  We analytically investigate the ground-state properties of two-component
Bose-Einstein condensates with few &#8312;&#8311;Rb atoms inside a high-quality
cavity quantum electrodynamics. In the SU(2) representation for atom, this
quantum system can be realized a generalized Dicke model with a quadratic term
arising from the interatomic interactions, which can be controlled
experimentally by Feshbach resonance technique. Moreover, this weak
interspecies interaction can give rise to an important zero-temperature quantum
phase transition from the normal to the superradiant phases, where the atomic
ensemble in the normal phase is collectively unexcited while is macroscopically
excited with coherent radiations in the superradiant phase. Finally, we propose
to observe this predicted quantum phase transition by measuring the direct and
striking signatures of the photon field in terms of a heterodyne detector out
of the cavity.
