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.

Relaxation in an Extended Bosonic Josephson Junction

“…Consequently, only the linear free Schrödinger equation needs to be solved in the second stage. An approximate solution can be computed by taking advantage of the fact that the spatial distribution approaches the momentum distribution of the initial condensate wave function as time tends to infinity, see, e.g., [40]. If the period until a TOF-image is taken is rather short, it is highly recommended to solve the original free Schrödinger initial value problem.…”

“…While in theory, this problem can be solved most easily by the application of two Fourier transforms and a simple pointwise multiplication, in practice one faces severe computer memory issues. For more details on these issues and how they can be overcome we would like to refer to [40].…”

Determination of Chern numbers with a phase-retrieval algorithm

“…A time-of-flight image shows the spatial density distribution I (r) of atoms after a time period t T OF of a free expansion that follows a sudden turning off an optical lattice and external trapping potentials. In the far field limit, I (r) is proportional to the initial distribution of atoms in the momentum space if we may neglect interaction between particles during the expansion of the atomic cloud [69][70][71][72]…”

Mesoscopic density grains in a 1D interacting Bose gas from the exact Yang–Yang solution

“…The most familiar domains in this case are phase grains -known to occur in the quasicondensate regime. Experimentally, their existence can be inferred from the behavior of a cloud after expansion [4][5][6][7][8]. There is also a warmer regime with profuse spontaneous solitons [9][10][11][12] separating phase and density domains.…”