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Physical Review A

Fourth-order coherence induced by spatial mode parity selection

J. O. de Almeida, Stephen Patrick Walborn, P. H. Souto Ribeiro, Malena O. Hor-Meyll

Published Sep 25, 2012• 4 citations
Publisher

Abstract

Fourth-order coherence determines the visibility of interference fringes observed in two-photon correlation measurements. In some cases, one photon triggers the presence of its conjugate twin in the interferometer. Therefore, spatial or spectral filtering of the trigger photon may change the visibility of the interference fringes and the degree of fourth-order coherence as well. We show that, contrary to the intuition developed from series of previous experiments, it is possible to increase the fourth-order coherence by reducing the degree of filtering. We present a theoretical approach and experimental results demonstrating this effect and interpret it in terms of spatial mode parity selection.

DOI
10.1103/physreva.86.033839

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Fourth-order coherence determines the visibility of interference fringes observed in two-photon correlation measurements. In some cases, one photon triggers the presence of its conjugate twin in the interferometer. Therefore, spatial or spectral filtering of the trigger photon may change the visibility of the interference fringes and the degree of fourth-order coherence as well. We show that, contrary to the intuition developed from series of previous experiments, it is possible to increase the fourth-order coherence by reducing the degree of filtering. We present a theoretical approach and experimental results demonstrating this effect and interpret it in terms of spatial mode parity selection.
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.
We report the results of two experiments performed with two-photon light, produced via collinear degenerate optical spontaneous parametric downconversion (SPDC), in which both second-order (one-photon) and fourth-order (two-photon) interferograms are recorded in a Mach-Zehnder interferometer (MZI). In the first experiment, high-visibility fringes are obtained for both the second- and fourth-order interferograms. In the second experiment, the MZI is modified by the removal of a mirror from one of its arms; this leaves the fourth-order interferogram unchanged, but extinguishes the second-order interferogram. A theoretical model that takes into consideration both the temporal and spatial degrees-of-freedom of the two-photon state successfully explains the results. While the temporal interference in the MZI is independent of the spatial coherence of the source, that of the modified MZI is not.
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.
The visibilities of second-order (one-photon) and fourth-order (two-photon) interference have been observed in a Young's double-slit experiment using light generated by spontaneous parametric down-conversion and a photon-counting intensified charge-coupled device camera. Coherence and entanglement underlie one- and two-photon interference, respectively. As the effective source size is increased, coherence is diminished while entanglement is enhanced, so that the visibility of one-photon interference decreases while that of two-photon interference increases. This experiment demonstrates the complementarity between one- and two-photon interference (coherence and entanglement) in the spatial domain.
The measurement of the correlation between two quantum systems or particles has a broad significance in physics and also plays a central role in the fields of quantum optics and quantum information science. We propose a method of measuring the correlation between the transverse momenta of two photons, in which one only needs to detect one of the photons. We show that it is possible to generate a single-photon fringe pattern by using two spatially separated identical biphoton sources. The fringes are similar to the ones observed in a Michelson interferometer and possess certain remarkable properties. A striking feature of the fringes is that although the pattern is obtained by detecting one photon only of each photon pair, the fringes shift due to a change in the optical path traversed by the undetected photon; the shift is characterized by a combination of wavelengths of both photons. Using this method one can, therefore, measure the wavelength of a photon without detecting it. The visibility of the fringes diminishes as the correlation between the transverse momenta of twin photons decreases: visibility is unity for maximum momentum correlation and zero for no momentum correlation. This dependence allows us to determine the momentum correlation between both photons from the visibility of the fringe pattern obtained by detecting one of the photons only. Our method can potentially be generalized to other quantum entities.