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We investigate the polarization of a two-component three-dimensionalfermionic gas made of repulsive alkali-metal atoms. The two pseudo-spincomponents correspond to two hyperfine states which are Rabi coupled. Thepresence of Rabi coupling implies that only the total number of atoms isconserved and a quantum phase transition between states dominated byspin-polarization along different axses is possible. By using a variationalHartree-Fock scheme we calculate analytically the ground-state energy of thesystem and determine analytically and numerically the conditions under whichthere is this quantum phase transition. This scheme includes the well-knowncriterion for the Stoner instability. The obtained phase diagram clearly showsthat the polarized phase crucially depends on the interplay among the Rabicoupling energy, the interaction energy per particle, and the kinetic energyper particle.

Polarization in a three-dimensional Fermi gas with Rabi coupling