Free expansion of lowest Landau level states of trapped atoms: a wavefunction microscope

TL;DR

This paper demonstrates that in free expansion experiments of trapped Bose gases in the lowest Landau level, the particle distribution can be directly related to the trapped state, enabling insights into quantum Hall transitions.

Contribution

It establishes a simple rescaling and rotation relation between in-trap and free-expansion particle distributions for lowest Landau level states, neglecting interactions during expansion.

Findings

Particle distributions relate via rescaling and rotation during free expansion.

Interactions can be neglected during expansion under lowest Landau level approximation.

Density correlations reveal information about quantum Hall transitions.

Abstract

We show that for any lowest-Landau-level state of a trapped, rotating, interacting Bose gas, the particle distribution in coordinate space in a free expansion (time of flight) experiment is related to that in the trap at the time it is turned off by a simple rescaling and rotation. When the lowest-Landau-level approximation is valid, interactions can be neglected during the expansion, even when they play an essential role in the ground state when the trap is present. The correlations in the density in a single snapshot can be used to obtain information about the fluid, such as whether a transition to a quantum Hall state has occurred.