Artificial gauge fields open the possibility to realize quantum many-body systems with ultracold atoms, by engineering Hamiltonians usually associated with electronic systems. In the presence of a periodic potential, artificial gauge fields may bring ultracold atoms closer to the quantum Hall regime. Here, we describe a one-dimensional lattice derived purely from effective Zeeman shifts resulting from a combination of Raman coupling and radio-frequency magnetic fields. In this lattice, the tunneling matrix element is generally complex. We control both the amplitude and the phase of this tunneling parameter, experimentally realizing the Peierls substitution for ultracold neutral atoms.

Electronic properties such as current flow are generally independent of the electron's spin angular momentum, an internal degree of freedom possessed by quantum particles. The spin Hall effect, first proposed 40 years ago, is an unusual class of phenomena in which flowing particles experience orthogonally directed, spin-dependent forces--analogous to the conventional Lorentz force that gives the Hall effect, but opposite in sign for two spin states. Spin Hall effects have been observed for electrons flowing in spin-orbit-coupled materials such as GaAs and InGaAs (refs 2, 3) and for laser light traversing dielectric junctions. Here we observe the spin Hall effect in a quantum-degenerate Bose gas, and use the resulting spin-dependent Lorentz forces to realize a cold-atom spin transistor. By engineering a spatially inhomogeneous spin-orbit coupling field for our quantum gas, we explicitly introduce and measure the requisite spin-dependent Lorentz forces, finding them to be in excellent agreement with our calculations. This 'atomtronic' transistor behaves as a type of velocity-insensitive adiabatic spin selector, with potential application in devices such as magnetic or inertial sensors. In addition, such techniques for creating and measuring the spin Hall effect are clear prerequisites for engineering topological insulators and detecting their associated quantized spin Hall effects in quantum gases. As implemented, our system realizes a laser-actuated analogue to the archetypal semiconductor spintronic device, the Datta-Das spin transistor.

Ultracold gases of interacting spin-orbit-coupled fermions are predicted to display exotic phenomena such as topological superfluidity and its associated Majorana fermions. Here, we experimentally demonstrate a route to strongly interacting single-component atomic Fermi gases by combining an s-wave Feshbach resonance (giving strong interactions) and spin-orbit coupling (creating an effective p-wave channel). We identify the Feshbach resonance by its associated atomic loss feature and show that, in agreement with our single-channel scattering model, this feature is preserved and shifted as a function of the spin-orbit-coupling parameters.

Interactions between particles can be strongly altered by their environment. We demonstrate a technique for modifying interactions between ultracold atoms by dressing the bare atomic states with light, creating an effective interaction of vastly increased range that scatters states of finite relative angular momentum at collision energies where only s-wave scattering would normally be expected. We collided two optically dressed neutral atomic Bose-Einstein condensates with equal, and opposite, momenta and observed that the usual s-wave distribution of scattered atoms was altered by the appearance of d- and g-wave contributions. This technique is expected to enable quantum simulation of exotic systems, including those predicted to support Majorana fermions.

Zitterbewegung, a force-free trembling motion first predicted for relativistic fermions like electrons, was an unexpected consequence of the Dirac equation's unification of quantum mechanics and special relativity. Though the oscillatory motion's large frequency and small amplitude have precluded its measurement with electrons, zitterbewegung is observable via quantum simulation. We engineered an environment for 87 Rb Bose-Einstein condensates where the constituent atoms behaved like relativistic particles subject to the one-dimensional Dirac equation. With direct imaging, we observed the submicrometre trembling motion of these clouds, demonstrating the utility of neutral ultracold quantum gases for simulating Dirac particles.

Spin-orbit coupling is an essential ingredient in topological materials, conventional and quantum-gas-based alike. Engineered spin-orbit coupling in ultracold-atom systems-unique in their experimental control and measurement opportunities-provides a major opportunity to investigate and understand topological phenomena. Here we experimentally demonstrate and theoretically analyze a technique for controlling spin-orbit coupling in a two-component Bose-Einstein condensate using amplitude-modulated Raman coupling.

