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Physical Review A

Direct and ghost interference in double-slit experiments with coincidence measurements

P. H. Souto Ribeiro, G. A. Barbosa

Published Oct 1, 1996• 38 citations
Publisher

Abstract

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.

DOI
10.1103/physreva.54.3489

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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.
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.
One of the most surprising consequences of quantum mechanics is entanglement of two or more distance particles. The two-particle entangled state was mathematically formulated by Schrodinger. Based on this unusual quantum behavior, EPR defined their 'physical reality' and then asked the question: 'Can Quantum-Mechanical Description of Physical Reality Be Considered Complete?' One may not appreciate EPR's criterion of physical reality and insist that 'no elementary quantum phenomenon is a phenomenon until it is a recorded phenomenon'. Optical spontaneous parametric down conversion (SPDC) is the most effective mechanism to generate an EPR type entangled two-photon state. In SPDC, an optical beam, called the pump, is incident on a birefringent crystal. The pump is intense enough so that nonlinear effects lead to the conversion of pump photons into pairs of photons, historically called signal and idler. Technically, the SPDC is said to be type-1 or type-2, depending on whether the signal and idler beams have parallel or orthogonal polarization. The SPDC conversion efficiency is typically on the order of 10(exp -9) to 10(exp -11), depending on the SPDC nonlinear material. The signal and idler intensities are extremely low, only single photon detection devices can register them. The quantum entanglement nature of SPDC has been demonstrated in EPR-Bohm experiments and Bell's inequality measurements. The following two experiments were recently performed in our laboratory, which are more closely related to the original 1935 EPR gedankenezperiment. The first experiment is a two-photon optical imaging type experiment, which has been named 'ghost image' by the physics community. The signal and idler beams of SPDC are sent in different directions, so that the detection of the signal and idler photons can be performed by two distant photon counting detectors. An aperture object (mask) is placed in front of the signal photon detector and illuminated by the signal beam through a convex lens. Surprisingly, an image of this aperture is observed in the idler beam, by scanning the idler photon detector in the transverse plane of the idler beam, if we are sure that the idler photon detector 'catches' the 'twin brother' of the signal, which can be easily performed by a coincidence measurement. This effect is even more striking when we found that the object-lens-image relationship satisfies the Gaussian thin lens equation. The second experiment demonstrates two-photon 'ghost' interference-diffraction. The experimental set up is similar to the image experiment, except that rather than a lens and an aperture it is a Young's double-slit (or a single-slit) inserted into the path of the signal beam. We could not find any interference (or diffraction) pattern behind the slit. Surprisingly, an interference (or diffraction) pattern is observed when scanning the detector in the idler beam, if we are sure that the idler photon detector 'catches' the 'twin brother' of the signal.
Is it possible to detect the interference from an extended incoherent source with Young's slits when the source-slits distance is such that all dimensions of the coherence area of the incident light beam are smaller than the distance between the slits? We have experimentally demonstrated that, under the above conditions, interference fringes can be obtained with a controlled degree of visibility by means of coincidence measurements between conujugated beams of the down-conversion luminescence.
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.