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 consider the ground state of a bilayer system of dipolar bosons, where dipoles are oriented by an external field in the direction perpendicular to the parallel planes. Quantum Monte Carlo methods are used to calculate the ground-state energy, the one-body and two-body density matrix, and the superfluid response as a function of the separation between layers. We find that by decreasing the interlayer distance for fixed value of the strength of the dipolar interaction, the system undergoes a quantum phase transition from a single-particle to a pair superfluid. The single-particle superfluid is characterized by a finite value of both the atomic condensate and the super-counterfluid density. The pair superfluid phase is found to be stable against formation of many-body cluster states and features a gap in the spectrum of elementary excitations. The study of quantum degenerate gases of dipolar particles has become in recent years one of the most active areas of experimental and theoretical research in the field of ultracold atoms [1,2]. The realization of systems featuring strong dipolar interactions opens prospects for investigating new and highly interesting many-body effects which arise from the anisotropic and long-range nature of the interatomic force. An example is the quest for p-wave superfluidity in a two-dimensional (2D) Fermi gas where dipoles are aligned by an external field at an angle formed with the plane of confinement larger than some critical value [3,4]. Another example involves fermionic dipoles in a bilayer geometry that allows for interlayer pairing of particles and displays superfluidity of pairs which, depending on the interlayer distance, ranges from a Bardeen-Cooper-Schrieffer (BCS) type to a Bose-Einstein condensate (BEC) of tightly bound dimers [5,6]. This latter system shares many analogies with the electron-hole bilayers realized in semiconductor coupled quantum wells [7,8] as well as graphene [9], where excitonic superfluidity is predicted to occur [10,11] even though a clear experimental observation is still lacking.In this paper, we investigate two-dimensional bilayers of bosonic dipoles, where the dipoles are oriented perpendicularly to the parallel planes which provide the 2D confinement. Tunneling between layers is assumed to be negligible due to the high potential barrier separating the planes. If one neglects short-range forces, in-plane interactions are purely repulsive and behave as 1/r 3 in terms of the interparticle distance. On the contrary, out-of-plane interactions are attractive at short distance and might induce pairing between particles in the two layers [12].In contrast to the fermionic counterpart, the bosonic system displays a quantum phase transition, as a function of the interlayer attraction, from a single-particle to a pair superfluid state (see Fig. 4). In the case of a tight-binding model of hardcore bosons on a lattice, the phase diagram at zero temperature has been investigated using mean field [13] and quantum Monte Carlo (QMC) methods [14] and was found ...

Strongly interacting systems of dipolar bosons in three dimensions confined by harmonic traps are analyzed using the exact Path Integral Ground State Monte Carlo method. By adding a repulsive two-body potential, we find a narrow window of interaction parameters leading to stable groundstate configurations of droplets in a crystalline arrangement. We find that this effect is entirely due to the interaction present in the Hamiltonian without resorting to additional stabilizing mechanisms or specific three-body forces. We analyze the number of droplets formed in terms of the Hamiltonian parameters, relate them to the corresponding s-wave scattering length, and discuss a simple scaling model for the density profiles. Our results are in qualitative agreement with recent experiments showing a quantum Rosensweig instability in trapped Dy atoms.Dipolar effects in quantum gases have been considered of major experimental and theoretical interest in the last decade since the initial studies of dilute clouds of Cr atoms, which present a relatively large magnetic dipolar moment. In the pioneering experiments of Ref.[1], the two-body scattering length of a cloud of 52 Cr atoms was drastically reduced by bringing it close to a Feshbach resonance. In this way, dipolar effects were enhanced and interesting new features, not observed before in other species like Rb or Cs, appeared. The long range and anisotropic character of the dipolar interaction has been largely explored since then, leading to interesting new phenomena such as d-wave superfluidity or d-wave collapse [2,3]. All these experiments have opened new perspectives on the field of dipolar quantum physics, and new systems with stronger dipolar interactions have since then been explored. The most promising ones, consisting initially in ultracold polar molecules of K and Rb or Cs and Rb, are unfortunately problematic due to the inherent difficulty to bring them down to the quantum degeneracy limit, although recent progress have been achieved with NaK [4] The anisotropy of the dipolar interaction plays a fundamental role on the behavior of the system, with different regimes and phases depending on the geometry and dimensionality. The particular form of the dipole-dipole potential makes the interaction be attractive or repulsive depending on the relative orientation of the dipoles, according to the expressionwhere C dd sets the strength of the interaction that is proportional to the square of the (magnetic or electric) dipolar moment, p j is the dipolar moment itself, and r is the relative position vector of the two interacting dipoles. The particular form of this interaction leads to surprising new features not present in other systems, like stripe phases in two-dimensional (2D) Bose systems [10]. Similar phases in Fermi systems have also been predicted [11,12], although these are more controversial [13]. One of the most interesting phenomenon recently reported in the field of dipolar quantum gases is the formation of self-bound droplets when a gas of trapped 164 Dy atoms...

