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arXiv:1308.6349 · Physical Review Letters

Spin-Orbit Coupling and Quantum Spin Hall Effect for Neutral Atoms without Spin Flips

Colin J. Kennedy, Georgios A. Siviloglou, Hirokazu Miyake, William Cody Burton, Wolfgang Ketterle

Published Nov 25, 2013• 148 citations
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Abstract

We propose a scheme which realizes spin-orbit coupling and the quantum spin Hall effect for neutral atoms in optical lattices without relying on near resonant laser light to couple different spin states. The spin-orbit coupling is created by modifying the motion of atoms in a spin-dependent way by laser recoil. The spin selectivity is provided by Zeeman shifts created with a magnetic field gradient. Alternatively, a quantum spin Hall Hamiltonian can be created by all-optical means using a period-tripling, spin-dependent superlattice.

DOI
10.1103/physrevlett.111.225301

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We propose a scheme which realizes spin-orbit coupling and the quantum spin Hall effect for neutral atoms in optical lattices without relying on near resonant laser light to couple different spin states. The spin-orbit coupling is created by modifying the motion of atoms in a spin-dependent way by laser recoil. The spin selectivity is provided by Zeeman shifts created with a magnetic field gradient. Alternatively, a quantum spin Hall Hamiltonian can be created by all-optical means using a period-tripling, spin-dependent superlattice.
We propose an optical means to realize the spin-Hall effect (SHE) in a neutral atomic system by coupling the internal spin states of atoms to radiation. The interaction between the external optical fields and the atoms creates effective magnetic fields that act in opposite directions on "electrically" neutral atoms with opposite spin polarizations. This effect leads to a Landau level structure for each spin orientation in direct analogy with the familiar SHE in semiconductors. The conservation and topological properties of the spin current, and the creation of a pure spin current are discussed.
We propose and demonstrate a new approach for realizing spin-orbit coupling with ultracold atoms. We use orbital levels in a double-well potential as pseudospin states. Two-photon Raman transitions between left and right wells induce spin-orbit coupling. This scheme does not require near resonant light, features adjustable interactions by shaping the double-well potential, and does not depend on special properties of the atoms. A pseudospinor Bose-Einstein condensate spontaneously acquires an antiferromagnetic pseudospin texture, which breaks the lattice symmetry similar to a supersolid.
We propose a scheme for generating Rashba spin-orbit coupling and a perpendicular Zeeman field simultaneously for cold fermionic atoms in a harmonic trap through the coupling between atoms and laser fields. The realization of Rashba spin-orbit coupling and a perpendicular Zeeman field provides opportunities for exploring many topological phenomena using cold fermionic atoms. We focus on the intrinsic anomalous Hall effect and show that it may be observed through the response of atomic density to a rotation of the harmonic trap.
Bloch oscillations appear for a particle in a weakly tilted periodic potential. The intrinsic spin Hall effect is an outcome of a spin-orbit coupling. We demonstrate that both of these phenomena can be realized simultaneously in a gas of weakly interacting ultracold atoms exposed to a tilted optical lattice and to a set of spatially dependent light fields inducing an effective spin-orbit coupling. It is found that both the spin Hall and the Bloch oscillation effects may coexist, showing, however, a strong correlation between the two. These correlations are manifested as a transverse spin current oscillating in-phase with the Bloch oscillations. On top of the oscillations originating from the periodicity of the model, a trembling motion is found which is believed to be atomic Zitterbewegung. It is argued that the damping of these Zitterbewegung oscillations may to a large extent be prevented in the present setup considering a periodic optical lattice potential.
Spin-orbit coupling (SOC) can give rise to interesting physics, from spin Hall to topological insulators, in condensed matter systems. Recently, this topical area has extended into atomic quantum gases in searching for artificial or synthetic gauge potentials. The prospects of tunable interaction and quantum state control promote neutral atoms as nature's quantum emulators for SOC. Lin et al. recently demonstrated a special form of the SOC ${k}_{x}{\ensuremath{\sigma}}_{y}$, which they interpret as an equal superposition of Rashba and Dresselhaus couplings in Bose-condensed atoms [Lin, Jim\'enez-Garc\'{\i}a, and Spielman, Nature (London) 471, 83 (2011)]. This work reports a method of implementing arbitrary forms of SOC by switching between two pairs of Raman laser pulses like the method used by Lin et al. While one pair affects ${k}_{x}{\ensuremath{\sigma}}_{y}$ for some time, a second pair creates ${k}_{y}{\ensuremath{\sigma}}_{y}$ at other times with Raman pulses from different directions and a subsequent spin rotation into $\ifmmode\pm\else\textpm\fi{}{k}_{y}{\ensuremath{\sigma}}_{x}$. With a sufficient number of pulses, the effective actions from different durations are small and accumulate in the same exponent despite the fact that ${k}_{x}{\ensuremath{\sigma}}_{y}$ and $\ifmmode\pm\else\textpm\fi{}{k}_{y}{\ensuremath{\sigma}}_{x}$ do not commute. Our scheme involves no added complication and can be demonstrated within current experiments. It applies equally to bosonic or fermionic atoms.