The spin Hall effect in a quantum gas

Abstract

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 ago, 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 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, 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 magnetic or inertial sensors. In addition, such techniques for creating and measuring the spin Hall effect are clear prerequisites for engineering topological insulators 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 transistor.

Global phase diagram of two-component Bose gases in antiparallel magnetic fields

“…[4] was still in a classical regime, the physical settings of Refs. [4][5][6] show striking resemblances with quantum spin Hall (QSH) systems studied in semiconductors.…”

“…By optically coupling internal states of atoms, a nearly uniform synthetic magnetic field has been created [3], opening up a new avenue towards the realization of quantum Hall (QH) states. Moreover, magnetic fields of mutually antiparallel directions have been optically generated in two-component (pseudospin- 1 2 ) Bose gases, allowing observation of a spin Hall effect arising from spin-dependent Lorentz forces [4]. There have also been proposals to realize similar gauge fields by inducing laser-assisted tunneling in tilted optical lattices [5,6].…”

Stroboscopic versus nonstroboscopic dynamics in the Floquet realization of the Harper-Hofstadter Hamiltonian

“…Experimentally, cold atoms' unique controllability was employed to observe dynamical localisation and phase-coherence in strongly shaken bosonic systems [19][20][21][22][23][24] . This paved the way towards generating extremely strong artificial magnetic fields 25 in lattice models, which recently culminated in the realisation of the Harper-Hofstadter model 26,27 , the Quantum Spin Hall Effect 28,29 , and Floquet topological insulators 30,31 .…”

Valley-dependent gauge fields for ultracold atoms in square optical superlattices

“…In this case, the pseudo-magnetic field can be nonuniform and even zero as A is a nonzero constant, which is much easer to be achieved by selecting the laser configurations [32]. Note that atomic spin Hall effects [36] have been observed in a very recent experiment [37]. Similarly, by subjecting the system to a valley-dependent electric field, we may produce an atomic topological edge current related to the valley degree of freedom [28].…”