Variational Study of $\lambda$- and $N$-Atomic Configurations   Interacting with an Electromagnetic Field of $2$ Modes
  A study of the $\lambda$- and $N$-atomic configurations under dipolar interaction with $2$ modes of electromagnetic radiation is presented. The corresponding quantum phase diagrams are obtained by means of a variational procedure. Both configurations exhibit normal and collective (super-radiant) regimes. While the latter in the $\lambda$-configuration divides itself into $2$ subregions, corresponding to each of the modes, that in the $N$-configuration may be divided into $2$ or $3$ subregions depending on whether the field modes divide the atomic system into $2$ separate subsystems or not.   Our variational procedure compares well with the exact quantum solution. The properties of the relevant field and matter observables are obtained. 
S. Cordero, O. Casta\~nos, R. L\'opez-Pe\~na and E. Nahmad-Achar
quant-ph