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An algebraic approach to the Tavis-Cummings problem

Ilya P. Vadeiko·Georgii P. Miroshnichenko·Andrei V. Rybin·Jussi Timonen
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Abstract

An algebraic method is introduced for an analytical solution of the eigenvalue problem of the Tavis-Cummings (TC) Hamiltonian, based on polynomially deformed su(2), i.e. su_n(2), algebras. In this method the eigenvalue problem is solved in terms of a specific perturbation theory, developed here up to third order. Generalization to the N-atom case of the Rabi frequency and dressed states is also provided. A remarkable enhancement of spontaneous emission of N atoms in a resonator is found to result from collective effects.

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Ilya P. Vadeiko, Georgii P. Miroshnichenko, Andrei V. Rybin, Jussi Timonen. 2002-08-26. An algebraic approach to the Tavis-Cummings problem. https://doi.org/10.1103/physreva.67.053808

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