The Wavefunction of the Collapsing Bose-Einstein Condensate

TL;DR

This paper models the wavefunction of a collapsing Bose-Einstein condensate, demonstrating that a nonlocal interaction leads to a stable high-density remnant, and introduces a variational approach with superposed Gaussians.

Contribution

It introduces a variational method with superposed Gaussians to accurately describe the ground state of an attractive condensate, accounting for nonlocal interactions and stability.

Findings

Remnant condensate is the energy minimum with nonlocal interactions.

Superposition of two Gaussians accurately models the wavefunction.

Experimental data supports the nonlocal interaction range model.

Abstract

Bose-Einstein condensates with tunable interatomic interactions have been studied intensely in recent experiments. The investigation of the collapse of a condensate following a sudden change in the nature of the interaction from repulsive to attractive has led to the observation of a remnant condensate that did not undergo further collapse. We suggest that this high-density remnant is in fact the absolute minimum of the energy, if the attractive atomic interactions are nonlocal, and is therefore inherently stable. We show that a variational trial function consisting of a superposition of two distinct gaussians is an accurate representation of the wavefunction of the ground state of the conventional local Gross-Pitaevskii field equation for an attractive condensate and gives correctly the points of emergence of instability. We then use such a superposition of two gaussians as a variational trial function in order to calculate the minima of the energy when it includes a nonlocal interaction term. We use experimental data in order to study the long range of the nonlocal interaction, showing that they agree very well with a dimensionally derived expression for this range.