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Physical Review A

Nontopological vortex in a two-component Bose-Einstein condensate

Q‐Han Park, Joseph H. Eberly

Published Aug 24, 2004• 31 citations
Publisher

Abstract

We present a systematic study on a class of stable vortex solutions in a two-component Bose-Einstein condensate. They are nontopological in nature and possess continuous angular momenta. When coupled to external fields, nontopological vortices exhibit ``spin'' dynamical behavior and develop a Berry's phase under the adiabatic change of external fields which can be directly measured. We explain a method to create them experimentally by using phase imprinting.

DOI
10.1103/physreva.70.021602

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We present a systematic study on a class of stable vortex solutions in a two-component Bose-Einstein condensate. They are nontopological in nature and possess continuous angular momenta. When coupled to external fields, nontopological vortices exhibit ``spin'' dynamical behavior and develop a Berry's phase under the adiabatic change of external fields which can be directly measured. We explain a method to create them experimentally by using phase imprinting.
Summary form only given. Vortex in a BEC is a circular flow with a quantized angular momentum. In a two-component BEC, the internal phase space can be enlarged to two sphere so that non topological vortices carrying continuous angular momentum are possible. In this talk, we present a novel class of non topological vortices and describe their rich static and dynamical properties. Each components of these non topological vortices can possess rich spatial structures while their total intensities have simple radial profiles similar to those of conventional topological vortices. These vortices carry continuous angular momenta varying between two integer momentum numbers m and -m, whose physical meaning will be explained in the Poincare sphere picture Particularly, we show that external drive can be coupled easily to a non topological vortex and be used to steer a vortex which sets internal spinor motions. We also make an experimental suggestion for a method to create such nontopological vortices.
In this brief review we summarize a number of recent developments in the study of vortices in Bose-Einstein condensates, a topic of considerable theoretical and experimental interest in the past few years. We examine the generation of vortices by means of phase imprinting, as well as via dynamical instabilities. Their stability is subsequently examined in the presence of purely magnetic trapping, and in the combined presence of magnetic and optical trapping. We then study pairs of vortices and their interactions, illustrating a reduced description in terms of ordinary differential equations for the vortex centers. In the realm of two vortices we also consider the existence of stable dipole clusters for two-component condensates. Last but not least, we discuss mesoscopic patterns formed by vortices, the so-called vortex lattices and analyze some of their intriguing dynamical features. A number of interesting future directions are highlighted.
In this brief review we summarize a number of recent developments in the study of vortices in Bose–Einstein condensates, a topic of considerable theoretical and experimental interest in the past few years. We examine the generation of vortices by means of phase imprinting, as well as via dynamical instabilities. Their stability is subsequently examined in the presence of purely magnetic trapping, and in the combined presence of magnetic and optical trapping. We then study pairs of vortices and their interactions, illustrating a reduced description in terms of ordinary differential equations for the vortex centers. In the realm of two vortices we also consider the existence of stable dipole clusters for two-component condensates. Last but not least, we discuss mesoscopic patterns formed by vortices, the so-called vortex lattices and analyze some of their intriguing dynamical features. A number of interesting future directions are highlighted.
We study vortex dynamics in trapped two-component Bose-Einstein condensates with a laser-induced spin-orbit coupling using the numerical analysis of the Gross-Pitaevskii equation. The spin-orbit coupling leads to three distinct ground-state phases, which depend on some experimentally controllable parameters. When a vortex is put in one or both of the two-component condensates, the vortex dynamics exhibits very different behaviors in each phase, which can be observed in experiments. These dynamical behaviors can be understood by clarifying the stable vortex structure realized in each phase.
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.