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Observation of a Geometric Hall Effect in a Spinor Bose-Einstein Condensate

Jae-yoon Choi, Seji Kang, Sang Won Seo, Woo Jin Kwon, Yong-il Shin

Published Oct 1, 2013• 1 citation
OpenAlex

Abstract

For a spin-carrying particle moving in a spatially varying magnetic field, effective electromagnetic forces can arise due to the geometric phase associated with adiabatic spin rotation of the particle. We report the observation of a geometric Hall effect in a spinor Bose-Einstein condensate with a skyrmion spin texture. Under translational oscillations of the spin texture, the condensate resonantly develops a circular motion in a harmonic trap, demonstrating the existence of an effective Lorentz force. When the condensate circulates, quantized vortices are nucleated in the boundary region of the condensate and the vortex number increases over 100 without significant heating. We attribute the vortex nucleation to the shearing effect of the effective Lorentz force from the inhomogeneous effective magnetic field.

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For a spin-carrying particle moving in a spatially varying magnetic field, effective electromagnetic forces can arise due to the geometric phase associated with adiabatic spin rotation of the particle. We report the observation of a geometric Hall effect in a spinor Bose-Einstein condensate with a skyrmion spin texture. Under translational oscillations of the spin texture, the condensate resonantly develops a circular motion in a harmonic trap, demonstrating the existence of an effective Lorentz force. When the condensate circulates, quantized vortices are nucleated in the boundary region of the condensate and the vortex number increases over 100 without significant heating. We attribute the vortex nucleation to the shearing effect of the effective Lorentz force from the inhomogeneous effective magnetic field.
For a spin-carrying particle moving in a spatially varying magnetic field, effective electromagnetic forces can arise due to the geometric phase associated with adiabatic spin rotation of the particle. We report the observation of a geometric Hall effect in a spinor Bose-Einstein condensate with a Skyrmion spin texture. Under translational oscillations of the spin texture, the condensate resonantly develops a circular motion in a harmonic trap, demonstrating the existence of an effective Lorentz force. When the condensate circulates, quantized vortices are nucleated in the boundary region of the condensate and the vortex number increases over 100 without significant heating. We attribute the vortex nucleation to the shearing effect of the effective Lorentz force from the inhomogeneous effective magnetic field.
A method to produce a spin-dependent rotating potential using near-resonant circularly polarized laser beams is proposed. It is shown that half-quantum vortices are nucleated in a spinor Bose-Einstein condensate (BEC) with an antiferromagnetic interaction. In contrast to the vortex nucleation in a scalar BEC, the spin-vortex nucleation occurs at a low rotation frequency ($\ensuremath{\simeq}0.1{\ensuremath{\omega}}_{\ensuremath{\perp}}$ with ${\ensuremath{\omega}}_{\ensuremath{\perp}}$ being the radial trap frequency) in a short nucleation time $\ensuremath{\simeq}50\phantom{\rule{0.3em}{0ex}}\mathrm{ms}$ without dissipation. A method for nondestructive measurement of half-quantum vortices is discussed.
We investigate an experimental method for imprinting Skyrmion spin textures in a spinor Bose–Einstein condensate by rapidly moving the zero-field center of a three-dimensional (3D) quadrupole magnetic field through the condensate. Various excitations such as 2D Skyrmions and coreless vortices were created in spin-1 sodium condensates, initially prepared in a uniform polar or ferromagnetic phase. The spin textures were characterized with the spatial distribution of the spin tilt angle, which is found to be in good quantitative agreement with the local description of single spins under the field rotation. We demonstrate the creation of a highly charged Skyrmion in a trapped condensate by applying the imprinting process multiple times.
The recently realized multicomponent Bose-Einstein condensates provide opportunities to explore the rich physics brought about by the spin degrees of freedom. For instance, we can study spin waves and phase separation, macroscopic quantum tunneling, Rabi oscillations, the coupling between spin gradients and superfluid flow, squeezed spin states, vortices and other topological excitations. Theoretically, there have been already some studies of the ground-state properties of these systems and their line-like vortex excitations. In analogy with nuclear physics or the quantum Hall effect, we explore here the possibility of observing point-like topological excitations or skyrmions. These are nontrivial spin textures that in principle can exist in a spinor Bose-Einstein condensate. In particular, we investigate the stability of skyrmions in a fictitious spin-1/2 condensate of Rb87 atoms. We find that skyrmions can exist in this case only as a metastable state, but with a lifetime of the order of, or even longer than, the typical lifetime of the condensate itself. In addition to determining the size and the lifetime of the skyrmion, we also present its spin texture and finally briefly consider its dynamical properties.
We investigate the rotational properties of a Bose-Einstein condensate (BEC) in an effective magnetic field. The corresponding gauge potential is optically generated, and based on the adiabatic motion of the atoms. We demonstrate that the nucleation of vortices is seeded by instabilities in surface excitations and show that this picture also holds when the applied effective magnetic field is not homogeneous. The eventual configuration of vortices in the cloud depends on the geometry of the applied field.
Gauge fields are ubiquitous in modern quantum physics. In superfluids, quantized vortices can be induced by gauge fields. Here we demonstrate the first experimental observation of vortex nucleations in light-dressed spinor Bose-Einstein condensates under radially localized synthetic magnetic fields. The light-induced spin-orbital-angular-momentum coupling creates azimuthal gauge potentials A[over →] for the lowest-energy spinor branch dressed eigenstate. The observation of the atomic wave function in the lowest-energy dressed eigenstate reveals that vortices nucleate from the cloud center of a vortex-free state with canonical momentum p[over →]=0. This is because a large circulating azimuthal velocity field ∝p[over →]-A[over →] at the condensate center results in a dynamically unstable localized excitation that initiates vortex nucleations. Furthermore, the long-time dynamics to reach the ground state stops in a metastable state when |A[over →]| is not sufficiently large. Our observation has reasonable agreement with the time-dependent Gross-Pitaevskii simulations.