On the Dynamics of the Tavis-Cummings Model

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.

16 pages, 8 figures, IEEE Transactions on Automatic Control, to appear

References in corpus (8)

• Coupling Superconducting Qubits via a Cavity Bus
• Coherent quantum state storage and transfer between two phase qubits via a resonant cavity
• Dressed Collective Qubit States and the Tavis-Cummings Model in Circuit QED
• Input-Output Formalism For Few-Photon Transport in One-Dimensional Nanophotonic Waveguides Coupled to a Qubit
• Signatures of two-photon pulses from a quantum two-level system
• Storage and on-demand release of microwaves using superconducting resonators with tunable coupling
• Coherent control of single photon states
• Photon distribution function for propagation of two-photon pulses in waveguide-qubit systems

Cited by in corpus (4)

• Entangled Matter-waves for Quantum Enhanced Sensing
• Analytical solution of the disordered Tavis-Cummings model and its Fano resonances
• Quantum coherent and measurement feedback control based on atoms coupled with a semi-infinite waveguide
• Quantum coherent feedback control of an N-level atom with multiple excitations