A tractable prescription for large-scale free flight expansion of wavefunctions

TL;DR

This paper presents an efficient numerical method for simulating large-scale free expansion of quantum wavefunctions, enabling accurate prediction of time-of-flight images in ultracold atom experiments with complex initial states.

Contribution

The authors introduce a computationally efficient recipe that avoids memory issues by using Fourier transforms on small initial lattices to accurately simulate large-scale wavefunction expansion.

Findings

The method accurately predicts images of defect-laden clouds.

Finite-time expansion modeling is crucial over far-field approximations.

Examples include soliton defects and 3D matter-wave interferometers.

Abstract

A numerical recipe is given for obtaining the density image of an initially compact quantum mechanical wavefunction that has expanded by a large but finite factor under free flight. The recipe given avoids the memory storage problems that plague this type of calculation by reducing the problem to the sum of a number of fast Fourier transforms carried out on the relatively small initial lattice. The final expanded state is given exactly on a coarser magnified grid with the same number of points as the initial state. An important application of this technique is the simulation of measured time-of-flight images in ultracold atom experiments, especially when the initial clouds contain superfluid defects. It is shown that such a finite-time expansion, rather than a far-field approximation is essential to correctly predict images of defect-laden clouds, even for long flight times. Examples shown are: an expanding quasicondensate with soliton defects and a matter-wave interferometer in 3D.