  Electronic properties like current flow are generally independent of the
electron's 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 phenomena 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.

Quantum Gases