Rotating trapped Bose-Einstein condensates

TLDR

Interactions modify the formation of a Bose‑Einstein condensate and affect the dynamics of small‑amplitude perturbations in harmonic traps. For rotation frequencies near the radial trap frequency, the lowest‑Landau‑level approximation provides a simple description of rapidly rotating condensates. Rapid rotation nucleates vortices that form a dense triangular lattice at higher speeds, whose collective dynamics drive a quantum phase transition to highly correlated, non‑superfluid states analogous to the fractional quantum Hall effect.

Abstract

After reviewing the ideal Bose-Einstein gas in a box and in a harmonic trap, the effect of interactions on the formation of a Bose-Einstein condensate are discussed, along with the dynamics of small-amplitude perturbations (the Bogoliubov equations). When the condensate rotates with angular velocity $\ensuremath{\Omega}$, one or several vortices nucleate, leading to many observable consequences. With more rapid rotation, the vortices form a dense triangular array, and the collective behavior of these vortices has additional experimental implications. For $\ensuremath{\Omega}$ near the radial trap frequency ${\ensuremath{\omega}}_{\ensuremath{\perp}}$, the lowest-Landau-level approximation becomes applicable, providing a simple picture of such rapidly rotating condensates. Eventually, as $\ensuremath{\Omega}\ensuremath{\rightarrow}{\ensuremath{\omega}}_{\ensuremath{\perp}}$, the rotating dilute gas is expected to undergo a quantum phase transition from a superfluid to various highly correlated (nonsuperfluid) states analogous to those familiar from the fractional quantum Hall effect for electrons in a strong perpendicular magnetic field.