Quantum Statistics Can Suppress Classical Interference

Dirac’s somewhat unfortunate statement about ‘interference between two (or more) photons never occurring‘ has led to fruitful discussions clarifying the understanding of interference from a quantum mechanical point of view. These days textbook presentations elucidate that single photon light fields behave just like classical states of light [1] when used in a Young’s double-slit interference experiment [2–4]. To exhibit non-classical features, measurements which detect twoor more photon coincidences, phase sensitive measurements such as homodyning and quantum tomography [5], and waiting-time distribution (anti-bunching) measurements can be performed [2–6]. Single photon detection, however, i.e. intensity or first-order coherence measurements [7], are often held to be classical in character [2,3]. This conclusion stems from the analysis of Young’s interference patterns for single photon and Glauber-coherent states of light [2], single photons emitted from two atoms [3] and thermal fields [3,4]. In these examples quantum and classical predictions for the form and visibility of interference patterns are identical [2–4]. Some physicists have therefore concluded that ”Experiments of this kind which measure the first-order correlation functions of the electromagnetic field do not distinguish between the quantum and classical theories of light” [2]. One can even find more generalized statements such as ”For fields with identical spectral properties it is not possible to distinguish the nature of the light source from only the first-order coherence properties” [3]. Differences between classical and quantum expressions for first-order coherence phenomena are commonly attributed to different frequency modes only [3,4], but we will see that they can occur for monochromatic fields as well [8]. To explain the perceived equivalence between the classical and quantum behaviour in first-order coherence phenomena some books refer to Dirac’s assertion regarding interference between two photons not occurring [2,4]. Let us seek a more detailed explanation instead. The purpose of this paper is twofold. Firstly I will give a simple general proof for the equivalence between the classical and quantum behaviour in first-order coherence phenomena for the conventional Young’s doubleslit setup. And then, I will derive the simplest possible example based on photon statistics which should show maximal violation of the classically expected behaviour: whereas in the classical case an interference pattern with perfect visibility is observed, one should find the same in one but zero visibility in another corresponding quantum case.