In a joint experimental and theoretical effort, we report on the formation of a macro-droplet state in an ultracold bosonic gas of erbium atoms with strong dipolar interactions. By precise tuning of the s-wave scattering length below the so-called dipolar length, we observe a smooth crossover of the ground state from a dilute Bose-Einstein condensate (BEC) to a dense macro-droplet state of more than 10 4 atoms. Based on the study of collective excitations and loss features, we quantitative prove that quantum fluctuations stabilize the ultracold gas far beyond the instability threshold imposed by mean-field interactions. Finally, we perform expansion measurements, showing the evolution of the normal BEC towards a three-dimensional self-bound state and show that the interplay between quantum stabilization and three-body losses gives rise to a minimal expansion velocity at a finite scattering length.

The concept of a roton, a special kind of elementary excitation, forming a minimum of energy at finite momentum, has been essential to understand the properties of superfluid 4He 1. In quantum liquids, rotons arise from the strong interparticle interactions, whose microscopic description remains debated 2. In the realm of highly-controllable quantum gases, a roton mode has been predicted to emerge due to magnetic dipole-dipole interactions despite of their weakly-interacting character 3. This prospect has raised considerable interest 4–12; yet roton modes in dipolar quantum gases have remained elusive to observations. Here we report experimental and theoretical studies of the momentum distribution in Bose-Einstein condensates of highly-magnetic erbium atoms, revealing the existence of the long-sought roton mode. Following an interaction quench, the roton mode manifests itself with the appearance of symmetric peaks at well-defined finite momentum. The roton momentum follows the predicted geometrical scaling with the inverse of the confinement length along the magnetisation axis. From the growth of the roton population, we probe the roton softening of the excitation spectrum in time and extract the corresponding imaginary roton gap. Our results provide a further step in the quest towards supersolidity in dipolar quantum gases 13.

Collapse in dipolar Bose-Einstein condensates may be arrested by quantum fluctuations. Due to the anisotropy of the dipole-dipole interactions, the dipole-driven collapse induced by soft excitations is compensated by the repulsive Lee-Huang-Yang contribution resulting from quantum fluctuations of hard excitations, in a similar mechanism as that recently proposed for Bose-Bose mixtures. The arrested collapse results in self-bound filament-like droplets, providing an explanation to recent dysprosium experiments. Arrested instability and droplet formation are novel general features directly linked to the nature of the dipole-dipole interactions, and should hence play an important role in all future experiments with strongly dipolar gases. PACS numbers:Dipole-dipole interactions (DDI) lead to qualitatively new physics for dipolar gases compared to non-dipolar ones [1,2]. As a result, this physics constitute the focus of a large interest, including experiments on magnetic atoms [3][4][5][6], polar molecules [7][8][9][10], and Rydbergdressed atoms [11]. A characteristic feature of dipolar Bose-Einstein condensates (BECs) is their geometrydependent stability [12]. If the condensate is elongated along the dipole orientation, the DDI are attractive in average, and the BEC may become unstable, in a similar, but not identical, way as a BEC with negative s-wave scattering length, a < 0. Chromium experiments showed that, as for a < 0, the unstable BEC collapses, albeit with a peculiar d-wave post-collapse dynamics [13].This picture has been challenged by recent dysprosium experiments [14], in which destabilization, induced by a quench to a sufficiently low a, is not followed by collapse, but rather by the formation of stable droplets that are only destroyed in a large time scale by weak three-body losses (3BL). This surprising result, which resembles the Rosensweig instability in ferrofluids [15,16], points to an up to now unknown stabilization mechanism that plays a similar role as that of surface tension in classical ferrofluids. It has been recently suggested that large conservative three-body forces, with a strength several orders of magnitude larger than the 3BL, may account for the observation [17,18]. There is however no justification of why large three-body forces should be present, or whether there is a link between them and the DDI.This Letter explores an alternative mechanism, based on quantum fluctuations, which is suggested by very recent experiments [19]. As recently shown [20], LeeHuang-Yang (LHY) corrections may stabilize droplets in unstable Bose-Bose mixtures. This interesting effect results from the presence of soft and hard elementary excitations. Whereas soft modes may become unstable, quantum fluctuations of the hard modes may balance the instability, resulting in an equilibrium droplet. As shown below, due to the anisotropy of the DDI, a dipolar BEC also presents soft and hard modes, characterized in free space by momenta perpendicular or parallel to the dipole (a) (b) FIG. 1: (Color online)Crystal-lik...

Recent experiments have revealed the formation of stable droplets in dipolar Bose-Einstein condensates. This surprising result has been explained by the stabilization given by quantum fluctuations. We study in detail the properties of a BEC in the presence of quantum stabilization. The ground-state phase diagram presents three main regimes: mean-field regime, in which the quantum correction is perturbative, droplet regime, in which quantum stabilization is crucial, and a multistable regime. In the absence of a multi-stable region, the condensate undergoes a crossover from the mean-field to the droplet solution marked by a characteristic growth of the peak density that may be employed to clearly distinguish quantum stabilization from other stabilization mechanisms. Interestingly quantum stabilization allows for three-dimensionally self-bound condensates. We characterized these self-bound solutions, and discuss their realization in experiments. We conclude with a discussion of the lowest-lying excitations both for trapped condensates, and for self-bound solutions.

Recent experiments have revealed that beyond-mean-field corrections are much more relevant in weakly-interacting dipolar condensates than in their non-dipolar counterparts. We show that in quasi-one-dimensional geometries quantum corrections in dipolar and non-dipolar condensates are strikingly different due to the peculiar momentum dependence of the dipolar interactions. The energy correction of the condensate presents not only a modified density dependence, but it may even change from attractive to repulsive at a critical density due to the surprising role played by the transversal directions. The anomalous quantum correction translates into a strongly modified physics for quantum-stabilized droplets and dipolar solitons. Moreover, and for similar reasons, quantum corrections of three-body correlations, and hence of three-body losses, are strongly modified by the dipolar interactions. This intriguing physics can be readily probed in current experiments with magnetic atoms.doi:10.1103/PhysRevLett.119.050403Introduction.-Quantum fluctuations introduce a shift of the ground-state energy of a Bose gas, which at first order is given by the well-known Lee-HuangYang (LHY) correction [1]. However, in the weaklyinteracting regime, experiments on Bose-Einstein condensates are well described within the mean-field approximation. The situation may be crucially different in the presence of competing interactions, as recently discussed in the context of Bose-Bose mixtures [2]. In that scenario, the interplay between inter-and intra-species interactions results, at the verge of mean-field instability, in a dominant LHY correction well within the weaklyinteracting regime. The LHY correction may stabilize a collapsing condensate, resulting in the formation of quantum droplets, a novel ultra-dilute liquid whose surface tension is provided by purely quantum effects.

By means of the Boltzmann-Vlasov kinetic equation we investigate dynamical properties of a trapped, one-component Fermi gas at zero temperature, featuring the anisotropic and long-range dipole-dipole interaction. To this end, we determine an approximate solution by rescaling both space and momentum variables of the equilibrium distribution, thereby obtaining coupled ordinary differential equations for the corresponding scaling parameters. Based on previous results on how the Fermi sphere is deformed in the hydrodynamic regime of a dipolar Fermi gas, we are able to implement the relaxation-time approximation for the collision integral. Then, we proceed by linearizing the equations of motion around the equilibrium in order to study both the frequencies and the damping of the low-lying excitation modes all the way from the collisionless to the hydrodynamic regime. Our theoretical results are expected to be relevant for understanding current experiments with trapped dipolar Fermi gases.