Measurement of the Excitation Spectrum of a Dipolar Gas in the Macrodroplet Regime.

The excitation spectrum of a cigar-shaped strongly dipolar quantum gas at the crossover from a Bose-Einstein condensate to a trapped macrodroplet is predicted to exhibit peculiar features-a strong upward shift of low momentum excitation energies together with a strong multiband response for high momenta. By performing Bragg spectroscopy over a wide range of momenta, we observe both key elements and also confirm the predicted stiffening of excitation modes when approaching the macrodroplet regime. Our measurements are in good agreement with numerical calculations taking into account finite size effects.

Two-Dimensional Supersolid Formation in Dipolar Condensates.

Dipolar condensates have recently been coaxed to form the long-sought supersolid phase. While one-dimensional supersolids may be prepared by triggering a roton instability, we find that such a procedure in two dimensions (2D) leads to a loss of both global phase coherence and crystalline order. Unlike in 1D, the 2D roton modes have little in common with the supersolid configuration. We develop a finite-temperature stochastic Gross-Pitaevskii theory that includes beyond-mean-field effects to explore the formation process in 2D and find that evaporative cooling directly into the supersolid phase-hence bypassing the first-order roton instability-can produce a robust supersolid in a circular trap. Importantly, the resulting supersolid is stable at the final nonzero temperature. We then experimentally produce a 2D supersolid in a near-circular trap through such an evaporative procedure. Our work provides insight into the process of supersolid formation in 2D and defines a realistic path to the formation of large two-dimensional supersolid arrays.

Excitation Spectrum of a Trapped Dipolar Supersolid and Its Experimental Evidence.

We study the spectrum of elementary excitations of a dipolar Bose gas in a three-dimensional anisotropic trap across the superfluid-supersolid phase transition. Theoretically, we show that, when entering the supersolid phase, two distinct excitation branches appear, respectively associated with dominantly crystal and superfluid excitations. These results confirm infinite-system predictions, showing that finite-size effects play only a small qualitative role, and connect the two branches to the simultaneous occurrence of crystal and superfluid orders. Experimentally, we probe compressional excitations in an Er quantum gas across the phase diagram. While in the Bose-Einstein condensate regime the system exhibits an ordinary quadrupole oscillation, in the supersolid regime we observe a striking two-frequency response of the system, related to the two spontaneously broken symmetries.

Probing the Roton Excitation Spectrum of a Stable Dipolar Bose Gas.

We measure the excitation spectrum of a stable dipolar Bose-Einstein condensate over a wide momentum range via Bragg spectroscopy. We precisely control the relative strength ε_{dd} of the dipolar to the contact interactions and observe that the spectrum increasingly deviates from the linear phononic behavior for increasing ε_{dd}. Reaching the dipolar-dominated regime ε_{dd}>1, we observe the emergence of a roton minimum in the spectrum and its softening towards instability. We characterize how the excitation energy and the strength of the density-density correlations at the roton momentum vary with ε_{dd}. Our findings are in excellent agreement with numerical calculations based on mean-field Bogoliubov theory. When including beyond-mean-field corrections, in the form of a Lee-Huang-Yang potential, we observe a quantitative deviation from the experiment, questioning the validity of such a description in the roton regime.

Dipolar Quantum Mixtures of Erbium and Dysprosium Atoms.

We report on the first realization of heteronuclear dipolar quantum mixtures of highly magnetic erbium and dysprosium atoms. With a versatile experimental setup, we demonstrate binary Bose-Einstein condensation in five different Er-Dy isotope combinations, as well as one Er-Dy Bose-Fermi mixture. Finally, we present first studies of the interspecies interaction between the two species for one mixture.

Realization of a Strongly Interacting Fermi Gas of Dipolar Atoms.

We realize a two-component dipolar Fermi gas with tunable interactions, using erbium atoms. Employing a lattice-protection technique, we selectively prepare deeply degenerate mixtures of the two lowest spin states and perform high-resolution Feshbach spectroscopy in an optical dipole trap. We identify a comparatively broad Feshbach resonance and map the interspin scattering length in its vicinity. The Fermi mixture shows a remarkable collisional stability in the strongly interacting regime, providing a first step towards studies of superfluid pairing, crossing from Cooper pairs to bound molecules, in presence of dipole-dipole interactions.

Ultracold Dipolar Molecules Composed of Strongly Magnetic Atoms.

In a combined experimental and theoretical effort, we demonstrate a novel type of dipolar system made of ultracold bosonic dipolar molecules with large magnetic dipole moments. Our dipolar molecules are formed in weakly bound Feshbach molecular states from a sample of strongly magnetic bosonic erbium atoms. We show that the ultracold magnetic molecules can carry very large dipole moments and we demonstrate how to create and characterize them, and how to change their orientation. Finally, we confirm that the relaxation rates of molecules in a quasi-two-dimensional geometry can be reduced by using the anisotropy of the dipole-dipole interaction and that this reduction follows a universal dipolar behavior.

Reaching Fermi degeneracy via universal dipolar scattering.

