Spinor Bose-Einstein Condensates of Rotating Polar Molecules

We propose a scheme to realize a pseudospin-$1\mathrm{/}2$ model of the ${}^1\mathrm{\Sigma }(v=0)$ bialkali polar molecules with the spin states corresponding to two sublevels of the first excited rotational level. We show that the effective dipole-dipole interaction between two spin-$1\mathrm{/}2$ molecules couples the rotational and orbital angular momenta and is highly tunable via a microwave field. We also investigate the ground state properties of a spin-$1\mathrm{/}2$ molecular condensate. A variety of nontrivial quantum phases, including the doubly-quantized vortex states, are discovered. Our scheme can also be used to create spin-$1$ model of polar molecules. Thus, we show that the ultracold gases of bialkali polar molecules provide a unique platform for studying the spinor condensates of rotating molecules.