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Optical Engineering

Ghost interference with spatially correlated photon resource

Mingyang Zheng, Lian Chen, Feng Li, Ge Jin

Published May 22, 2013• 2 citations
Publisher

Abstract

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.

DOI
10.1117/1.oe.52.5.058002

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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.
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.
It is known that the entanglement present in the transverse spatial properties of photon pairs generated by spontaneous parametric down-conversion depends explicitly on the characteristics of the pump laser beam. Here we show that, for pump beams described by a Hermite-Gaussian mode, the entanglement depends on the beam width as well as the order of the beam. The amount of entanglement generally increases with the order of the beam and is less dependent on the beam width for higher orders. We propose a method to measure the spatial entanglement directly, independent of the dimension of the subsystems.
Theory and experiment of two-photon lquotlquotlquotdirectrquotrquotrquot interference for type-II spontaneous parametric down-conversion with an ultrafast pulse laser pump
Fourth-order spatial interference of entangled photon pairs generated in the process of spontaneous parametric down-conversion pumped by a femtosecond pulse laser has been performed for the first time. In theory, it takes into account the transverse correlation between the two photons and is used to calculate the dependence of the visibility of the interference pattern obtained in Young’s double-slit experiment. In this experiment, a short focal length lens and two narrow band interference filters were adopted to eliminate the effects of the broadband pump laser and improve the visibility of the interference pattern under the condition of nearly collinear light and degenerate phase matching.
Coherence properties of the down-converted beams generated in spontaneous parametric down-conversion are investigated in detail using an iCCD camera. Experimental results are compared with those from a theoretical model developed for pulsed pumping with a Gaussian transverse profile. The results allow us to tailor the shape of correlation area of the signal and idler photons using pump-field and crystal parameters. As an example, splitting of a correlation area caused by a two-peak pump-field spectrum is experimentally studied.
We examine experimentally how the degree of position-momentum entanglement of photon pairs depends on the transverse coherence of the pump beam that excites them in a process of spontaneous parametric down-conversion. Using spatially incoherent light from a light-emitting diode, we obtain strong position correlation of the photons, but we find that transverse momentum correlation, and thus entanglement, is entirely absent. When we continuously vary the degree of spatial coherence on the pump beam, we observe the emergence of stronger momentum correlations and entanglement. We present theoretical arguments that explain our experimental results. Our results shed light on entanglement generation and can be applied to control entanglement for quantum information applications.