Dipolar quantum droplets are exotic quantum objects that are self-bound due to the subtle balance of attraction, repulsion and quantum correlations. Here we present a systematic study of the critical atom number of these self-bound droplets, comparing the experimental results with extended mean-field Gross-Pitaevskii equation (eGPE) and quantum Monte-Carlo simulations of the dilute system. The respective theoretical predictions differ, questioning the validity of the current theoretical state-of-the-art description of quantum droplets within the eGPE framework and indicating that correlations in the system are significant. Furthermore, we show that our system can serve as a sensitive testing ground for many-body theories in the near future.

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 superfluid properties of a system of fully polarized dipolar bosons moving in the XY plane. We focus on the general case where the polarization field forms an arbitrary angle α with respect to the Z axis, while the system is still stable. We use the diffusion Monte Carlo and the path integral ground state methods to evaluate the one-body density matrix and the superfluid fractions in the region of the phase diagram where the system forms stripes. Despite its oscillatory behavior, the presence of a finite largedistance asymptotic value in the s-wave component of the one-body density matrix indicates the existence of a Bose condensate. The superfluid fraction along the stripes direction is always close to 1, while in the Y direction decreases to a small value that is nevertheless different from zero. These two facts confirm that the stripe phase of the dipolar Bose system is a clear candidate for an intrinsic supersolid without the presence of defects as described by the Andreev-Lifshitz mechanism. DOI: 10.1103/PhysRevLett.119.250402 Supersolid many-body systems appear in nature when two continuous U(1) symmetries are broken. The first one is associated with the translational invariance of the crystalline structure, while the second one corresponds to the appearance of a nontrivial global phase of the superfluid state [1]. Supersolid phases were predicted to exist in helium already in the late 1960s [2], though their experimental observation has been elusive. In fact, the claims for detection made at the beginning of this century have been refuted, as the observed behavior is not caused by finite nonconventional rotational inertia but rather to elastic effects [3]. In this way, a neat observation of supersolidity in 4 He is still lacking. In fact, it is not clear yet whether a pure, defect-free supersolid structure like the one that would be expected in 4 He really exists. Recently, the issue of supersolidity has emerged again, but now in the field of ultracold atoms. Two different experimental teams have claimed that spatial local order and superfluidity have been simultaneously observed in lattice setups [4] and in stripe phases [5]. In this way, the definition of what a supersolid really is seems to still be under discussion [6].Superfluid properties of solidlike phases are also of fundamental interest in quantum condensed matter. One of these is the stripe phase, where the system presents spatial order in one direction but not in the others. For instance, stripe phases have been of major interest since 1990, when nonhomogeneous metallic structures with broken spatial symmetry were found to favor superconductivity [7,8]. More recently, stripe phases have been observed in Bose-Einstein condensates with synthetically created spin-orbit coupling [5], where the momentum dependence of the interaction induces spatial ordering along a single direction in some regions of the phase diagram [9]. Stripe phases have also been discussed in the context of quantum dipolar physics, including very recent theoret...

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...