arXiv:1803.03129 · Physical Review A

Quantum phases of a three-level matter-radiation interaction model using SU(3) coherent states with different cooperation numbers

Luis Fernando Quezada, Eduardo Nahmad-Achar

Published Jun 11, 2018• 5 citations

Abstract

We use coherent states as trial states for a variational approach to study a system of a finite number of three-level atoms interacting in a dipolar approximation with a one-mode electromagnetic field. The atoms are treated as semidistinguishable using different cooperation numbers and representations of SU(3). We focus our analysis on the quantum phases of the system as well as the behavior of the most relevant observables near the phase transitions. The results are computed for all three possible configurations ($\mathrm{\ensuremath{\Xi}}, \mathrm{\ensuremath{\Lambda}}$, and $V$) of the three-level atoms.

DOI: 10.1103/physreva.97.063819

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arXiv:1803.03129 · Physical Review A

Quantum phases of a three-level matter-radiation interaction model using SU(3) coherent states with different cooperation numbers

Luis Fernando Quezada, Eduardo Nahmad-Achar

Published Jun 11, 2018• 5 citations

arXiv HTML PDF

Abstract

\mathrm{\ensuremath{\Xi}}, \mathrm{\ensuremath{\Lambda}}

, and

V

) of the three-level atoms.

DOI: 10.1103/physreva.97.063819

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\mathrm{\ensuremath{\Xi}}, \mathrm{\ensuremath{\Lambda}}

, and

V

) of the three-level atoms.

We apply the energy surface method to study a system of

{N}_{a}

three-level atoms interacting with a one-mode radiation field in the $\ensuremath{\Xi}$, $\ensuremath{\Lambda}$, and

\mathsf{V}

configurations. We obtain an estimation of the ground-state energy, the expectation value of the total number of excitations, and the phase diagram of the model in the interaction parameter space and compare the results with the exact solutions. The phase diagram separates the behavior of, in general, a dominant single state without excitations (

M=0

) from a collective state with excitations ($M\ensuremath{\ne}0$). We have first- and second-order phase transitions, except for the

\mathsf{V}

configuration, which only presents second-order phase transitions.

A system of

{N}_{a}

atoms of

n

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

\mathrm{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.