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

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.

17 pages, 7 figures. v2: Adding explicit statement that the wavevector values used in the prescription must be centered around zero, and a note about odd lattice sizes

References in corpus (13)

• Spontaneous symmetry breaking in a quenched ferromagnetic spinor Bose condensate
• Spontaneous vortices in the formation of Bose-Einstein condensates
• Dynamics and statistical mechanics of ultra-cold Bose gases using c-field techniques
• Extension of Bogoliubov theory to quasi-condensates
• Emergence of coherence in a uniform quasi-two-dimensional Bose gas
• Finite Temperature Models of Bose-Einstein Condensation
• Observation of Solitonic Vortices in Bose-Einstein Condensates
• Violation of the Cauchy-Schwarz inequality with matter waves
• Sub-Poissonian number differences in four-wave mixing of matter waves
• Dynamics and interaction of vortex lines in an elongated Bose-Einstein condensate
• Proposal for a motional-state Bell inequality test with ultracold atoms
• Classical field records of a quantum system: their internal consistency and accuracy
• Density fluctuations in a quasi-one-dimensional Bose gas as observed in free expansion

Cited by in corpus (6)

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• Multi-time correlations in the positive-P, Q, and doubled phase-space representations
• Mesoscopic density grains in the 1d interacting Bose gas from the exact Yang-Yang solution
• Determination of Chern numbers with a phase retrieval algorithm
• Scaling dynamics of the ultracold Bose gas
• Systematic analysis of relative phase extraction in one-dimensional Bose gases interferometry