N-slit interference: Path integrals, Bohmian trajectories

TL;DR

This paper uses path integrals and Bohmian trajectories to analyze N-slit interference, revealing detailed particle routes, wavepacket formation, and interference patterns, supported by neutron and fullerene molecule experiments.

Contribution

It introduces a detailed analysis of N-slit interference using path integrals and Bohmian trajectories, including near- and far-field behaviors and experimental simulations.

Findings

Bohmian trajectories show wavy near-field behavior and straight far-field paths.

Interference patterns are simulated for neutrons and fullerene molecules.

The transition from near-field to far-field involves divergence of principal rays.

Abstract

Path integrals give a possibility to compute in details routes of particles from particle sources through slit gratings and further to detectors. The path integral for a particle passing through the Gaussian slit results in the Gaussian wavepacket. The wavepackets prepared on N slits and superposed together give rise to interference pattern in the near-field zone. It transforms to diffraction in the far-field zone represented by divergent principal rays, at that all rays are partitioned from each other by (N-2) subsidiary rays. The Bohmian trajectories in the near-field zone of N-slit gratings show wavy behavior. And they become straight in the far-field zone. The trajectories show zigzag behavior on the interference Talbot carpet (ratio of particle wavelength to a distance between slits are much smaller than 1 and N>>1). Interference from the the N-slit gratings is simulated by scattering monochromatic neutrons (wavelength=0.5 nm). Also we have considered simulation of interference fringes arising at scattering on an N-slit grating of fullerene molecules (according to the real experiment stated in e-print 1001.0468).