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Journal of Physics Conference Series

Couplingn-level Atoms withl-modes of Quantised Light in a Resonator

Octavio Castaños, Sergio Cordero, Eduardo Nahmad-Achar, Ramón López–Peña

Published Mar 1, 2016• 2 citations
Publisher

Abstract

We study the quantum phase transitions associated to the Hamiltonian of a system of n -level atoms interacting with l modes of electromagnetic radiation in a resonator. The quantum phase diagrams are determined in analytic form by means of a variational procedure where the test function is constructed in terms of a tensorial product of coherent states describing the matter and the radiation field. We demonstrate that the system can be reduced to a set of Dicke models.

DOI
10.1088/1742-6596/698/1/012006

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A system of Na{N}_{a}Na​ atoms of nnn levels interacting dipolarly with $\ensuremath{\ell}$ modes of an electromagnetic field is considered. The energy surface of the system is constructed from the direct product of the coherent states of U(n)\mathrm{U}(n)U(n) in the totally symmetric representation for the matter times the $\ensuremath{\ell}$ coherent states of the electromagnetic field. A variational analysis shows that the collective region is divided into $\ensuremath{\ell}$ zones, inside each of which only one mode of the electromagnetic field contributes to the ground state. In consequence, the polychromatic phase diagram for the ground state naturally divides itself into monochromatic regions. For the case of three-level atoms in the $\mathrm{\ensuremath{\Xi}}$ configuration in the presence of two modes, the variational calculation is compared with the exact quantum solution showing that both are in agreement.
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