Observation of many-body localization in a one-dimensional system with single-particle mobility edge

We experimentally study many-body localization (MBL) with ultracold atoms in a weak one-dimensional quasiperiodic potential, which in the noninteracting limit exhibits an intermediate phase that is characterized by a mobility edge. We measure the time evolution of an initial charge density wave after a quench and analyze the corresponding relaxation exponents. We find clear signatures of MBL, when the corresponding noninteracting model is deep in the localized phase. We also critically compare and contrast our results with those from a tight-binding Aubry-Andr\'{e} model, which does not exhibit a single-particle intermediate phase, in order to identify signatures of a potential many-body intermediate phase

Observing non-ergodicity due to kinetic constraints in tilted Fermi-Hubbard chains

The thermalization of isolated quantum many-body systems is deeply related to fundamental questions of quantum information theory. While integrable or many-body localized systems display non-ergodic behavior due to extensively many conserved quantities, recent theoretical studies have identified a rich variety of more exotic phenomena in between these two extreme limits. The tilted one-dimensional Fermi-Hubbard model, which is readily accessible in experiments with ultracold atoms, emerged as an intriguing playground to study non-ergodic behavior in a clean disorder-free system. While non-ergodic behavior was established theoretically in certain limiting cases, there is no complete understanding of the complex thermalization properties of this model. In this work, we experimentally study the relaxation of an initial charge-density wave and find a remarkably long-lived initial-state memory over a wide range of parameters. Our observations are well reproduced by numerical simulations of a clean system. Using analytical calculations we further provide a detailed microscopic understanding of this behavior, which can be attributed to emergent kinetic constraints.Comment: accepted in Nature Communication

Non-Equilibrium Mass Transport in the 1D Fermi-Hubbard Model

We experimentally and numerically investigate the sudden expansion of fermions in a homogeneous one-dimensional optical lattice. For initial states with an appreciable amount of doublons, we observe a dynamical phase separation between rapidly expanding singlons and slow doublons remaining in the trap center, realizing the key aspect of fermionic quantum distillation in the strongly-interacting limit. For initial states without doublons, we find a reduced interaction dependence of the asymptotic expansion speed compared to bosons, which is explained by the interaction energy produced in the quench

Optical lattice quantum simulator for QED in strong external fields: spontaneous pair creation and the Sauter-Schwinger effect

Spontaneous creation of electron-positron pairs out of the vacuum due to a strong electric field is a spectacular manifestation of the relativistic energy-momentum relation for the Dirac fermions. This fundamental prediction of Quantum Electrodynamics (QED) has not yet been confirmed experimentally as the generation of a sufficiently strong electric field extending over a large enough space-time volume still presents a challenge. Surprisingly, distant areas of physics may help us to circumvent this difficulty. In condensed matter and solid state physics (areas commonly considered as low energy physics), one usually deals with quasi-particles instead of real electrons and positrons. Since their mass gap can often be freely tuned, it is much easier to create these light quasi-particles by an analogue of the Sauter-Schwinger effect. This motivates our proposal of a quantum simulator in which excitations of ultra-cold atoms moving in a bichromatic optical lattice represent particles and antiparticles (holes) satisfying a discretized version of the Dirac equation together with fermionic anti-commutation relations. Using the language of second quantization, we are able to construct an analogue of the spontaneous pair creation which can be realized in an (almost) table-top experiment.Comment: 21 pages, 10 figure

