Shenkar College of Engineering and Design, Anna Frank St. 12, Ramat Gan, Israel.
Chemical and Biological Physics Department, Weizmann Institute of Science, 76100 Rehovoth, Israel.
J Chem Phys. 2018 Oct 28;149(16):164114. doi: 10.1063/1.5051800.
Scattering through a double slit potential is one of the most fundamental problems in quantum mechanics. It is well understood that due to the superposition of amplitudes, one observes a spatial interference pattern in the scattered wavefunction reflecting the superposition of amplitudes coming from both slits. However, the effect of the double slit on the mean time it takes to traverse the slit has not been considered previously. Using a transition path time formalism, we show that when a single Gaussian wavepacket is scattered through a double slit potential, one finds not only oscillations in the scattered density resulting from the spatial interference created by the splitting of the wavepacket but also an oscillatory pattern in the mean scattering time. Long times are associated with low values of a suitably defined momentum, and short times with higher values. The double slit thus serves as a momentum filtering device. We also find an interference pattern in the time averaged momentum weak value profile of the scattered particle implying that the double slit also acts as a weak momentum filter. These results not only demonstrate the value of considering transition path time distributions in their quantum mechanical context but also present a challenge to semiclassical approximations-can they account for temporal interference?
双缝势散射是量子力学中最基本的问题之一。众所周知，由于振幅的叠加，人们在散射波函数中观察到空间干涉图案，反映了来自两个狭缝的振幅叠加。然而，双缝对穿过狭缝所需的平均时间的影响以前没有被考虑过。我们使用跃迁路径时间形式理论，表明当单个高斯波包通过双缝势散射时，人们不仅会发现由于波包分裂而产生的空间干涉引起的散射密度的振荡，而且还会发现散射时间的平均出现振荡模式。长时间与适当定义的动量的低值相关，短时间与较高值相关。因此，双缝起到了动量过滤装置的作用。我们还在散射粒子的时间平均动量弱值分布中发现了干涉图案，这意味着双缝也起到了弱动量过滤的作用。这些结果不仅证明了在量子力学背景下考虑跃迁路径时间分布的价值，而且对半经典近似提出了挑战——它们能否解释时间干涉？
