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arXiv · 1305.7188

A semi-classical versus quantum description of the ground state of three-level atoms interacting with a one-mode electromagnetic field

S. Cordero·O. Castaños·R. López-Peña·E. Nahmad-Achar
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Abstract

We consider $N_a$ three-level atoms (or systems) interacting with a one-mode electromagnetic field in the dipolar and rotating wave approximations. The order of the quantum phase transitions is determined explicitly for each of the configurations $Ξ$, $Λ$ and $V$, with and without detuning. The semi-classical and exact quantum calculations for both the expectation values of the total number of excitations $\cal{M}=\langle \bm{M} \rangle$ and photon number $n=\langle \bm{n} \rangle$ have an excellent correspondence as functions of the control parameters. We prove that the ground state of the collective regime obeys sub-Poissonian statistics for the ${\cal M}$ and $n$ distribution functions. Therefore, their corresponding fluctuations are not well described by the semiclassical approximation. We show that this can be corrected by projecting the variational state to a definite value of ${\cal M}$.

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S. Cordero, O. Castaños, R. López-Peña, E. Nahmad-Achar. 2013-11-28. A semi-classical versus quantum description of the ground state of three-level atoms interacting with a one-mode electromagnetic field. https://doi.org/10.1088/1751-8113/46/50/505302

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