Matthew C. Beeler, Ross A. Williams, Karina K. Jimenez Garcia, Lindsay J. LeBlanc, Abigail R. Perry, Ian B. Spielman
Electronic properties like current ﬂow are usually unaffected by the electrons spin angular momentum, an internal degree of freedom present in quantum particles that can usually be either up or down. The spin-Hall effects (SHEs), ﬁrst proposed 40 years ago [1, 2], are an unusual class of phenomena where currents of ﬂowing particles can induce orthogonally di- rected Lorentz-like forces, opposite in sign for the two spin states: current-dependent spin- motive forces [3, 4] analogous to the Hall effects current-dependent electro-motive force. Such spin-Hall effects have been observed for electrons ﬂowing in materials such as GaAs or InGaAs [5, 6]; for laser light traversing dielectric junctions ; and now for the ﬁrst time in quantum gases moving through an optical ﬁeld. By engineering a spatially inhomogenous spin-orbit coupling ﬁeld for our quantum gas, we explicitly introduce and measure the req- uisite spin-dependent Lorentz forces (in excellent agreement with our calculations). This technique for both creating and measuring the SHE is a clear prerequisite for design- ing topological insulators and detecting their associated quantized spin-Hall effects  in quantum gases. Even as constructed, our system realizes an analog to the Datta-Das spin transistor, here actuated by laser ﬁelds.
, Williams, R.
, Jimenez, K.
, LeBlanc, L.
, Perry, A.
and Spielman, I.
The Spin Hall Effect in a Quantum Gas, Nature, [online], https://doi.org/10.1038/nature12185
(Accessed December 1, 2023)