1305.7188 (S. Cordero et al.)

Semi-classical vs. quantum description of the ground state of
three-level atoms interacting with a one-mode electromagnetic field    [PDF]

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

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 are determined explicitly for each of the configurations $\Xi$, $\Lambda$ and $V$, with and without detuning. There are first- and second-order transitions for the $\Xi$ configuration, depending on the detuning the $\Lambda$ configuration presents first- and/or second-order transitions, and there are only second-order transitions for the $V$ configuration. In all cases, the ground state of the collective regime obeys sub-Poissonian statistics for the total number of excitations ${\cal M}$ and the photon number $n$ distribution functions. The semi-classical and exact quantum calculations for both the expectation values of $\bm{M}$ and $\bm{n}$ have an excellent correspondence as functions of the control parameters. That is not the case, however, for the fluctuation in the number of photons, but this can be achieved by projecting the variational state to a definite value of ${\cal M}$.

View original: http://arxiv.org/abs/1305.7188