Role of indistinguishability and entanglement in Hong-Ou-Mandel interference and finite bandwidth effects of frequency entangled photons

Abstract

We investigate the relation between indistinguishability and quantum entanglement in Hong-Ou-Mandel-interference experiments theoretically and relate these quantum mechanical principles to the theorem of entanglement monogamy. We use Glauber's theory of quantum coherence to predict the detection statistics in HOM-interference of photons produced by three different photonpair sources: sources of spectrally indistinguishable frequency uncorrelated photons, sources of spectrally distinguishable frequency detuned photons and sources of spectrally indistinguishable frequency entangled photons. In the case of frequency entangled photon sources, we find a new additional term in the coincidence detection probability of HOM-interference compared to existing results, which is relevant for the case of low frequency separations or large single-photon bandwidths. Compared to previous work in that context we treat all photonic degrees of freedom (DOF) on equal footing.

Observer dependence of photon bunching: The influence of the relativistic redshift on Hong-Ou-Mandel interference

“…However, there is a striking difference between frequency detuned and frequency entangled photons, namely that the interference term (10b) of frequency detuned photons vanishes for increasing frequency separations µ where the one of frequency entangled photons (10c) does not. As extensively discussed in [23] the physical reason for this is the increasing spectral distinguishability of frequency detuned photons, which grows for larger values of µ and thus suppresses both photon bunching and photon anti-bunching. Mathematically perfect spectral distinguishability is expressed through a vanishing overlap of the spectral wave function with itself under exchange of the function arguments, i.e.…”

“…In this section we briefly review a theoretical framework previously developed to predict the detection statistics of HOM experiments with realistic broadband photons. We leave details to the interested reader [23]. In this section we work in a non-relativistic context, i.e., all temporal quantities are functions of a universal background time and not of the proper time of the observers.…”

“…The (unnormalized) probabilities P σ1σ2 (τ 1 , τ 2 ) to detect one photon in a quantum state, which is characterized by σ 1 and another photon in a quantum state, which is characterized by σ 2 , in the two-photon quantum state (1) have been obtained previously [23], and read…”

“…σ = (U, L)) as the only left photonic DOF and do not consider for instance the polarization of the photons and so forth. We consider two-photon sources which posses photonic wave functions which can be written in matrix form (see [23] for details) as…”

“…This work is organized as follows. In Section II we briefly review our results on HOM-interference from previous work [23]. In Section III we provide the tools to compute the relativistic deformation of the spectral wave function.…”