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arXiv:cond-mat/0405589

Vortices in Atomic Bose-Einstein Condensates: an Introduction

Sankalpa Ghosh

Published May 25, 2004• 0 citations
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Abstract

The occurrence of vortices in atomic Bose-Einstein condensates (BEC) enables a description of their superfluid behaviour. In this article we present a pedagogical introduction to the vortex physics in trapped atomic BECs. The mechanism of the vortex nucleation in an atomic BEC is discussed in detail. We also discuss a recently proposed approach which treats the problem of vortex nucleation using a one-particle Schr$\ddot{o}$dinger equation with non-local and chiral boundary conditions.

DOI
10.48550/arxiv.cond-mat/0405589

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The occurrence of vortices in atomic Bose-Einstein condensates (BEC) enables a description of their superfluid behaviour. In this article we present a pedagogical introduction to the vortex physics in trapped atomic BECs. The mechanism of the vortex nucleation in an atomic BEC is discussed in detail. We also discuss a recently proposed approach which treats the problem of vortex nucleation using a one-particle Schro¨\ddot{o}o¨dinger equation with non-local and chiral boundary conditions.
One of the key issues related to superfluidity is the existence of quantized vortices. Following recent experiments on Bose–Einstein condensates exhibiting vortices, we investigate the behavior of the wave function which solves the Gross–Pitaevskii equation. For a rotating Bose–Einstein condensate in a harmonic trap, we give a simplified expression of the Gross–Pitaevskii energy in the Thomas–Fermi regime, which only depends on the number and shape of the vortex lines. This allows us to study in detail the structure of the line of a single quantized vortex, which has a U or S shape. S type vortices exist for all values of the angular velocity Ω but are not minimizers of the energy while U vortices are minimizers and exist only for Ω sufficiently large. Finally, we study the drag created by the movement of a detuned laser beam in a condensate and the nucleation of vortices in the low density region close to the boundary layer of the cloud.
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We report on the observation of vortex formation in a Bose-Einstein condensate of 87Rb^{87}\text{R}\text{b}87Rb atoms. Vortices are generated by superimposing an oscillating excitation to the trapping potential introduced by an external magnetic field. For small amplitudes of the external excitation field we observe a bending of the cloud axis. Increasing the amplitude we observe formation of a growing number of vortices in the sample. Shot-to-shot variations in both vortex number and position within the condensed cloud are observed, probably due to the intrinsic vortex nucleation dynamics. We discuss the possible formation of vortices and antivortices in the sample as well as possible mechanisms for vortex nucleation.
We study the vortex nucleation in a finite Bose-Einstein condensate. Using a set of non-local and chiral boundary conditions to solve the Schro¨\ddot{o}o¨dinger equation of non-interacting bosons in a rotating trap, we obtain a quantitative expression for the characteristic angular velocity for vortex nucleation in a condensate which is found to be 35% of the transverse harmonic trapping frequency.
Abstract Chapter 4 addresses the progress of studies on superfluid dynamics, mainly related to the dynamics of quantized vortices, in cold-atom BECs. First, we give a minimal description of the physics of cold atoms, e.g. cooling, trapping, control of interatomic interactions by external fields. We then turn to the argument of superfluid hydrodynamics in a scalar BEC characterized by a single-component order parameter. The properties of the vortices can be well described on the basis of the GP model, which allows a quantitative comparison between theory and experiment. We will discuss topics such as single vortex dynamics, interacting dynamics of a few vortices, vortex lattice formation in a rotating BEC, and collective properties of a vortex lattice in a rapidly rotating BEC, which have been unraveled experimentally by direct visualization of vortices in condensed gases. Next, we will discuss the properties of vortices in multicomponent BECs characterized by the multicomponent order parameters. We will first explain the vortex physics in two-component BECs as a simple case, finding that their structures and dynamics are highly nontrivial due to the presence of the intercomponent interaction; we will cover the topics of vortex structure composed of two-component order parameters, dynamics of composite vortices, exotic vortex lattices, and hydrodynamic instabilities associated with the interface dynamics between immiscible condensates. Finally, we explain the vortices in a spinor BEC. The vortex structures are extremely rich due to the complicated order parameter manifold, which is clarified by the discussion on vortices in spin-1 and spin-2 spinor BECs.