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 $\Xi$, $\Lambda$, 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 ($M\ne 0$). We have first- and second-order phase transitions, except for the $\mathsf{V}$ configuration, which only presents second-order phase transitions.

• Received 15 November 2012

DOI:https://doi.org/10.1103/PhysRevA.87.023805