First-order correlation function of the stream of single-electron wave-packets

TL;DR

This paper investigates how the first-order correlation function of a stream of single-electron wave-packets reveals whether the state is multi-particle or a product of single-particle states, highlighting differences in time and energy domain analyses.

Contribution

It demonstrates that the time-domain correlation function can distinguish between separated and overlapping wave-packets, unlike the energy domain function.

Findings

Time-domain correlation function is factorizable for separated wave-packets.

Overlapping wave-packets lead to non-factorizable time-domain correlation.

Energy domain correlation function is always factorizable, regardless of wave-packet overlap.

Abstract

The first-order correlation function, which is accessible experimentally, contains all essential information about the state of the system of non-interacting electrons. Here I discuss how this function can be used to answer the question whether the state of a periodic stream of single-electron wave-packets is a multi-particle state or it is the product of single-particle states. In the latter case the correlation function is expected to be factorizable while in the former case it is not. As an example I consider a train of Lorentzian in shape single-electron excitations, levitons. I demonstrate that the correlation function in time domain is factorizable or not depending on whether the wave-packets are separated or overlapping. In contrast, the correlation function in energy domain is always factorizable and thus cannot be used to distinguish single- and multi-particle states.