THE SPIN HALL EFFECT IN A QUANTUM GAS
Matthew Beeler, Ross Williams, Karina Jiménez-García, Lindsay LeBlanc, Abigail Perry, and Ian Spielman
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 materials such as GaAs or InGaAs or laser light traversing dielectric junctions. Here we present the realization of a SHE in a quantum gas moving through an optical ﬁeld. By engineering a spatially inhomogenous 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 technique – for both creating and measuring the SHE – is a clear prerequisite for understanding exotic materials such as 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.