Probing the circulation of ring-shaped Bose-Einstein condensates

TL;DR

This study combines theoretical simulations and experiments to demonstrate that the size of the hole in ring-shaped Bose-Einstein condensates after release can reliably indicate the initial circulation, aiding future atomtronic research.

Contribution

It provides a detailed analysis of the dynamics of ring-shaped BECs after release, establishing a quantitative link between initial circulation and observable hole size in TOF images.

Findings

Hole area scales quadratically with initial circulation when released directly from the stirred trap.

Hole area scales linearly with initial circulation if the trap is relaxed before release.

Theoretical TOF images agree well with experimental data.

Abstract

This paper reports the results of a theoretical and experimental study of how the initial circulation of ring-shaped Bose-Einstein condensates (BECs) can be probed by time-of-flight (TOF) images. We have studied theoretically the dynamics of a BEC after release from a toroidal trap potential by solving the 3D Gross-Pitaevskii (GP) equation. The trap and condensate characteristics matched those of a recent experiment. The circulation, experimentally imparted to the condensate by stirring, was simulated theoretically by imprinting a linear azimuthal phase on the initial condensate wave function. The theoretical TOF images were in good agreement with the experimental data. We find that upon release the dynamics of the ring--shaped condensate proceeds in two distinct phases. First, the condensate expands rapidly inward, filling in the initial hole until it reaches a minimum radius that depends on the initial circulation. In the second phase, the density at the inner radius increases to a maximum after which the hole radius begins slowly to expand. During this second phase a series of concentric rings appears due to the interference of ingoing and outgoing matter waves from the inner radius. The results of the GP equation predict that the hole area is a quadratic function of the initial circulation when the condensate is released directly from the trap in which it was stirred and is a linear function of the circulation if the trap is relaxed before release. These scalings matched the data. Thus, hole size after TOF can be used as a reliable probe of initial condensate circulation. This connection between circulation and hole size after TOF will facilitate future studies of atomtronic systems that are implemented in ultracold quantum gases.