Anomalous second order coherence and $g^{(2)}$ complementarity

TL;DR

This paper explores higher order coherence and $g^{(2)}$ complementarity, revealing anomalous behaviors such as oscillations in $g^{(2)}$ when detector and field spectra are mismatched, suggesting a non-monotonic form of quantum complementarity.

Contribution

It introduces the concept of higher order complementarity and demonstrates anomalous $g^{(2)}$ oscillations through analysis of a two-particle quantum state.

Findings

$g^{(2)}(\tau=0)=1/2$ for indistinguishable particles

$g^{(2)}$ oscillates with detector bandwidth when particles are distinguishable

Proposes a new interpretation of $g^{(2)}$ complementarity

Abstract

This paper is a summary of my talk at SPIE2013. The organizers were kind enough to invite me to talk about anything I wanted, and I chose to bring up the notion of higher order complementarity and the fact that it may not be monotonic. I enter this discussion, which is rather speculative at this stage, by calculating a specific example. This is to be regarded as work in progress. We analyze a two-particle state and show that when mismatching the detector frequency response and the field frequency spectrum, several anomalous features become apparent. In particular, while we find several well known features, such as $g^{(2)}(\tau=0)=1/2$ for completely indistinguishable particles, we also find that as the photons are slightly separated and may be distinguished, $g^{(2)}$ may oscillate as a function of the detector bandwidth. Beyond the latter interesting observation for which we cannot find a simple physical origin, we also suggest, an interpretation with regard to an oscillating $g^{(2)}$ complementarity.