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arXiv:cond-mat/0603083 · Physical Review Letters

Optically Induced Spin-Hall Effect in Atoms

Xiong-Jun Liu, Xin Liu, L. C. Kwek, C. H. Oh

Published Jan 11, 2007• 115 citations
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Abstract

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.

DOI
10.1103/physrevlett.98.026602

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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 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 a scheme to create an effective magnetic field for ultracold atoms in a planar geometry. The setup allows the experimental study of classical and quantum Hall effects in close analogy to solid-state systems including the possibility of finite currents. The present scheme is an extention of the proposal in Phys. Rev. Lett. 93, 033602 (2004), where the effective magnetic field is now induced for three-level $\ensuremath{\Lambda}$-type atoms by two counterpropagating laser beams with shifted spatial profiles. Under conditions of electromagnetically induced transparency the atom-light interaction has a space-dependent dark state, and the adiabatic center-of-mass motion of atoms in this state experiences effective vector and scalar potentials. The associated magnetic field is oriented perpendicular to the propagation direction of the laser beams. The field strength achievable is one flux quantum over an area given by the transverse beam separation and the laser wavelength. For a sufficiently dilute gas the field is strong enough to reach the lowest Landau level regime.
In this paper,the spin Hall effects induced by gauge fields is presented in cold atoms.For multi-level atoms interacting with external laser fields,e.g.,6Li,two-fold degenerate dressed states can be obtained under appropriate parameters configuration,which are defined as spin-up and spin-down in analogy with the spin-1/2 charged system.When the cold atoms moving in a spatially varying laser field,the effective spin-dependent gauge potential will lead to observable spin Hall currents that indicates the spin Hall effects.
We theoretically show that the spin Hall effect arises in a Bose-Einstein condensate (BEC) of neutral atoms interacting via the magnetic dipole-dipole interactions (MDDIs). Since the MDDI couples the total spin angular momentum and the relative orbital angular momentum of two colliding atoms, it works as a spin-orbit coupling. Thus, when we prepare a BEC in a magnetic sublevel m=0m=0m=0, thermally and quantum-mechanically excited atoms in the m=1m=1m=1 and $\ensuremath{-}1$ states feel the Lorentz-like forces in the opposite directions. This is the origin for the emergence of the spin Hall effect. We define the mass-current and spin-current operators from the equations of continuity and calculate the spin Hall conductivity from the off-diagonal current-current correlation function within the Bogoliubov approximation. We find that the correction of the current operators due to the MDDI significantly contributes to the spin Hall conductivity. A possible experimental situation is also discussed.
The alignment-orientation process is exactly treated for an alkali-like atom with purely electronic couplings. Analytic expressions for the circular polarization of the optical emission are given for specific types of anisotropic excitation in terms of the magnetic field and the spin-orbit parameter. No advanced formalism is used. It is shown how the hyperfine interaction with the electron orbital motion operates in a manner very similar to the purely electronic spin-orbit coupling, again leading to orbital orientation and to circularly polarized optical emission. Detailed computed results for alignment-orientation conversion for neutral helium are summarized, as are the results of experiments which directly exhibit circularly polarized emission due to the alignment-orientation effect in gases.