Excitations and stripe phase formation in a two-dimensional dipolar Bose gas with tilted polarization

We present calculations of the ground state and excitations of an anisotropic dipolar Bose gas in two dimensions, realized by a nonperpendicular polarization with respect to the system plane. For sufficiently high density, an increase of the polarization angle leads to a density instability of the gas phase in the direction where the anisotropic interaction is strongest. Using a dynamic many-body theory, we calculate the dynamic structure function in the gas phase which shows the anisotropic dispersion of the excitations. We find that the energy of roton excitations in the strongly interacting direction decreases with increasing polarization angle and almost vanishes close to the instability. Exact path integral ground state Monte Carlo simulations show that this instability is indeed a quantum phase transition to a stripe phase, characterized by long-range order in the strongly interacting direction.