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.

By combining theory and experiments, we demonstrate that dipolar quantum gases of both 166 Er and 164 Dy support a state with supersolid properties, where a spontaneous density modulation and a global phase coherence coexist. This paradoxical state occurs in a well defined parameter range, separating the phases of a regular Bose-Einstein condensate and of an insulating droplet array, and is rooted in the roton mode softening, on the one side, and in the stabilization driven by quantum fluctuations, on the other side. Here, we identify the parameter regime for each of the three phases. In the experiment, we rely on a detailed analysis of the interference patterns resulting from the free expansion of the gas, quantifying both its density modulation and its global phase coherence. Reaching the phases via a slow interaction tuning, starting from a stable condensate, we observe that 166 Er and 164 Dy exhibit a striking difference in the lifetime of the supersolid properties, due to the different atom loss rates in the two systems. Indeed, while in 166 Er the supersolid behavior only survives a few tens of milliseconds, we observe coherent density modulations for more than 150 ms in 164 Dy. Building on this long lifetime, we demonstrate an alternative path to reach the supersolid regime, relying solely on evaporative cooling starting from a thermal gas. arXiv:1903.04375v1 [cond-mat.quant-gas]

The Hubbard model underlies our understanding of strongly correlated materials. While its standard form only comprises interaction between particles at the same lattice site, its extension to encompass long-range interaction, which activates terms acting between different sites, is predicted to profoundly alter the quantum behavior of the system. We realize the extended Bose-Hubbard model for an ultracold gas of strongly magnetic erbium atoms in a three-dimensional optical lattice. Controlling the orientation of the atomic dipoles, we reveal the anisotropic character of the onsite interaction and hopping dynamics, and their influence on the superfluidto-Mott insulator quantum phase transition. Moreover, we observe nearest-neighbor interaction, which is a genuine consequence of the long-range nature of dipolar interactions. Our results lay the groundwork for future studies of novel exotic many-body quantum phases. PACS numbers: 67.85.Hj, 37.10.De, 51.60.+a, 05.30.Rt Dipolar interactions, reflecting the forces between a pair of magnetic or electric dipoles, account for many physically and biologically significant phenomena. These range from novel phases appearing at low temperatures in quantum many-body systems [1,2], liquid crystals and ferrofluids in soft condensed matter physics [3,4], to the mechanism underlying protein folding [5]. The distinguishing feature of dipole-dipole interactions (DDI) is their long-range and anisotropic character [6]: a pair of dipoles oriented in parallel will repel each other, while the interaction between two head to tail dipoles will be attractive. While remarkable progress has been made with gases of polar molecules [7] and Rydberg ensembles [8] comprising electric dipoles, it is the recent experimental advances in creating quantum degenerate gases of bosonic and fermionic magnetic atoms, including Cr [9-11] and the Lanthanides Er [12] and Dy [13], which have now opened the door to a study of magnetic dipolar interactions, and their unique role in Hubbard dynamics of a quantum lattice gas.Ultracold Lanthanide atoms with their open electronic fshells, and their anisotropic interactions are characterized by unconventional low energy scattering properties, including the proliferation of Feshbach resonances [14]. This complexity of Lanthanides manifests itself in quantum many-body dynamics: by preparing quantum degenerate Lanthanide gases in optical lattices we realize extended Hubbard models for bosonic and fermionic atoms. Here, in addition to the familiar single particle tunneling and isotropic onsite interactions (as for contact interactions in Alkali) dipolar interactions give rise to anisotropic onsite and nearest-neighbor (offsite) interactions (NNI), and density-assisted tunneling (DAT) [15]. Such extended Hubbard models have been studied extensively in theoretical condensed matter physics and quantum material science [16,17], and it is the competition between these unconventional Hubbard interactions, which underlies the prediction of exotic quantum phases such as super...

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.

Phase transitions are ubiquitous in our three-dimensional world. By contrast, most conventional transitions do not occur in infinite uniform low-dimensional systems because of the increased role of thermal fluctuations. The crossover between these situations constitutes an important issue, dramatically illustrated by Bose-Einstein condensation: a gas strongly confined along one direction of space may condense along this direction without exhibiting true long-range order in the perpendicular plane. Here we explore transverse condensation for an atomic gas confined in a novel trapping geometry, with a flat in-plane bottom, and we relate it to the onset of an extended (yet of finite-range) in-plane coherence. By quench crossing the transition, we observe topological defects with a mean number satisfying the universal scaling law predicted by Kibble-Zurek mechanism. The approach described can be extended to investigate the topological phase transitions that take place in planar quantum fluids.

