Spinor boson droplets stabilized by spin fluctuations

Self-trapped droplets stabilized by quantum fluctuations have been experimentally realized in dipolar gases and binary boson mixtures. We investigate spinor Bose gases as another candidate for droplet formation. For spin-1 gas, we find that spin fluctuations give a dilute but self-trapped state for two different order parameters where the mean-field picture predicts collapse. A polar droplet phase can be stabilized by spin fluctuations for antiferromagnetic and ferromagnetic spin-dependent coupling. An antiferromagnetic droplet phase can be stabilized similarly with a negative quadratic Zeeman shift. The beyond mean-field energy of the system depends on the quadratic Zeeman coupling, which provides a mechanism to tune the droplet formation and its density. Similarly, the total magnetic polarization of the system provides another tunable parameter for controlling the droplets. We calculate the phase diagram of the system as a function of polarization and quadratic Zeeman shift.