Polarization in a three-dimensional Fermi gas with Rabi coupling

We investigate the polarization of a two-component three-dimensional fermionic gas made of repulsive alkali-metal atoms. The two pseudo-spin components correspond to two hyperfine states which are Rabi coupled. The presence of Rabi coupling implies that only the total number of atoms is conserved and a quantum phase transition between states dominated by spin-polarization along different axses is possible. By using a variational Hartree-Fock scheme we calculate analytically the ground-state energy of the system and determine analytically and numerically the conditions under which there is this quantum phase transition. This scheme includes the well-known criterion for the Stoner instability. The obtained phase diagram clearly shows that the polarized phase crucially depends on the interplay among the Rabi coupling energy, the interaction energy per particle, and the kinetic energy per particle.