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arXiv:cond-mat/9908276 · Physical Review A

Topological phase preparation in a pair of atomic Bose-Einstein condensates

Janne Ruostekoski

Published Mar 13, 2000• 18 citations
arXivHTMLPDF

Abstract

We propose a method of generating skyrmion vortices in a pair of Bose-Einstein condensates occupying two internal states of the same atom. We show that a variety of different periodic arrays of vortices may be prepared with an appropriate superposition of orthogonal standing electromagnetic waves inducing a coherent coupling between the two condensates.

DOI
10.1103/physreva.61.041603

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We propose a method of generating skyrmion vortices in a pair of Bose-Einstein condensates occupying two internal states of the same atom. We show that a variety of different periodic arrays of vortices may be prepared with an appropriate superposition of orthogonal standing electromagnetic waves inducing a coherent coupling between the two condensates.
We propose a method of generating a vortex ring in a Bose-Einstein condensate by means of electromagnetically induced atomic transitions. Some remnant population of atoms in a second internal state remains within the toroidal trap formed by the mean-field repulsion of the vortex ring. This population can be removed, or it can be made to flow around the torus (i.e., within the vortex ring). If this flow has a unit topological winding number, the entire structure formed by the two condensates is an example of a three-dimensional Skyrmion texture.
Abstract Observations of Bose–Einstein condensates—macroscopic populations of ultracold atoms occupying a single quantum state—in dilute alkali-metal and hydrogen gases have stimulated a great deal of research into the statistical physics of weakly interacting quantum degenerate systems1, 2. Recent experiments offer a means of exploring fundamental low-temperature physics in a controllable manner. A current experimental goal in the study of trapped Bose gases is the observation of superfluid-like behaviour, analogous to the persistent currents seen in superfluid liquid helium which flow without observable viscosity. The ‘super’ properties of Bose-condensed systems occur because the macroscopic occupation of a quantized mode provides a stabilizing mechanism that inhibits decay through thermal relaxation3. Here we show how to selectively generate superfluid vortex modes with different angular momenta in a Bose–Einstein condensate. Our approach involves solving the time-dependent equation of motion of a two-component condensate with strongly coupled internal atomic states, as recently investigated experimentally4, 5. The generation of vortices relies on the coupling between the states (achieved by applying an electromagnetic field), combined with mechanical rotation of the trapping potentials which confine the condensate.
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.
Coupled coaxially stacked toroidal condensates with persistent currents suggest an appealing physical platform for investigation of various phenomena related to interacting superflows from Josephson effects in the regime of weak interactions to the quantum Kelvin-Helmholtz instability for merging rings. We suggest experimentally accessible methods to prepare states with different topological charges in two coupled coaxial ring-shaped atomic Bose-Einstein condensates. Our results open up the way to direct observation of rotational Josephson vortices in atomic Bose-Einstein condensates.
The recent experimental realization of spin-orbit coupling (SOC) in spin-1 ultracold atoms opens up an interesting avenue for exploring new quantum states and novel quantum phenomena in large-spin systems. Two types of two-dimensional double-pair vortices that are connected by a domain-wall can be accommodated in the antiferromagnetic spin-1 Bose–Einstein condensate (BEC). One type, named a 2D double-pair skyrmion, which differs from the conventional 2D skyrmion in the F = 1 polar BEC, hosts a pair of vortices and displays a meron-pair texture with a unit topological charge. The other type has a meron-pair texture but with null topological charge. These two types of double-pair vortices can be naturally generated from a vortex-free Gaussian wave packet by incorporating a non-Abelian gauge field into the spinor condensate.