Owing to thermal fluctuations, two-dimensional (2D) systems cannot undergo a conventional phase transition associated with the breaking of a continuous symmetry 1 . Nevertheless they may exhibit a phase transition to a state with quasi-longrange order via the Berezinskii-Kosterlitz-Thouless (BKT) mechanism 2 . A paradigm example is the 2D Bose fluid, such as a liquid helium film 3 , which cannot condense at non-zero temperature although it becomes superfluid above a critical phase space density. The quasi-long-range coherence and the microscopic nature of the BKT transition were recently explored with ultracold atomic gases 4-6 . However, a direct observation of superfluidity in terms of frictionless flow is still missing for these systems. Here we probe the superfluidity of a 2D trapped Bose gas using a moving obstacle formed by a micrometre-sized laser beam. We find a dramatic variation of the response of the fluid, depending on its degree of degeneracy at the obstacle location.'Flow without friction' is a hallmark of superfluidity 7 . It corresponds to a metastable state in which the fluid has a non-zero relative velocity v with respect to an external body such as the wall of the container or an impurity. This metastable state is separated from the equilibrium state of the system (v = 0) by a large energy barrier, so that the flow can persist for a macroscopic time. The height of the barrier decreases as v increases, and eventually passes below a threshold (proportional to the thermal energy) for a critical velocity v c . The microscopic mechanism limiting the barrier height depends on the nature of the defect and is associated with the creation of phonons and/or vortices 7 . Whereas the quantitative comparison between experiments and theory is complicated for liquid 4 He, cold atomic gases in the weakly interacting regime are well suited for precise tests of many-body physics. In particular, superfluidity was observed in 3D atomic gases by stirring a laser beam or an optical lattice through bosonic [8][9][10][11][12] or fermionic 13 fluids and by observing the resulting heating or excitations. Here we transpose this search for dissipation-less motion to a disc-shaped, non-homogeneous 2D Bose gas. We use a small obstacle to locally perturb the system. The obstacle moves at constant velocity on a circle centred on the cloud, allowing us to probe the gas at a fixed density. We repeat the experiment for various atom numbers, temperatures and stirring radii and identify a critical point for superfluid behaviour.Our experiments are performed with 2D Bose gases of N = 35,000-95,000 87 Rb atoms confined in the vertical direction by the harmonic potential W (z) and in the horizontal plane by the radially symmetric harmonic potential V (r) (see ref. perturbed by a focussed laser beam, which moves at constant velocity on a circle centred on the cloud. The stirring beam has a frequency greater than the 87 Rb resonance frequency ('blue detuning' of ≈2 nm) and thus creates a repulsive potential which causes a dip in the d...

We create supercurrents in annular two-dimensional Bose gases through a temperature quench of the normal-to-superfluid phase transition. We detect the magnitude and the direction of these supercurrents by measuring spiral patterns resulting from the interference of the cloud with a central reference disk. These measurements demonstrate the stochastic nature of the supercurrents. We further measure their distribution for different quench times and compare it with predictions based on the Kibble-Zurek mechanism.

We show that for ultracold magnetic lanthanide atoms chaotic scattering emerges due to a combination of anisotropic interaction potentials and Zeeman coupling under an external magnetic field. This scattering is studied in a collaborative experimental and theoretical effort for both dysprosium and erbium. We present extensive atom-loss measurements of their dense magnetic Feshbach-resonance spectra, analyze their statistical properties, and compare to predictions from a random-matrix-theory-inspired model. Furthermore, theoretical coupled-channels simulations of the anisotropic molecular Hamiltonian at zero magnetic field show that weakly bound, near threshold diatomic levels form overlapping, uncoupled chaotic series that when combined are randomly distributed. The Zeeman interaction shifts and couples these levels, leading to a Feshbach spectrum of zero-energy bound states with nearest-neighbor spacings that changes from randomly to chaotically distributed for increasing magnetic field. Finally, we show that the extreme temperature sensitivity of a small, but sizable fraction of the resonances in the Dy and Er atom-loss spectra is due to resonant nonzero partial-wave collisions. Our threshold analysis for these resonances indicates a large collision-energy dependence of the three-body recombination rate.