دانلود رایگان مقاله نسخه سست مهار برای مقیاس بزرگ انبساط پرواز آزاد تابعهای موج

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.

7.5. Conclusions

To conclude, an algorithm (42) has been presented that allows the exact calculation of the density of a wavefunction freely expanding into vacuum for practically arbitrary flight times without filling up the computer memory. The memory requirements do not depend on flight time and are the same size as the initial input state. Computation time is slightly faster than using an FFT on a large vacuum padded lattice. It is implemented using standard FFT libraries and some summing of terms. The approach relies crucially on two physical inputs: (1) That the initially compact wavefunction expands into vacuum, and (2) that the density length scale of the expanded cloud grows approximately linearly with time. The approach makes no assumptions about symmetries of the system or about the input wavefunction, so that it is a black box tool that can be immediately applied to general cases. This makes it well suited to the study of wavefunctions containing defects or samples of a thermal ensemble, a topic of many recent experiments [1,20– 25]. The flight times over which nontrivial defect evolution occurs during free flight are estimated in Section 2.4.