  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.

Quantum Physics