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arXiv:1310.0134 · Physical Review Letters

Observation of a Geometric Hall Effect in a Spinor Bose-Einstein Condensate with a Skyrmion Spin Texture

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

Published Dec 10, 2013• 37 citations
arXivHTMLPDF

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.

DOI
10.1103/physrevlett.111.245301

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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.
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 present the creation and time evolution of two-dimensional Skyrmion excitations in an antiferromagnetic spinor Bose-Einstein condensate. Using a spin rotation method, the Skyrmion spin textures were imprinted on a sodium condensate in a polar phase, where the two-dimensional Skyrmion is topologically protected. The Skyrmion was observed to be stable on a short time scale of a few tens of ms but to dynamically deform its shape and eventually decay to a uniform spin texture. The deformed spin textures reveal that the decay dynamics involves breaking the polar phase inside the condensate without having topological charge density flow through the boundary of the finite-sized sample. We discuss the possible formation of half-quantum vortices in the deformation process.
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.
Abstract We explore the spin texture dynamics of a harmonically trapped spin-1 Bose–Einstein condensate with Rashba spin–orbit coupling and ferromagnetic spin-exchange interactions under a sinusoidally varying magnetic field along the x-direction. This interplay yields an intrinsic spin texture in the ground state, forming a linear chain of alternating skyrmions at the saddle points of the magnetic field. Our study analyzes the spin-mixing dynamics for both a freely evolving and a controlled longitudinal magnetization. The spin-1 system exhibits the Einstein–de Haas effect for the first case, for which an exchange between the total orbital angular momentum and the spin angular momentum is observed, resulting in minimal oscillations about the initial position of the skyrmion chain. However, for the fixed magnetization dynamics, the skyrmion chain exhibits ample angular oscillations about the equilibrium position, with the temporary formation of new skyrmions to facilitate the oscillatory motion. For the case of fixed magnetization, this contrast now stems from the exchange between the canonical and spin-dependent contribution to the orbital angular momentum. The variation in canonical angular momentum is linked to the angular oscillations, while the spin-dependent angular momentum accounts for the creation or annihilation of skyrmions. We confirm the presence of scissors mode excitations in the spin texture due to the angular skyrmion oscillations.