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Optics Letters

Ghost interference with partially coherent radiation

Yangjian Cai, Shi-Yao Zhu

Published Dec 1, 2004• 195 citations
Publisher

Abstract

Ghost interference with partially coherent radiation sources is studied using optical coherence theory. The visibility of the ghost interference fringes is strongly influenced by the transverse size and transverse coherence width of the source. An increase of the transverse source size leads to a decrease of the fringes' visibility. An increase of the transverse coherence results in an increase of the visibility. The difference between ghost interference formed with entangled photon pairs and with partially coherent light is discussed.

DOI
10.1364/ol.29.002716

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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.

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Ghost interference with partially coherent radiation sources is studied using optical coherence theory. The visibility of the ghost interference fringes is strongly influenced by the transverse size and transverse coherence width of the source. An increase of the transverse source size leads to a decrease of the fringes' visibility. An increase of the transverse coherence results in an increase of the visibility. The difference between ghost interference formed with entangled photon pairs and with partially coherent light is discussed.
Ghost interference is experimentally investigated by varying the pseudothermal light source's transverse size and coherence width. Our results show that by increasing the transverse size of the source the quality of the interference pattern is improved, while the visibility is reduced. On the other hand, by increasing the coherence width of the source, the visibility of the interference pattern is improved, while the quality is reduced. These experimental results corroborate previous theoretical results.
Ghost interference with entangled photon pairs are studied theoretically. The pump beam in parametric down-conversion is treated as the Gaussian profile, while for the function describing phase matching in the longitudinal direction, both a Gaussian and a sinc function are considered. The numerical results show that the transverse size of the pump beam and transverse coherence width of the parametric fluorescence strongly influence the interference pattern. With the increase of the pump transverse size and the decrease of transverse coherence width, the interference pattern becomes more and more prominent. When the transverse coherence width is small to 0.01 mm category, the Gaussian and sinc models give the same results.
The spatial correlation between down-converted photons allows for non-local spatial filtering when two-photon coincidences are registered. This allows one to non-locally control the visibility of interference fringes, to observe ghost images and interference patterns, and to "retrieve" a coherent quantum image from an incoherent field distribution. We show theoretically that non-local spatial filtering can lead to counter-intuitive effects when the pump beam is no longer given by a Gaussian profile. Namely, increased non-local filtering can actually decrease the visibility of interference fringes, contrary to what has been observed so far. We explain this behavior through the transverse spatial parity entanglement of the down-converted photons.
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.
Partially coherent quantum-entangled beams combine quantum correlation with partial coherence, allowing them to maintain quantum characteristics while being more resistant to distortions caused by random media during propagation. In this study, we investigate the effect of coherence variation of such beams on non-local double-slit quantum interference. The spatial coherence variation is achieved by controlling the transverse coherence length of the Gaussian Schell model pump in the spontaneous parametric down conversion process. For a fixed beam size, the momentum correlation width of partially coherent biphotons increases with the decrease in the transverse coherence length. This results in a biphoton beam exhibiting multiple spatial modes, making it more suitable for studying the non-local features of quantum states in imaging, interference, and diffraction experiments. Our findings infer both high-quality and near-unity visibility of nonlocal interference using the partially coherent twin beams, even with the substantial decrease in the coherence of the pump. We believe these results can enhance robustness against the deleterious effects of the medium during propagation and can have potential applications in optical image cryptography, biomedical imaging, quantum lithography, and quantum holography.
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.