Polychromatic phase diagram for $n$-level atoms interacting with $\ell$ modes of electromagnetic field

Abstract

A system of $N_a$ atoms of $n$-levels interacting dipolarly with $\ell$ modes of electromagnetic field is considered. The energy surface of the system is constructed from the direct product of the coherent states of U$(n)$ in the totally symmetric representation for the matter times the $\ell$ coherent states of the electromagnetic field. A variational analysis shows that the collective region is divided into $\ell$ 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 $3$-level atoms in the $\Xi$-configuration in the presence of $2$ modes, the variational calculation is compared with the exact quantum solution showing that both are in agreement.

16 pages, 9 figures

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• Information diagrams in the study of entanglement in symmetric multi-quDit systems and applications to quantum phase transitions in Lipkin-Meshkov-Glick D-level atom models
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• Quantum phase transition of two-level atoms interacting with a finite radiation field
• Effect of the Atomic Dipole-Dipole Interaction on the Phase Diagrams of Field-Matter Interactions I: Variational procedure
• Entanglement and U(D)-spin squeezing in symmetric multi-quDit systems and applications to quantum phase transitions in Lipkin-Meshkov-Glick D-level atom models
• Lieb-Mattis ordering theorem of electronic energy levels in the thermodynamic limit