波函数大尺度自由飞行展开的一个易处理的公式
A tractable prescription for large-scale free flight expansion of wavefunctions
摘要：
给出了一个数值方法，用于获得一个最初紧凑的量子力学波函数的密度图像，该波函数在自由飞行条件下扩展了一个大的但有限的因子。给出的配方避免了困扰这种类型的计算的存储器存储问题，通过将问题简化为在相对小的初始网格上进行的许多快速傅立叶变换的总和。最终的扩展状态是精确地在一个粗的放大网格上给出的，该网格具有与初始状态相同的点数。该技术的一个重要应用是模拟超冷原子实验中测量的飞行时间图像，特别是当初始云包含超流缺陷时。它示出，这样的有限时间的扩展，而不是远场近似是必不可少的正确预测图像的缺陷载货云，即使是长的飞行时间。所示的例子是：一个扩展的准凝聚孤子缺陷和物质波干涉仪在3D。
英文摘要：
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.
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