sqrt{N}$</tex></formula>- 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.

Original languageEnglish
Pages (from-to)1-15
Number of pages15
JournalIEEE Transactions on Automatic Control
DOIs
Publication statusE-pub ahead of print - 26 Apr 2022

Keywords

  • Analytical models
  • Couplings
  • Indium tin oxide
  • Linear systems
  • Mathematical models
  • open quantum systems
  • Quantum control
  • Quantum system
  • Tavis-Cummings model
  • twolevel systems
  • Vacuum systems

ASJC Scopus subject areas

  • Control and Systems Engineering
  • Computer Science Applications
  • Electrical and Electronic Engineering

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