We consider an oblate Bose-Einstein condensate of heteronuclear polar molecules in a weak applied electric field. This system supports a rich quasiparticle spectrum that plays a critical role in determining its bulk dielectric properties. In particular, in sufficiently weak fields the system undergoes a polarization wave rotonization, leading to the development of textured electronic structure and a dielectric instability that is characteristic of the onset of a negative static dielectric function.
We show that, under achievable experimental conditions, a Bose–Einstein condensate of polar molecules can exhibit dielectric character. In particular, we derive a set of self-consistent mean-field equations that couple the condensate density to its electric dipole field, leading to the emergence of polarization modes that are coupled to the rich quasi-particle spectrum of the condensate. While the usual roton instability is suppressed in this system, the coupling can give rise to a phonon-like instability that is characteristic of a dielectric material with a negative static dielectric function.
We propose a scheme to realize a pseudospin-
1/2 model of the ${}^{1}\mathrm{\ensuremath{\Sigma}}(v=0)$ 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-
1/2 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-
1/2 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.