Particle statistics and interference pattern

Question

Does the particle statistics have some observational effect on interference (for ex. double slit experiment)? My doubt arises because of following reasoning:

1. One particle at a time (Tonomura): Particle statistics won't play any role because we don't have any position to interchange. We get the old interference pattern.
2. Many particles at a time: Here lies my issue if we are sending a lot of them together so they are described by a grand wavefunction. This wavefunction is constraint to statistics. How is interference seen in this experiment?

Answer 1

Lets discuss photons instead of electrons. See this single photon at a time experiment

1. Single-photon camera recording of photons from a double slit illuminated by very weak laser light. Left to right: single frame, superposition of 200, 1’000, and 500’000 frames.

You must agree that the interference pattern will appear even if all the photons came in a single pulse. Classical electromagnetic waves and the final Maxwell theory is based by this observation. No quantum mechanics. Quantum mechanics enters in the observation that single photon spots look random but are controlled by the probability distribution computed by the quantum mechanical wavefunction of the experiment "photon scattering off two slits given width given distance".

The same behavior is seen for single electrons in Tonamura experiment. You are asking if one sends a beam of electrons whether this would make a difference. In this 1974 experiment with a beam of electrons, the same interference pattern is seen. In this article they are working with coherent electron beams and they do observe different effects, which may be what you are wondering about. But the wave like behavior in the ensemble of electrons is still seen.

Answer 2

The problem with a stream of electrons is that they will interact via Coulomb interaction, which may lead to dephasing (via inelastic processes), and hence to the loss of interference - this has been quite extensively studied in solid state: in Aharonov-Bohm interferometers and experiments onw eak localization.

If we limit ourselves to non-interacting particles, the statistics leads to bunching/antibunching of bosons/fermions, although these are usually expressed in terms of particle numbers rather than interference pattern.