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 ago1, 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 junctions4. 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 magnetic5 or inertial6 sensors. In addition, such techniques for creating and measuring the spin Hall effect are clear prerequisites for engineering topological insulators7,8 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 transistor9,10.
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This work was partially supported by the DARPA OLE programme; the ARO atomtronics MURI, NIST, and the US NSF through the PFC at the JQI. M.C.B. acknowledges NIST-ARRA, L.J.L. acknowledges support from NSERC and K.J.-G. acknowledges CONACYT.
The authors declare no competing financial interests.
This file contains a Supplementary Discussion, additional references and a Supplementary Figure. The Supplementary Discussion and figure contain a specific proposal to extend the technique used in our manuscript to realize the quantum spin Hall effect in a similar experimental system. Calculations are explained and illustrated for realistic example experimental parameters. (PDF 194 kb)
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Beeler, M., Williams, R., Jiménez-García, K. et al. The spin Hall effect in a quantum gas. Nature 498, 201–204 (2013). https://doi.org/10.1038/nature12185
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