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arXiv:cond-mat/0402584 · Physical Review A

Vortex sorter for Bose-Einstein condensates

Graeme Whyte, John Veitch, Patrik Öhberg, Johannes Courtial

Published Jul 15, 2004• 3 citations
arXivHTMLPDF

Abstract

We have designed interferometers that sort Bose-Einstein condensates into their vortex components. The Bose-Einstein condensates in the two arms of the interferometer are rotated with respect to each other through fixed angles; different vortex components then exit the interferometer in different directions. The method we use to rotate the Bose-Einstein condensates involves asymmetric phase imprinting and is itself new. We have modeled rotation through fixed angles and sorting into vortex components with even and odd values of the topological charge of two-dimensional Bose-Einstein condensates in a number of states (pure or superposition vortex states for different values of the scattering length). Our scheme may have applications for quantum information processing.

DOI
10.1103/physreva.70.011603

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We have designed interferometers that sort Bose-Einstein condensates into their vortex components. The Bose-Einstein condensates in the two arms of the interferometer are rotated with respect to each other through fixed angles; different vortex components then exit the interferometer in different directions. The method we use to rotate the Bose-Einstein condensates involves asymmetric phase imprinting and is itself new. We have modeled rotation through fixed angles and sorting into vortex components with even and odd values of the topological charge of two-dimensional Bose-Einstein condensates in a number of states (pure or superposition vortex states for different values of the scattering length). Our scheme may have applications for quantum information processing.
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We propose a scheme for the generation of arbitrary coherent superpositions of vortex states in Bose-Einstein condensates (BEC) using the orbital-angular-momentum states of light. We devise a scheme to generate coherent superpositions of two such counterrotating states of light using well-known experimental techniques. We show that a specially designed Raman scheme allows for transfer of the optical vortex-superposition state onto an initially nonrotating BEC. This creates an arbitrary and coherent superposition of a vortex and antivortex pair in the BEC. The ideas presented here could be extended to generate entangled vortex states, design memories for the orbital-angular-momentum states of light, and perform other quantum information tasks. Applications to inertial sensing are also discussed.
We review the topic of quantized vortices in multicomponent Bose–Einstein condensates of dilute atomic gases, with an emphasis on the two-component condensates. First, we review the fundamental structure, stability and dynamics of a single vortex state in a slowly rotating two-component condensates. To understand recent experimental results, we use the coupled Gross–Pitaevskii equations and the generalized nonlinear sigma model. An axisymmetric vortex state, which was observed by the JILA group, can be regarded as a topologically trivial skyrmion in the pseudospin representation. The internal, coherent coupling between the two components breaks the axisymmetry of the vortex state, resulting in a stable vortex molecule (a meron pair). We also mention unconventional vortex states and monopole excitations in a spin-1 Bose–Einstein condensate. Next, we discuss a rich variety of vortex states realized in rapidly rotating two-component Bose–Einstein condensates. We introduce a phase diagram with axes of rotation frequency and the intercomponent coupling strength. This phase diagram reveals unconventional vortex states such as a square lattice, a double-core lattice, vortex stripes and vortex sheets, all of which are in an experimentally accessible parameter regime. The coherent coupling leads to an effective attractive interaction between two components, providing not only a promising candidate to tune the intercomponent interaction to study the rich vortex phases but also a new regime to explore vortex states consisting of vortex molecules characterized by anisotropic vorticity. A recent experiment by the JILA group vindicated the formation of a square vortex lattice in this system.
Three types of vortex-pair are identified in two-component Bose–Einstein condensates (BEC) of different kinds of spin-orbit coupling. One type holds the two vortices in one component of the twocomponent condensates. Both the other two types hold a vortex in each component of the twocomponent condensates, and exhibit meron-pair textures that have either null or unit topological charge, respectively. The cores of the two vortices are connected by a string of the relative phase jump. These vortex pairs can be generated from a vortex-free wave packet by incorporating different non- Abelian gauge field into the BEC. When a Rabi coupling is introduced, the distance between the two cores is effectively controlled by the Rabi coupling strength and a transition of vortex configurations is observed.
A vortex molecule is predicted in rotating two-component Bose-Einstein condensates whose internal hyperfine states are coupled coherently by an external field. A vortex in one component and one in the other are connected by a domain wall of the relative phase, constituting a "vortex molecule," which features a nonaxisymmetric (pseudo)spin texture with a pair of merons. The binding mechanism of the vortex molecule is discussed based on a generalized nonlinear sigma model and a variational ansatz. The anisotropy of vortex molecules is caused by the difference in the scattering lengths, yielding a distorted vortex-molecule lattice in fast rotating condensates.