We derive a general effective many-body theory for bosonic polar molecules in strong interaction regime, which cannot be correctly described by previous theories within the first Born approximation. The effective Hamiltonian has additional interaction terms, which surprisingly reduces the anisotropic features of dipolar interaction near the shape resonance regime. In the 2D system with dipole moment perpendicular to the plane, we find that the phonon dispersion scales as p |p| in the low momentum (p) limit, showing the same low energy properties as a 2D charged Bose gas with Coulomb (1/r) interactions.
I. INTRODUCTIONRecent developments in the trapping and cooling of chromium atoms [1] and polar molecules [2] provide a new direction for investigating quantum states resulting from the anisotropic dipole interaction. Dipolar effects on the condensate profile [3] and elementary excitations [4] have been extensively studied both theoretically and experimentally. Several exotic many-body states resulted from dipolar interactions are also proposed [5]. However, most theoretical works so far are based on the pseudo-potential developed by Yi and You [12] within the first Born approximation (FBA). As a result, these results become not justified when applied to the systems of polar molecules, which can have large electric dipole moments and hence strong dipolar interaction to renormalize the scattering amplitude beyond the FBA.In Ref.[6], Derevianko extended Huang and Yang's approach [7] to the anisotropic dipolar interaction, and for the first time shew how it may be possible to go beyond the Born approximation in a dipolar gas system. The derived pseudo-potential, however, is non-hermitian in the low energy limit, and therefore cannot be easily used for constructing the effective theory of strongly interacting dipolar gases. In Ref. [8], the authors studied the systems of bosonic dipoles via Monte Carlo calculation, and found that the ground state energy can be well-explained by the Yi and You's pseudo-potential within FBA if using a dipole-dependent s-wave scattering. Results of Ref.[8] can certainly be applied to a regime of stronger dipole momentum (beyond the valid regime of Yi and You's original pseudo-potential), because the higher order renormalization of the s-wave scattering amplitude has been included. But its validity to apply to polar molecules with large dipole moment in strong field is still questionable, because the higher order renormalization to the scattering amplitude (FBA is the first order perturbation) of the non-s-wave scattering channels are not included at all. As a example, in Ref.[9], Deb and You found that the scattering matrix element between s-wave and d-wave channels also has strong deviation from their weak interaction result when near the shape resonance. It is reasonable to believe that there will be such kind of deviation from the FBA results in other channels in stronger dipole moment regime, as usually considered in the polar molecule systems. Therefore developing a correct and widel...