Measurement techniques based upon the Hall effect are invaluable tools in condensed-matter physics. When an electric current flows perpendicular to a magnetic field, a Hall voltage develops in the direction transverse to both the current and the field. In semiconductors, this behavior is routinely used to measure the density and charge of the current carriers (electrons in conduction bands or holes in valence bands)-internal properties of the system that are not accessible from measurements of the conventional resistance. For strongly interacting electron systems, whose behavior can be very different from the free electron gas, the Hall effect's sensitivity to internal properties makes it a powerful tool; indeed, the quantum Hall effects are named after the tool by which they are most distinctly measured instead of the physics from which the phenomena originate. Here we report the first observation of a Hall effect in an ultracold gas of neutral atoms, revealed by measuring a Bose-Einstein condensate's transport properties perpendicular to a synthetic magnetic field. Our observations in this vortex-free superfluid are in good agreement with hydrodynamic predictions, demonstrating that the system's global irrotationality influences this superfluid Hall signal.superfluidity | synthetic gauge fields | ultracold atoms M icroscopically, the Hall effect (1) results from the Lorentz force F ¼ qv × B experienced by particles with charge q and velocity v moving in a uniform magnetic field B. In the plane perpendicular to B ¼ Be z , this force acts on a current with density J ¼ J x e x þ J y e y to generate an electrochemical potential gradient ∇V ¼ρ H J normal to J, where the Hall part of the 2D resistivity tensorρis antisymmetric. In conventional metals and semiconductors, the Hall resistivity ρ xy ¼ B∕qnðrÞ is related to the carriers' charge q and density nðrÞ, but not to the dissipative resistivity tensor ρ 0 ¼ ρ xx1 , where1 is the 2 × 2 identity matrix. Typically, experiments measure a sample's longitudinal and transverse voltages V xx and V xy (Fig. 1A) from which the resistivity tensor can be inferred (2). Here, we report an analogous transport measurement of the full resistivity tensor, including the antisymmetric contributions from the Hall effect, in a flattened elongated Bose-Einstein condensate (BEC) subjected to a synthetic magnetic field B à e z (in which only the charge-field product q à B à is defined; ref.3). The transport characteristics of systems with many particles and sufficiently strong interactions (Coulomb repulsion in electron gases and plasmas, or s-wave contact interactions in BECs) resemble those of classical fluids and are described by hydrodynamics. These hydrodynamics can describe ultracold Bose (4) and Fermi (5) gases, or characterize the collective modes-plasmons (6) and magnetoplasmons (7)-of 2D electron gases (2DEGs). We show that a BEC in a synthetic magnetic field obeys hydrodynamic equations similar to those describing a 2DEG in a uniform magnetic field. Drude Model and Hydrodynamic...

We experimentally investigate the role of localization on the adiabaticity of loading a Bose-Einstein condensate into a one-dimensional optical potential comprised of a shallow primary lattice plus one or two perturbing lattice(s) of incommensurate period. We find that even a very weak perturbation causes dramatic changes in the momentum distribution and makes adiabatic loading of the combined lattice much more difficult than for a single period lattice. We interpret our results using a band structure model and the one-dimensional Gross-Pitaevskii equation.Disorder plays an important role in many condensed matter systems, [1,2] with deep connections to quantum chaos [3], but can be difficult to systematically study due to the challenge of creating reproducible and quantifiable disorder. The control available in ultra-cold atom systems [4] makes it an attractive platform to study disorder [5,6,7,8]. To date much of the work adding disorder to ultra-cold atom systems has explored timeindependent properties, but the long timescales associated with cold atoms allows investigation of dynamical properties as well (see [5, 9, 10, 11] and ref. therein). In this work we examine the ability of a quasi-disordered system to adiabatically follow changes in the Hamiltonian. The presence of disorder produces a complicated eigenvalue spectrum, which greatly affects the adiabaticity criteria. The physics of localization phenomena also has a significant impact on time-dependent processes, such as adiabaticity. Small perturbations to the Hamiltonian can cause large changes to the ground state wavefunction over large length scales, making it difficult for the system to adiabatically follow changes. One recent theoretical study shows that adiabaticity in gapless systems is non-trivial, particularly in lower dimensions [12]. Here we show that even in a gapped system such as ours, adiabaticity is complicated by the presence of disorder.We study adiabaticity in a quasi-disordered system by adding one or two weak incommensurate lattices to a one-dimensional optical lattice loaded with a BoseEinstein condensate (BEC). Localization occurs in both disordered and strictly incommensurate potentials [8,13,14,15] although with distinct differences, which tend to disappear in finite-sized systems such as ours. We observe a complex momentum distribution of the atoms due to the presence of weak perturbing lattices following a ramped loading process that would be nearly adiabatic for a single lattice. We gain insight into the distributions from single-particle band structure, and observe that the effects of the perturbations disappear as interactions increase, as they suppress the long wavelength density modulation of the wavefunction.We form a BEC of ∼10 4 87 Rb atoms in the state |F = 2, m f = 2 in a magnetic trap with ω x ≈ ω z ≈ 2π×410 Hz and ω y ≈ 2π×120 Hz. To reduce the effects of interactions, the trap is subsequently weakened giving final frequencies ω x ≈ 2π×40 Hz, ω y ≈ 2π×20 Hz, and ω z ≈ 2π×30 Hz. We load the BEC into a 1D optical pot...