Theoretical progress in many-body physics with ultracold dipolar gases

Recent experimental progress in trapping and cooling of molecular gases boosts interest in the interdisciplinary field of quantum gases with dominant dipole-dipole interactions. An unprecedented level of experimental control together with specific physical properties of dipole-dipole interaction provide a unique possibility to find new physical phenomena and practical applications. In this review, recent achievements in theoretical studies of ultracold dipolar gases, both fermionic and bosonic, are presented. We focus our attention on many-body properties of such systems and discuss how the characteristic features of dipole-dipole interaction, long range and anisotropy, affect their collective behavior and result in novel macroscopic quantum phenomena. The consideration covers spatially homogeneous and trapped cases, and includes analysis of the properties of dipolar gases in both the mean-field regime (dipolar Bose-Einstein condensates and superfluid BCS pairing transition) and in the strongly correlated one (dipolar gases in optical lattices and in rotating traps).