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Journal of South China Normal University

LIGHT-INDUCED SPIN HALL EFFECTS IN COLD ATOMS

Gao Zong-ren

Published Jan 1, 2008• 0 citations
OpenAlex

Abstract

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.

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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.
The adiabatic motion of ultra-cold, multi-level atoms in spatially varying laser fields creating a dark state can give rise to effective gauge potentials. We show that these potentials lead to effective magnetic fields if the light fields possess a relative orbital angular momentum. This allows to study quantum-Hall like effects in ultra-cold atomic gases in various geometries. If the atom-light interaction creates several degenerate adiabatic eigenstates, the associated gauge potentials are non-Abelian. A pair of such degenerate dark states emerges e.g. if laser fields couple three internal states of an atom to a fourth common one under pairwise two--photon-resonance conditions. For this so-called tripod scheme we derive general conditions for truly non-Abelian gauge potentials and discuss special examples. In particular we show that using orthogonal laser beams with orbital angular momentum an effective magnetic field can be generated that has a monopole component.
A technique is described by which light-induced gauge potentials allow systems of ultracold neutral atoms to behave like charged particles in a magnetic field. Here, atoms move in a uniform laser field with a spatially varying Zeeman shift and experience an effective magnetic field. This technique is applicable for atoms with two or more internal ground states. Finally, an explicit model of the system using a single-mode two-dimensional Gross-Pitaevskii equation yields the expected vortex lattice.
Synthetic gauge fields for ultracold neutral atoms-engineered using the interaction between laser fields and the atoms' internal 'spin' degrees of freedom-provide promising techniques for generating the large (synthetic) magnetic fields required to reach the fractional quantum Hall (FQH) limit in quantum gases, bosonic or fermionic alike.Because neutral atoms can move in a nearly disorder-free environment and they have extremely simple contact interactions, the resulting FQH states would be revealed in their most essential form.Moreover, bosonic FQH states represent a new frontier and have never been seen in any setting.Going beyond electromagnetismʼs conventional scalar gauge field, it is possible to create more general non-Abelian gauge potentials.When these are spatially uniform, they are equivalent to spin-orbit coupling familiar in material systems, and can lead to cold atom analogs of topological insulators and topological superconductors.In this tutorial, we introduce basic concepts underlying these gauge fields, making connections to the Aharonov-Bohm phase and geometric phase.We focus on the system of neutral atoms 'dressed' by multiple laser beams, where the eigenstates of the resulting Hamiltonian are known as dressed states.Synthetic gauge potentials arise from the unitary transformation required to express these dressed states in terms of the laser-free eigenstates.We discuss stability of laser-dressed atoms corresponding to the adiabatic condition and the probability of non-adiabatic transitions.Adopting both the semiclassical and quantum mechanical approaches, we demonstrate they agree in the suitable limit.We also analyze using both the conventional adiabatic picture and exact picture, where the kinetic energy is neglected in the former and retained in the latter picture.
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.
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.