Vortices and dynamics in trapped Bose-Einstein condensates

TL;DR

This paper reviews the physics of ultracold Bose-Einstein condensates, focusing on vortices, their dynamics, and the potential for quantum phase transitions to highly correlated states using synthetic gauge fields.

Contribution

It provides a comprehensive overview of vortex behavior, dynamics, and the possibility of observing quantum phase transitions in trapped Bose-Einstein condensates.

Findings

Observation of vortex precession and dipole motion

Study of vortex lattice oscillations (Tkachenko modes)

Prediction of quantum phase transition to correlated states

Abstract

I review the basic physics of ultracold dilute trapped atomic gases, with emphasis on Bose-Einstein condensation and quantized vortices. The hydrodynamic form of the Gross-Pitaevskii equation (a nonlinear Schr{\"o}dinger equation) illuminates the role of the density and the quantum-mechanical phase. One unique feature of these experimental systems is the opportunity to study the dynamics of vortices in real time, in contrast to typical experiments on superfluid $^4$He. I discuss three specific examples (precession of single vortices, motion of vortex dipoles, and Tkachenko oscillations of a vortex array). Other unusual features include the study of quantum turbulence and the behavior for rapid rotation, when the vortices form dense regular arrays. Ultimately, the system is predicted to make a quantum phase transition to various highly correlated many-body states (analogous to bosonic quantum Hall states) that are not superfluid and do not have condensate wave functions. At present, this transition remains elusive. Conceivably, laser-induced synthetic vector potentials can serve to reach this intriguing phase transition.