Superconductivity in a Topological Lattice Model with Strong Repulsion

The highly tunable nature of synthetic quantum materials -- both in the solid-state and cold atom contexts -- invites examining which microscopic ingredients aid in the realization of correlated phases of matter such as superconductors. Recent experimental advances in moir\'e materials suggest that unifying the features of the Fermi-Hubbard model and quantum Hall systems creates a fertile ground for the emergence of such phases. Here, we introduce a minimal 2D lattice model that incorporates exactly these features: time-reversal symmetry, band topology, and strong repulsive interactions. By using infinite cylinder density matrix renormalization group methods (cylinder iDMRG), we investigate the ground state phase diagram of this model. We find that it hosts an interaction-induced quantum spin Hall (QSH) insulator and demonstrate that weakly hole-doping this state gives rise to a superconductor at a finite circumference, with indications that this behavior persists on larger cylinders. At the aforementioned circumference, the superconducting phase is surprisingly robust to perturbations including additional repulsive interactions in the pairing channel. By developing a technique to probe the superconducting gap function in iDMRG, we phenomenologically characterize the superconductor. Namely, we demonstrate that it is formed from the weak pairing of holes atop the QSH insulator. Furthermore, we determine the pairing symmetry of the superconductor, finding it to be $p$-wave -- reminiscent of the unconventional superconductivity reported in experiments on twisted bilayer graphene (TBG). Motivated by this, we elucidate structural similarities and differences between our model and those of TBG in its chiral limit. Finally, to provide a more direct experimental realization, we detail an implementation of our Hamiltonian in a system of cold fermionic alkaline-earth atoms in an optical lattice.Comment: 27 pages (with 8 figures) + 35 pages supplementary (with 14 figures

Quantum transport in ultracold atoms

Ultracold atoms confined by engineered magnetic or optical potentials are ideal systems for studying phenomena otherwise difficult to realize or probe in the solid state because their atomic interaction strength, number of species, density, and geometry can be independently controlled. This review focuses on quantum transport phenomena in atomic gases that mirror and oftentimes either better elucidate or show fundamental differences with those observed in mesoscopic and nanoscopic systems. We discuss significant progress in performing transport experiments in atomic gases, contrast similarities and differences between transport in cold atoms and in condensed matter systems, and survey inspiring theoretical predictions that are difficult to verify in conventional setups. These results further demonstrate the versatility offered by atomic systems in the study of nonequilibrium phenomena and their promise for novel applications.Comment: 24 pages, 7 figures. A revie

Identifying topological edge states in 2D optical lattices using light scattering

We recently proposed in a Letter [Physical Review Letters 108 255303] a novel scheme to detect topological edge states in an optical lattice, based on a generalization of Bragg spectroscopy. The scope of the present article is to provide a more detailed and pedagogical description of the system - the Hofstadter optical lattice - and probing method. We first show the existence of topological edge states, in an ultra-cold gas trapped in a 2D optical lattice and subjected to a synthetic magnetic field. The remarkable robustness of the edge states is verified for a variety of external confining potentials. Then, we describe a specific laser probe, made from two lasers in Laguerre-Gaussian modes, which captures unambiguous signatures of these edge states. In particular, the resulting Bragg spectra provide the dispersion relation of the edge states, establishing their chiral nature. In order to make the Bragg signal experimentally detectable, we introduce a "shelving method", which simultaneously transfers angular momentum and changes the internal atomic state. This scheme allows to directly visualize the selected edge states on a dark background, offering an instructive view on topological insulating phases, not accessible in solid-state experiments.Comment: 17 pages, 10 figures. Revised and extended version, to appear in EJP Special Topic for the special issue on "Novel Quantum Phases and Mesoscopic Physics in Quantum Gases". Extended version of arXiv:1203.124

Magnetic crystals and helical liquids in alkaline-earth fermionic gases

The joint action of a synthetic gauge potential and of atomic contact repulsion in a one-dimensional alkaline-earth(-like) fermionic gas with nuclear spin I leads to the existence of a hierarchy of fractional insulating and conducting states with intriguing properties. We unveil the existence and the features of those phases by means of both analytical bosonization techniques and numerical methods based on the density-matrix renormalization group algorithm. In particular, we show that the gapless phases can support helical modes, whereas the gapped states, which appear under certain conditions, are characterised both by density and magnetic order. Several distinct features emerge solely for spin I larger than 1/2, thus making their study with cold-atoms unique. We will finally argue that these states are related to the properties of an unconventional fractional quantum Hall effect in the thin-torus limit. The properties of this hierarchy of states can be experimentally studied in state-of-the-art cold-atom laboratories