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Conference on Lasers and Electro-Optics Europe & European Quantum Electronics Conference (CLEO/Europe-EQEC)

The Role of Detector Position in Quantum Ghost Diffraction

Andres Vega, Elkin A. Santos, Sina Saravi, Thomas Pertsch, Frank Setzpfandt

Published Jun 1, 2019• 0 citations
Publisher

Abstract

Quantum ghost diffraction enables the measurement of the spatial diffraction pattern of an object without measuring the spatial distribution of the photons that actually interacted with the object [1]. It uses photon pairs generated e.g. by spontaneous parametric down conversion (SPDC) in a nonlinear optical crystal, and relies on the correlation of the generated signal and idler photons in their spatial and temporal degrees of freedom. This measurement scheme is sketched in Fig. 1 (a). After the source, the two photons are separated into two different paths. The object, here we consider a grating, is located only in the signal path and thus interacts only with the signal photons. To measure the diffraction pattern, two detectors of small cross sections are used in the signal and idler arms. The signal detector is usually at a fixed position, collecting photons that interacted with the object. The idler detector can have varying positions, allowing to spatially resolve the collected photons that never interacted with the object. Through measuring the two-photon coincidence counting rate p, there exists the potential for recovering the diffraction pattern of the object, which allows to retrieve the grating period.

DOI
10.1109/cleoe-eqec.2019.8873217

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Quantum ghost diffraction enables the measurement of the spatial diffraction pattern of an object without measuring the spatial distribution of the photons that actually interacted with the object [1]. It uses photon pairs generated e.g. by spontaneous parametric down conversion (SPDC) in a nonlinear optical crystal, and relies on the correlation of the generated signal and idler photons in their spatial and temporal degrees of freedom. This measurement scheme is sketched in Fig. 1 (a). After the source, the two photons are separated into two different paths. The object, here we consider a grating, is located only in the signal path and thus interacts only with the signal photons. To measure the diffraction pattern, two detectors of small cross sections are used in the signal and idler arms. The signal detector is usually at a fixed position, collecting photons that interacted with the object. The idler detector can have varying positions, allowing to spatially resolve the collected photons that never interacted with the object. Through measuring the two-photon coincidence counting rate p, there exists the potential for recovering the diffraction pattern of the object, which allows to retrieve the grating period.
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.
Ghost imaging can be performed using either quantum or classical states of light that possess strong spatial correlations. In both cases, the image is formed by averaging over many optical events. Here we show that it is possible to distinguish an object from a preestablished basis set of objects by using a small number of position-correlated photon pairs produced by spontaneous parametric down-conversion. The signal photon is incident on one member of a set of spatially nonoverlapping objects. The "ghost" image information is impressed upon the spatially separated idler photon and is extracted by means of holographic filtering and coincidence detection. We were able to distinguish among sets of two and four spatially nonoverlapping objects with confidence levels higher than 87% and 81%, respectively. This method of ghost imaging can be performed in situations requiring extremely low light levels.
In this work, pairs of entangled photons are aimed at two spatially separated detectors: the path to one detector contains a physical object, while the path to the second detector does not. Yet, the second detector can be used to create an image of the object, even though none of the photons arriving at that detector have ever interacted with the object! This “ghost” imaging takes advantage of information that is shared between entangled photon pairs. This work aims to explore the underlying principles in a ghost imaging system that utilizes spontaneous parametric down-conversion (SPDC) as the source of entangled photons, with the larger goal of understanding the principles and operation of key parts of the system.
Ghost imaging and ghost diffraction can be realized by using the spatial correlations between signal and idler photons produced by spontaneous parametric down-conversion. If an object is placed in the signal (idler) path, the spatial correlations between the transmitted photons as measured by a single, non-imaging, "bucket" detector and a scanning detector placed in the idler (signal) path can reveal either the image or diffraction pattern of the object, whereas neither detector signal on its own can. The details of the bucket detector, such as its collection area and numerical aperture, set the number of transverse modes supported by the system. For ghost imaging these details are less important, affecting mostly the sampling time required to produce the image. For ghost diffraction, however, the bucket detector must be filtered to a single, spatially coherent mode. We examine this difference in behavour by using either a multi-mode or single-mode fibre to define the detection aperture. Furthermore, instead of a scanning detector we use a heralded camera so that the image or diffraction pattern produced can be measured across the full field of view. The importance of a single mode detection in the observation of ghost diffraction is equivalent to the need within a classical diffraction experiment to illuminate the aperture with a spatially coherent mode.