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arXiv:quant-ph/0407169 · Physical Review A

Ghost interference with an optical parametric amplifier

Sulakshana Thanvanthri, Morton H. Rubin

Published Dec 20, 2004• 15 citations
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Abstract

The ``ghost'' interference experiment is analyzed when the source of entangled photons is a multimode optical parametric amplifier (OPA) whose weak limit is the two-photon spontaneous parametric down-conversion beam. The visibility of the double-slit pattern is calculated, taking the finite coincidence time window of the photon counting detectors into account. It is found that the coincidence window and the bandwidth of light reaching the detectors play a crucial role in the loss of visibility on coincidence detection, not only in the ghost interference experiment but in all experiments involving coincidence detection. The differences between the loss of visibility with two-mode and multimode OPA sources are also discussed.

DOI
10.1103/physreva.70.063811

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The ``ghost'' interference experiment is analyzed when the source of entangled photons is a multimode optical parametric amplifier (OPA) whose weak limit is the two-photon spontaneous parametric down-conversion beam. The visibility of the double-slit pattern is calculated, taking the finite coincidence time window of the photon counting detectors into account. It is found that the coincidence window and the bandwidth of light reaching the detectors play a crucial role in the loss of visibility on coincidence detection, not only in the ghost interference experiment but in all experiments involving coincidence detection. The differences between the loss of visibility with two-mode and multimode OPA sources are also discussed.
The transverse spatial properties of the twin light beams of the down-conversion have been recently investigated in experiments using double-slit and coincidence measurements. Fringes are obtained, with a controlled degree of visibility, placing the slits in the signal beam and scanning the signal detector [direct interference---Phys. Rev. A 49, 4176 (1994)] and also, for the degenerated type II down-conversion, with slits in the signal beam and scanning the idler detector [ghost interference---Phys. Rev. Lett. 74, 3600 (1995)]. The idea of a ghost source is used to discuss the direct interference experiment. Using a nondegenerated type I down-conversion, experimental results are obtained showing that the visibility of the ghost interference patterns can be controlled by the ghost source size, analogously as it can be done for a real light source. \textcopyright{} 1996 The American Physical Society.
An approach for calculating fourth-order coherence functions between fields produced in the parametric down-conversion process is proposed. It takes into account the transverse correlations between twin photons and is used to calculate the visibility of the interference patterns obtained in double-slit experiments with coincidence detection. The finite dimension of the light source and detectors are shown to be responsible for a kind of partial coherence which affects the visibility of the fringes. The results explain known features and predict other ones.
A double-slit ghost interference experiment performed on an entangled resource using type-II non-collinear degenerate spontaneous parametric down-conversion (SPDC) is demonstrated.The influence of the distance between the double-slit and the bucket detector preceded by a pinhole is studied.The experimental results show that the interference fringes become increasingly distinct with higher visibility when the pinhole-double-slit distance increases.A first-order classical theory based on the Klyshko's two-photon advanced-wave picture, and a second-order quantum-image theory are provided for explanations.The fitting results indicate that the divergence of the converted fluorescence significantly affects the ghost fringes.