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arXiv:1306.2829 · Physical Review A

Atomic spin-orbit coupling synthesized with magnetic-field-gradient pulses

Zhi-Fang Xu, Li You, Masahito Ueda

Published Jun 25, 2013• 113 citations
arXivHTMLPDF

Abstract

We discuss a general scheme for creating atomic spin-orbit coupling (SOC) such as the Rashba or Dresselhaus types using magnetic-field-gradient pulses. In contrast to conventional schemes based on adiabatic center-of-mass motion with atomic internal states restricted to a dressed-state subspace, our scheme works for the complete subspace of a hyperfine-spin manifold by utilizing the coupling between the atomic magnetic moment and external magnetic fields. A space-dependent pulsed magnetic field acts as an internal-state-dependent impulse, thereby coupling the atomic internal spin with its orbital center-of-mass motion, as in the Einstein--de Haas effect. This effective coupling can be dynamically manipulated to synthesize SOC of any type (Rashba, Dresselhaus, or any linear combination thereof). Our scheme can be realized with most experimental setups of ultracold atoms and is especially suited for atoms with zero nuclear spins.

DOI
10.1103/physreva.87.063634

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We discuss a general scheme for creating atomic spin-orbit coupling (SOC) such as the Rashba or Dresselhaus types using magnetic-field-gradient pulses. In contrast to conventional schemes based on adiabatic center-of-mass motion with atomic internal states restricted to a dressed-state subspace, our scheme works for the complete subspace of a hyperfine-spin manifold by utilizing the coupling between the atomic magnetic moment and external magnetic fields. A space-dependent pulsed magnetic field acts as an internal-state-dependent impulse, thereby coupling the atomic internal spin with its orbital center-of-mass motion, as in the Einstein--de Haas effect. This effective coupling can be dynamically manipulated to synthesize SOC of any type (Rashba, Dresselhaus, or any linear combination thereof). Our scheme can be realized with most experimental setups of ultracold atoms and is especially suited for atoms with zero nuclear spins.
Spin orbit coupling (SOC) for neutral atoms can be synthesized with pulsed or time modulating gradient magnetic field (GMF). This is confirmed through the studies of collective dipole oscillations for a spin-1 atomic condensate in a harmonic trap after abruptly turning on SOC and adiabatically adjusted equilibrium states when SOC strength is slowly ramped up. Further measurements reveal that SOC can be enhanced when the GMF modulation frequency approaches harmonic trap frequency. Additionally, we discuss how the technique of pulsed GMF can be used to synthesize space-period magnetic fields, or magnetic lattices.
We report the observation of synthesized spin-orbit coupling (SOC) for ultracold spin-1 (87)Rb atoms. Different from earlier experiments where a one dimensional (1D) atomic SOC of pseudo-spin-1/2 is synthesized with Raman laser fields, the scheme we demonstrate employs a gradient magnetic field (GMF) and ground-state atoms, thus is immune to atomic spontaneous emission. The strength of SOC we realize can be tuned by changing the modulation amplitude of the GMF, and the effect of the SOC is confirmed through the studies of: 1) the collective dipole oscillation of an atomic condensate in a harmonic trap after the synthesized SOC is abruptly turned on; and 2) the minimum energy state at a finite adiabatically adjusted momentum when SOC strength is slowly ramped up. The condensate coherence is found to remain very good after driven by modulating GMFs. Our scheme presents an alternative means for studying interacting many-body systems with synthesized SOC.
We study the possibility for generating a new type of spin-orbit coupling for the center-of-mass motion of cold atoms, using laser beams that resonantly couple NNN atomic internal ground states to an extra state. After a general analysis of the scheme, we concentrate on the tetrapod setup (N=4N=4N=4) where the atomic state can be described by a three-component spinor, evolving under the action of a Rashba-Dresselhaus-type spin-orbit coupling for a spin 1 particle. We illustrate a consequence of this coupling by studying the negative refraction of atoms at a potential step and show that the amplitude of the refracted beam is significantly increased in comparison to the known case of spin 1/21/21/2 Rashba-Dresselhaus coupling. Finally, we explore a possible implementation of this tetrapod setup, using stimulated Raman couplings between Zeeman sublevels of the ground state of alkali-metal atoms.
Spin-orbit coupling (SOC) is at the heart of many exotic band structures and can give rise to many-body states with topological order. Here we present a general scheme based on a combination of microwave driving and lattice shaking for the realization of two-dimensional SOC with ultracold atoms in systems with inversion symmetry. We show that the strengths of Rashba and Dresselhaus SOC can be independently tuned in a spin-dependent square lattice. More generally, our method can be used to open gaps between different spin states without breaking time-reversal symmetry. We demonstrate that this allows for the realization of topological insulators with nontrivial spin textures closely related to the Kane-Mele model.
We explore a way of producing the Rashba spin-orbit coupling (SOC) for ultracold atoms by using a two-component (spinor) atomic Bose-Einstein condensate (BEC) confined in a bilayer geometry. The SOC of the Rashba type is created if the atoms pick up a $\ensuremath{\pi}$ phase after completing a cyclic transition between four combined spin-layer states composed of two spin and two layer states. The cyclic coupling of the spin-layer states is carried out by combining an intralayer Raman coupling and an interlayer laser assisted tunneling. We theoretically determine the ground-state phases of the spin-orbit-coupled BEC for various strengths of the atom-atom interaction and the laser-assisted coupling. It is shown that the bilayer scheme provides a diverse ground-state phase diagram. In an intermediate range of the atom-light coupling two interlacing lattices of half-skyrmions and half-antiskyrmions are spontaneously created. In the strong-coupling regime, where the SOC of the Rashba type is formed, the ground state represents plane-wave or standing-wave phases depending on the interaction between the atoms. A variational analysis is shown to be in good agreement with the numerical results.