Geometrically protected triple-point crossings in an optical lattice

We show how to realize topologically protected crossings of three energy bands, integer-spin analogs of Weyl fermions, in three-dimensional optical lattices. Our proposal only involves ultracold atom techniques that have already been experimentally demonstrated and leads to isolated triple-point crossings (TPCs) which are required to exist by a novel combination of lattice symmetries. The symmetries also allow for a new type of topological object, the type-II, or tilted, TPC. Our Rapid Communication shows that spin-1 Weyl points, which have not yet been observed in the bandstructure of crystals, are within reach of ultracold atom experiments.Comment: 5 pages, 2 figures + 3 pages, 3 figures supplemental material. Added appendix on model symmetries, fixed typos and added references. This is the final, published versio

Multi-band spectroscopy of inhomogeneous Mott-insulator states of ultracold bosons

In this work, we use inelastic scattering of light to study the response of inhomogeneous Mott-insulator gases to external excitations. The experimental setup and procedure to probe the atomic Mott states are presented in detail. We discuss the link between the energy absorbed by the gases and accessible experimental parameters as well as the linearity of the response to the scattering of light. We investigate the excitations of the system in multiple energy bands and a band-mapping technique allows us to identify band and momentum of the excited atoms. In addition the momentum distribution in the Mott states which is spread over the entire first Brillouin zone enables us to reconstruct the dispersion relation in the high energy bands using a single Bragg excitation with a fixed momentum transfer.Comment: 19 pages, 7 figure

Localization in momentum space of ultracold atoms in incommensurate lattices

We characterize the disorder induced localization in momentum space for ultracold atoms in one-dimensional incommensurate lattices, according to the dual Aubry-Andr\'e model. For low disorder the system is localized in momentum space, and the momentum distribution exhibits time-periodic oscillations of the relative intensity of its components. The behavior of these oscillations is explained by means of a simple three-mode approximation. We predict their frequency and visibility by using typical parameters of feasible experiments. Above the transition the system diffuses in momentum space, and the oscillations vanish when averaged over different realizations, offering a clear signature of the transition

Majorana Quasi-Particles Protected by Z2\mathbb{Z}_2 Angular Momentum Conservation

We show how angular momentum conservation can stabilise a symmetry-protected quasi-topological phase of matter supporting Majorana quasi-particles as edge modes in one-dimensional cold atom gases. We investigate a number-conserving four-species Hubbard model in the presence of spin-orbit coupling. The latter reduces the global spin symmetry to an angular momentum parity symmetry, which provides an extremely robust protection mechanism that does not rely on any coupling to additional reservoirs. The emergence of Majorana edge modes is elucidated using field theory techniques, and corroborated by density-matrix-renormalization-group simulations. Our results pave the way toward the observation of Majorana edge modes with alkaline-earth-like fermions in optical lattices, where all basic ingredients for our recipe - spin-orbit coupling and strong inter-orbital interactions - have been experimentally realized over the last two years.Comment: 12 pages (6 + 6 supplementary material

Superradiant light scattering from a moving Bose-Einstein condensate

We investigate the interaction of a moving BEC with a far detuned laser beam. Superradiant Rayleigh scattering arises from the spontaneous formation of a matter-wave grating due to the interference of two wavepackets with different momenta. The system is described by the CARL-BEC model which is a generalization of the Gross-Pitaevskii model to include the self-consistent evolution of the scattered field. The experiment gives evidence of a damping of the matter-wave grating which depends on the initial velocity of the condensate. We describe this damping in terms of a phase-diffusion decoherence process, in good agreement with the experimental results

A strongly interacting gas of two-electron fermions at an orbital Feshbach resonance

We report on the experimental observation of a strongly interacting gas of ultracold two-electron fermions with orbital degree of freedom and magnetically tunable interactions. This realization has been enabled by the demonstration of a novel kind of Feshbach resonance occurring in the scattering of two 173Yb atoms in different nuclear and electronic states. The strongly interacting regime at resonance is evidenced by the observation of anisotropic hydrodynamic expansion of the two-orbital Fermi gas. These results pave the way towards the realization of new quantum states of matter with strongly correlated fermions with orbital degree of freedom.Comment: 5 pages, 4 figure

A Bose-Einstein condensate in a random potential

An optical speckle potential is used to investigate the static and dynamic properties of a Bose-Einstein condensate in the presence of disorder. For strong disorder the condensate is localized in the deep wells of the potential. With smaller levels of disorder, stripes are observed in the expanded density profile and strong damping of dipole and quadrupole oscillations is seen. Uncorrelated frequency shifts of the two modes are measured for a weak disorder and are explained using a sum-rules approach and by the numerical solution of the Gross-Pitaevskii equation

Momentum-resolved study of an array of 1D strongly phase-fluctuating Bose gases

We investigate the coherence properties of an array of one-dimensional Bose gases with short-scale phase fluctuations. The momentum distribution is measured using Bragg spectroscopy and an effective coherence length of the whole ensemble is defined. In addition, we propose and demonstrate that time-of-flight absorption imaging can be used as a simple probe to directly measure the coherence-length of 1D gases in the regime where phase-fluctuations are strong. This method is suitable for future studies such as investigating the effect of disorder on the phase coherence.Comment: 4 pages, 4 figure

Localized and extended states in a disordered trap

We study Anderson localization in a disordered potential combined with an inhomogeneous trap. We show that the spectrum displays both localized and extended states, which coexist at intermediate energies. In the region of coexistence, we find that the extended states result from confinement by the trap and are weakly affected by the disorder. Conversely, the localized states correspond to eigenstates of the disordered potential, which are only affected by the trap via an inhomogeneous energy shift. These results are relevant to disordered quantum gases and we propose a realistic scheme to observe the coexistence of localized and extended states in these systems.Comment: Published versio