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

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.