Rapid rotation of a Bose-Einstein condensate in a harmonic plus quartic trap

TL;DR

This paper investigates the behavior of a rapidly rotating Bose-Einstein condensate in an anharmonic trap, revealing vortex formation, a critical angular velocity for hole creation, and a transition to a giant vortex at high rotation speeds.

Contribution

It provides analytical and numerical analysis of vortex dynamics and phase transitions in a BEC with combined harmonic and quartic trapping potentials at high rotation speeds.

Findings

Dense vortex array forms at high rotation speeds

Critical angular velocity for central hole matches predictions

Transition to giant vortex occurs at very high rotation speeds

Abstract

A two-dimensional rapidly rotating Bose-Einstein condensate in an anharmonic trap with quadratic and quartic radial confinement is studied analytically with the Thomas-Fermi approximation and numerically with the full time-independent Gross-Pitaevskii equation. The quartic trap potential allows the rotation speed $\Omega$ to exceed the radial harmonic frequency $\omega_\perp$. In the regime $\Omega \gtrsim \omega_\perp$, the condensate contains a dense vortex array (approximated as solid-body rotation for the analytical studies). At a critical angular velocity $\Omega_h$, a central hole appears in the condensate. Numerical studies confirm the predicted value of $\Omega_h$, even for interaction parameters that are not in the Thomas-Fermi limit. The behavior is also investigated at larger angular velocities, where the system is expected to undergo a transition to a giant vortex (with pure irrotational flow).