We analyze the ground state of a system of dipolar bosons moving in the XY plane and such that their dipolar moments are all aligned in a fixed direction in space. We focus on the general case where the polarization field forms a generic angle α with respect to the Z axis. We use the path-integral ground-state method to analyze the static properties of the system as both α and the density n vary over a wide range where the system is stable. We use the maximum of the static structure function as an order parameter to characterize the different phases and the transition lines among them. We find that, in addition to a superfluid gas and a solid phase, the system reaches a stripe phase at large tilting angles that is entirely induced by the anisotropic character of the interaction. We also show that the quantum phase transition from the gas to the stripe phase is of second order and report approximate values for the critical exponents. In recent years, dipolar Bose gases have received much attention. The study of quantum degenerate gases of dipolar species has become one of the most active areas of experimental and theoretical research in the field of ultracold atoms [1][2][3]. From the theoretical point of view, the anisotropic and long-range character of the interaction makes dipolar systems unique, exhibiting features such as p-wave superfluidity in two-dimensional (2D) Fermi gases [4] or roton instability [5][6][7][8].Up to now, little attention has been paid to the 2D case where dipoles are polarized along an arbitrary direction, including the analysis of scattering properties [9] or the superfluid and collapse instabilities of a quasi-two-dimensional gas of dipolar fermions aligned by an external field [4]. Experiments such as those reported in Ref. [10] have also investigated the effect of (quasi-)2D confinement of a cloud of dipolar particles. One remarkable feature induced by the anisotropy of the interaction is the emergence of a stripe phase, which has been predicted to appear in both Bose [7] and Fermi [11][12][13] systems. Some calculations, in the mean-field approximation, predict the appearance of stripes even in the isotropic case where all dipoles are polarized perpendicular to the plane of movement, although recent Monte Carlo calculations for dipolar fermions arrived at a different conclusion [14]. In Ref.[7] we used path-integral ground-state (PIGS) calculations to reveal the existence of a stripe phase at large densities and polarization angles in 2D dipolar bosonic systems. In this work we extend the previous analysis and discuss the complete phase diagram at zero temperature, characterizing the stripe phase as a function of the density and polarization angle and determining the corresponding solid and stripe transition lines together with the critical exponents.In previous works we discussed the low-density properties [15] and elementary excitation spectrum [7] of the fully anisotropic 2D dipolar interaction. In this work we extend the analysis and investigate the phase diagram of a 2D system...

A microscopic description of the zero-energy two-body ground state and many-body static properties of anisotropic homogeneous gases of bosonic dipoles in two dimensions at low densities is presented and discussed. By changing the polarization angle with respect to the plane, we study the impact of the anisotropy, present in the dipole-dipole interaction, on the energy per particle, comparing the results with mean-field predictions. We restrict the analysis to the regime where the interaction is always repulsive, although the strength of the repulsion depends on the orientation with respect to the polarization field. We present a series expansion of the solution of the zero-energy two-body problem, which allows us to find the scattering length of the interaction and to build a suitable Jastrow factor that we use as a trial wave function for both a variational and diffusion Monte Carlo simulation of the infinite system. We find that the anisotropy has an almost negligible impact on the ground-state properties of the many-body system in the universal regime where the scattering length governs the physics of the system. We also show that scaling in the gas parameter persists in the dipolar case up to values where other isotropic interactions with the same scattering length yield different predictions.

Abstract. We present a quantum Monte Carlo study of two-dimensional dipolar Bose gases in the limit of zero temperature. The analysis is mainly focused on the anisotropy effects induced in the homogeneous gas when the polarization angle with respect to the plane is changed. We restrict our study to the regime where the dipolar interaction is strictly repulsive, although the strength of the pair repulsion depends on the vector interparticle distance. Our results show that the effect of the anisotropy in the energy per particle scales with the gas parameter at low densities as expected, and that this scaling is preserved for all polarization angles even at the largest densities considered here. We also evaluate the excitation spectrum of the dipolar Bose gas in the context of the Feynman approximation and compare the results obtained with the Bogoliubov ones. As expected, we find that these two approximations agree at very low densities, while they start to deviate from each other as the density increases. For the largest densities studied, we observe a significant influence of the anisotropy of the dipole-dipole interaction in the excitation spectrum.