Electronic properties like current flow are generally independent of the electrons spin angular momentum, an internal degree of freedom present in quantum particles. The spin Hall effects (SHEs), first proposed 40 years ago, are an unusual class of p
henomena where flowing particles experience orthogonally directed spin-dependent Lorentz-like forces, analogous to the conventional Lorentz force for the Hall effect, but opposite in sign for two spin states. Such spin Hall effects have been observed for electrons flowing in spin-orbit coupled materials such as GaAs or InGaAs 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, in excellent agreement with our calculations. This atomtronic circuit element behaves as a new type of velocity-insensitive adiabatic spin-selector, with potential application in devices such as magnetic or inertial sensors. In addition, such techniques --- for both creating and measuring the SHE --- are clear prerequisites for engineering topological insulators and detecting their associated quantized spin Hall effects in quantum gases. As implemented, our system realized a laser-actuated analog to 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-co
mponent 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.
Zitterbewegung, a force-free trembling motion first predicted for relativistic fermions like electrons, was an unexpected consequence of the Dirac equations unification of quantum mechanics and special relativity. Though the oscillatory motions large
frequency and small amplitude have precluded its measurement with electrons, zitterbewegung is observable via quantum simulation. We engineered an environment for 87Rb Bose-Einstein condensates where the constituent atoms behaved like relativistic particles subject to the one-dimensional Dirac equation. With direct imaging, we observed the sub-micrometer trembling motion of these clouds, demonstrating the utility of neutral ultracold quantum gases for simulating Dirac particles.
