Magnetic phase diagram of a spin-1 condensate in two dimensions with dipole interaction

Several new features arise in the ground-state phase diagram of a spin-1\ncondensate trapped in an optical trap when the magnetic dipole interaction\nbetween the atoms is taken into account along with confinement and spin\nprecession. The boundaries between the regions of ferromagnetic and polar\nphases move as the dipole strength is varied and the ferromagnetic phases can\nbe modulated. The magnetization of the ferromagnetic phase perpendicular to the\nfield becomes modulated as a helix winding around the magnetic field direction,\nwith a wavelength inversely proportional to the dipole strength. This\nmodulation should be observable for current experimental parameters in\n$^{87}$Rb. Hence the much-sought supersolid state, with broken continuous\ntranslation invariance in one direction and broken global U(1) invariance,\noccurs generically as a metastable state in this system as a result of dipole\ninteraction. The ferromagnetic state parallel to the applied magnetic field\nbecomes striped in a finite system at strong dipolar coupling.\n