We report on the creation of a degenerate dipolar Fermi gas of erbium atoms. We force evaporative cooling in a fully spin-polarized sample down to temperatures as low as 0.2 times the Fermi temperature. The strong magnetic dipole-dipole interaction enables elastic collisions between identical fermions even in the zero-energy limit. The measured elastic scattering cross section agrees well with the predictions from the dipolar scattering theory, which follow a universal scaling law depending only on the dipole moment and on the atomic mass. Our approach to quantum degeneracy proceeds with very high cooling efficiency and provides large atomic densities, and it may be extended to various dipolar systems.

Anisotropic relaxation dynamics in a dipolar Fermi gas driven out of equilibrium.

We report on the observation of a large anisotropy in the rethermalization dynamics of an ultracold dipolar Fermi gas driven out of equilibrium. Our system consists of an ultracold sample of strongly magnetic 167Er fermions, spin polarized in the lowest Zeeman sublevel. In this system, elastic collisions arise purely from universal dipolar scattering. Based on cross-dimensional rethermalization experiments, we observe a strong anisotropy of the scattering, which manifests itself in a large angular dependence of the thermal relaxation dynamics. Our result is in good agreement with recent theoretical predictions. Furthermore, we measure the rethermalization rate as a function of temperature for different angles and find that the suppression of collisions by Pauli blocking is not influenced by the dipole orientation.

Heating a dipolar quantum fluid into a solid.

Raising the temperature of a material enhances the thermal motion of particles. Such an increase in thermal energy commonly leads to the melting of a solid into a fluid and eventually vaporises the liquid into a gaseous phase of matter. Here, we study the finite-temperature physics of dipolar quantum fluids and find surprising deviations from this general phenomenology. In particular, we describe how heating a dipolar superfluid from near-zero temperatures can induce a phase transition to a supersolid state with a broken translational symmetry. We discuss the observation of this effect in experiments on ultracold dysprosium atoms, which opens the door for exploring the unusual thermodynamics of dipolar quantum fluids.

Bose-Einstein condensation of erbium.

We report on the achievement of Bose-Einstein condensation of erbium atoms and on the observation of magnetic Feshbach resonances at low magnetic fields. By means of evaporative cooling in an optical dipole trap, we produce pure condensates of 168Er, containing up to 7×10(4) atoms. Feshbach spectroscopy reveals an extraordinary rich loss spectrum with six loss resonances already in a narrow magnetic-field range up to 3 G. Finally, we demonstrate the application of a low-field Feshbach resonance to produce a tunable dipolar Bose-Einstein condensate and we observe its characteristic d-wave collapse.

Universality of the three-body parameter for Efimov states in ultracold cesium.

We report on the observation of triatomic Efimov resonances in an ultracold gas of cesium atoms. Exploiting the wide tunability of interactions resulting from three broad Feshbach resonances in the same spin channel, we measure magnetic-field dependent three-body recombination loss. The positions of the loss resonances yield corresponding values for the three-body parameter, which in universal few-body physics is required to describe three-body phenomena and, in particular, to fix the spectrum of Efimov states. Our observations show a robust universal behavior with a three-body parameter that stays essentially constant.

Magnetically controlled exchange process in an ultracold atom-dimer mixture.

We report on the observation of an elementary exchange process in an optically trapped ultracold sample of atoms and Feshbach molecules. We can magnetically control the energetic nature of the process and tune it from endoergic to exoergic, enabling the observation of a pronounced threshold behavior. In contrast to relaxation to more deeply bound molecular states, the exchange process does not lead to trap loss. We find excellent agreement between our experimental observations and calculations based on the solutions of three-body Schrödinger equation in the adiabatic hyperspherical representation. The high efficiency of the exchange process is explained by the halo character of both the initial and final molecular states.

Observation of Roton Mode Population in a Dipolar Quantum Gas.

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.

Extended Bose-Hubbard models with ultracold magnetic atoms.

The Hubbard model underlies our understanding of strongly correlated materials. Whereas its standard form only comprises interactions between particles at the same lattice site, extending it to encompass long-range interactions 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 superfluid-to-Mott insulator quantum phase transition. Moreover, we observe nearest-neighbor interactions, a genuine consequence of the long-range nature of dipolar interactions. Our results lay the groundwork for future studies of exotic many-body quantum phases.

Emergence of Chaotic Scattering in Ultracold Er and Dy.

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.

Quantum gases. Observation of Fermi surface deformation in a dipolar quantum gas.

In the presence of isotropic interactions, the Fermi surface of an ultracold Fermi gas is spherical. Introducing anisotropic interactions can deform the Fermi surface, but the effect is subtle and challenging to observe experimentally. Here, we report on the observation of a Fermi surface deformation in a degenerate dipolar Fermi gas of erbium atoms. The deformation is caused by the interplay between strong magnetic dipole-dipole interaction and the Pauli exclusion principle. We demonstrate the many-body nature of the effect and its tunability with the Fermi energy. Our observation provides a basis for future studies on anisotropic many-body phenomena in normal and superfluid phases.

Evidence for universal four-body states tied to an Efimov trimer.

We report on the measurement of four-body recombination rate coefficients in an atomic gas. Our results obtained with an ultracold sample of cesium atoms at negative scattering lengths show a resonant enhancement of losses and provide strong evidence for the existence of a pair of four-body states, which is strictly connected to Efimov trimers via universal relations. Our findings confirm recent theoretical predictions and demonstrate the enrichment of the Efimov scenario when a fourth particle is added to the generic three-body problem.