Polarized Rabi-coupled and spinor boson droplets

Self-bound quantum droplets form when the mean-field tendency of the gas to collapse is stabilized by the effectively repulsive beyond-mean-field fluctuations. The beyond-mean-field effects depend on Rabi frequency omega R and quadratic Zeeman effect q for the Rabi-coupled Bose mixtures and the spinor gases, respectively. For a quantum droplet, the effects of varying omega R and q have recently been examined only for unpolarized Rabi-coupled Bose mixtures and unpolarized spinor gases. In this paper, we theoretically explore the stability of the droplet phase for polarized Rabi-coupled Bose mixtures and polarized spinor gases. We calculate the beyond-mean-field corrections for both gases with polarized order parameters and obtain the phase diagram of the droplets on the parameter space of Rabi frequency omega R and detuning delta for Rabi-coupled mixtures and quadratic Zeeman energy q and linear Zeeman energy p for spinor gases. Finally, we highlight the similarities and differences between the two systems and discuss their experimental feasibility.