The wavefunction of the collapsing Bose–Einstein condensate

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.

Nonlocal energy functionals and long range interactions in collapsing condensates in a box

“…This interaction range is of the same order of magni-tude as the one found in Ref. [5] for condensates in harmonic oscillator traps. Now that we have found d, we can use it for every value of a examined in Ref.…”

“…Hence the dimensionless d is given by 2.637 84 . 16 This interaction range is of the same order of magnitude as the one found in [5] for condensates in harmonic oscillator traps.…”

“…The collapse of the metastable condensate and the formation of the remnant condensate is nothing else then than the transition from the local to the absolute minimum [4]. A recent work [5] used this idea in order to explain in detail the experimental observations of Ref. 1. This remarkable stability of the remnant condensates for times as long as one second has been studied thoroughly recently for attractive Bose-Einstein 39 K condensates with tunable interactions in the uniform potential of a cylindrical optical-box trap [6].…”

“…The collapse of the metastable condensate and the formation of the remnant condensate is nothing else then than the transition from the local to the absolute minimum [4]. A recent work [5] used this idea in order to explain in detail the experimental observations of [1].…”

A variational model for the delayed collapse of Bose Einstein condensates

“…( 23) is not very accurate. We can obtain a much more accurate trial wavefunction if we use the sum of two such anisotropic gaussians [11]. However, the resulting expressions are too lengthy and complicated.…”