  In this paper we analytically investigate the ground-state properties of a
two-dimensional polarized degenerate Fermi gas in a high-finesse optical
cavity, which is governed by a generalized Fermi-Dicke model with tunable
parameters. By solving the photon-number dependent Bogoliubov-de-Gennes
equation, we find rich quantum phases and phase diagrams, which depend
crucially on the fermion-photon coupling strength, the fermion-fermion
interaction strength, and the atomic resonant frequency (effective Zeeman
field). In particular, without the fermion-fermion interaction and with a weak
atomic resonant frequency, we find a mixed phase that the normal phase with two
Fermi surfaces and the superradiant phase coexist, and reveal a first-order
phase transition from this normal phase to the superradiant phase. With the
intermediate fermion-fermion interaction and fermion-photon coupling strengths,
we predict another mixed phase that the superfluid and superradiant phases
coexist. Finally, we address briefly how to detect these predicted quantum
phases and phase diagrams in experiments.
