Roton Instability and Phonon Collapse of Two-dimensional Tilted Dipoles

Bose-Einstein condensed gas of two-dimensional tilted dipoles in a thin layer is under consideration. The problem of stability is resolved. Phase diagram for system of two-dimensional dipole atoms in a thin layer is obtained. A formation of density waves and their orientation control possibility via polarizing field are considered. These effects can be experimentally observed for magnetically dipolar atoms at the Feshbach resonance or polar molecules in one-dimensional optical lattices.