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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.

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...

Atomic and molecular samples reduced to temperatures below one microkelvin, yet still in the gas phase, afford unprecedented energy resolution in probing and manipulating the interactions between their constituent particles. As a result of this resolution, atoms can be made to scatter resonantly on demand, through the precise control of a magnetic field. For simple atoms, such as alkalis, scattering resonances are extremely well characterized. However, ultracold physics is now poised to enter a new regime, where much more complex species can be cooled and studied, including magnetic lanthanide atoms and even molecules. For molecules, it has been speculated that a dense set of resonances in ultracold collision cross-sections will probably exhibit essentially random fluctuations, much as the observed energy spectra of nuclear scattering do. According to the Bohigas-Giannoni-Schmit conjecture, such fluctuations would imply chaotic dynamics of the underlying classical motion driving the collision. This would necessitate new ways of looking at the fundamental interactions in ultracold atomic and molecular systems, as well as perhaps new chaos-driven states of ultracold matter. Here we describe the experimental demonstration that random spectra are indeed found at ultralow temperatures. In the experiment, an ultracold gas of erbium atoms is shown to exhibit many Fano-Feshbach resonances, of the order of three per gauss for bosons. Analysis of their statistics verifies that their distribution of nearest-neighbour spacings is what one would expect from random matrix theory. The density and statistics of these resonances are explained by fully quantum mechanical scattering calculations that locate their origin in the anisotropy of the atoms' potential energy surface. Our results therefore reveal chaotic behaviour in the native interaction between ultracold atoms.

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.

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.

We report on the direct conversion of laser-cooled 41K and 87Rb atoms into ultracold 41K87Rb molecules in the rovibrational ground state via photoassociation followed by stimulated Raman adiabatic passage. High-resolution spectroscopy based on the coherent transfer revealed the hyperfine structure of weakly bound molecules in an unexplored region. Our results show that a rovibrationally pure sample of ultracold ground-state molecules is achieved via the all-optical association of laser-cooled atoms, opening possibilities to coherently manipulate a wide variety of molecules.

The deformation of a Fermi surface is a fundamental phenomenon leading to a plethora of exotic quantum phases. Understanding these phases, which play crucial roles in a wealth of systems, is a major challenge in atomic and condensed-matter physics. 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 basis for future studies on anisotropic many-body phenomena in normal and superfluid phases.PACS numbers: 03.75. Ss, 37.10.De, 51.60.+a, 67.85.Lm The Fermi-liquid theory, formulated by Landau in the late 50's, is one of the most powerful tools in modern condensedmatter physics [1]. It captures the behavior of interacting Fermi systems in the normal phase, such as electrons in metals and liquid 3 He [2]. Within this theory the interaction is accounted by dressing the fermions as quasi-particles with an effective mass and an effective interaction. The ground state is the so-called Fermi sea, in which the quasi-particles fill one-by-one all the states up to the Fermi momentum, k F . The Fermi surface (FS), which separates occupied from empty states in k-space, is a sphere of radius k F for isotropically interacting fermions in uniform space. The FS is crucial for understanding system excitations and Cooper pairing in superconductors. When complex interactions act, the FS can get modified. For instance, strongly-correlated electron systems violates the Fermi-liquid picture, giving rise to a deformed FS, which spontaneously breaks the rotational invariance of the system [3]. Symmetry-breaking FSs have been studied in connection with electronic liquid crystal phases [4] and Pomeranchuk instability [5] in solid state systems. Particularly relevant is the nematic phase, in which anisotropic behaviors spontaneously emerge and the system acquires an orientational order, while preserving its translational invariance. This exotic phase has recently been observed by transport and thermodynamics studies in ruthenates [6], in high-transitiontemperature superconductors such as cuprates [7], and in other systems [3].A completely distinct approach to study FSs is provided by ultracold quantum gases. These systems are naturally free from impurities and crystal structures, realizing a situation close to the ideal uniform case. Here, the shape of the FS can directly reveal the fundamental interactions among particles. Studies of FSs in strongly interacting Fermi gases have been crucial in understanding the BEC-to-BCS crossover, where the isotropic s-wave (contact) interaction causes a broadening of the always-spherical FS [8]. Recently, Fermi gases with anisotropic interactions have attracted remarkable attention in the context of p-wave superfluidity [9, 10] and dipolar physics [11]. Many theoretical studies have focused on dipol...

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.

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