We present calculations of the ground state and excitations of an anisotropic dipolar Bose gas in two dimensions, realized by a non-perpendicular 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.Strongly correlated dipolar Bose gases in two dimensions (2D) polarized along the direction normal to the system plane have been extensively investigated in recent years [1][2][3][4]. The ratio between the dipolar length r 0 = mC dd /(4πh 2 ) and the average interparticle distance provides a measure of the strength of the interaction. C dd is the coupling constant proportional to the square of the (magnetic µ or electric d) dipole moment, resulting in a dipolar length that can range from a fewÅ for magnetic dipolar systems like 52 Cr (µ = 6µ B , with µ B the Bohr magneton), to thousands ofÅ for heteronuclear polar molecules like KRb, LiCs [5], or RbCs [6]. However, chemical reactions and three-body losses impose limitations on what can be measured in experiments with polar molecules. Therefore, recent efforts focus also on exotic lanthanide magnetic systems like 164 Dy or 168 Er, [7] where the combined effect of a large magnetic moment (µ = 10µ B for 164 Dy and µ = 7µ B for 168 Er) and a large mass, lead to dipolar length scales that, although still significantly lower than the corresponding value for polar molecules, is several times larger than that of 52 Cr. Er 2 with µ = 14µ B and twice the mass of Er would reach even higher values of r 0 [8].A 2D dipolar Bose gas polarized along the normal direction to the confining plane develops a roton excitation at high density due to the strong repulsion between dipoles at short distances [3]. Other works have revealed competing effects in a quasi-2D geometry due to the head-to-tail attraction of the dipole-dipole interaction when the third spatial dimension is added, to the point that the system becomes unstable against density fluctuation below a critical trapping frequency in that direction [9][10][11]. This leads to the question of whether a similar situation can hold in a purely 2D geometry when a head-to-tail component to the dipole-dipole interaction is added by tilting the polarization with respect to the direction normal to the system plane. The interaction becomes anisotropic, V (r) = V (x, y) = C dd 4πr 3 1 − 3 x 2 r 2 sin 2 α , with particles moving in the x, y...

We study the pair correlations and excitations of a dipolar Bose gas layer. The anisotropy of the dipole-dipole interaction allows us to tune the strength of pair correlations from strong to weak perpendicular and weak to strong parallel to the layer by increasing the perpendicular trap frequency. This change is accompanied by a roton-roton crossover in the spectrum of collective excitations, from a roton caused by the head-to-tail attraction of dipoles to a roton caused by the side-by-side repulsion, while there is no roton excitation for intermediate trap frequencies. We discuss the nature of these two kinds of rotons and the relation to instabilities of dipolar Bose gases. In both regimes of trap frequencies where rotons occur, we observe strong damping of collective excitations by decay into two rotons.

We study correlation effects and excitations in a dipolar Bose gas bilayer which is modeled by a one-dimensional double well trap that determines the width of an individual layer, the distance between the two layers, and the height of the barrier between them. For the ground state calculations we use the hypernetted-chain Euler Lagrange method and for the calculation of the excitations we use the correlated basis function method. We observe instabilities both for wide, well-separated layers dominated by intra-layer attraction of the dipoles, and for narrow layers that are close to each other dominated by inter-layer attraction. The behavior of the pair distribution function leads to the interpretation that the monomer phase becomes unstable when pairing of two dipoles becomes energetically favorable between or within layers, respectively. In both cases we observe a tendency towards "rotonization", i.e. the appearance of a soft mode with finite momentum in the excitation spectrum. The dynamic structure function is not simply characterized by a single excitation mode, but has a non-trivial multi-peak structure that is not captured by the Bijl-Feynman approximation. The dipole-dipole interaction between different layers leads to additional damping compared to the damping obtained for uncoupled layers.