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.

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 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.

The distribution of entangled states across the nodes of a future quantum internet will unlock fundamentally new technologies. Here, we report on the realization of a three-node entanglement-based quantum network. We combine remote quantum nodes based on diamond communication qubits into a scalable phase-stabilized architecture, supplemented with a robust memory qubit and local quantum logic. In addition, we achieve real-time communication and feed-forward gate operations across the network. We demonstrate two quantum network protocols without postselection: the distribution of genuine multipartite entangled states across the three nodes and entanglement swapping through an intermediary node. Our work establishes a key platform for exploring, testing, and developing multinode quantum network protocols and a quantum network control stack.