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Physical Review Applied

Tailoring entanglement with a symmetry: Anomalous ghost diffraction

Yue Zeng, Yuan Li, Wuhong Zhang, Yangjian Cai, Lixiang Chen

Published Oct 9, 2025• 2 citations
Publisher

Abstract

Coherence is a fundamental property of light. Recent years have witnessed a growing interest in coherence structuring, yielding a new type of partially coherent source with spatially tailored nonuniform correlations. However, the routine way of producing entangled photons via parametric down-conversion is to use a highly coherent laser source to pump nonlinear crystals. Here, we present a new strategy of exploiting such nonuniformly partially coherent sources to excite parametric down-conversion and thus endow the generated entanglement with a tailored and unusual spatial symmetry. To reveal the spatially varying degree of entanglement, we demonstrate the observation of an unusual Einstein-Podolsky-Rosen (EPR) correlation by transferring the circular structure of the coherence of the pump beam onto that of down-converted photons. For this, we observe both anomalous ghost diffraction and normal ghost images to examine the EPR-type inequalities and showcase the transition from nonentanglement to entanglement. Our work suggests that coherence structuring can offer a new dimension to generate and control quantum entanglement.

DOI
10.1103/3s4n-t7bb

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Coherence is a fundamental property of light. Recent years have witnessed a growing interest in coherence structuring, yielding a new type of partially coherent source with spatially tailored nonuniform correlations. However, the routine way of producing entangled photons via parametric down-conversion is to use a highly coherent laser source to pump nonlinear crystals. Here, we present a new strategy of exploiting such nonuniformly partially coherent sources to excite parametric down-conversion and thus endow the generated entanglement with a tailored and unusual spatial symmetry. To reveal the spatially varying degree of entanglement, we demonstrate the observation of an unusual Einstein-Podolsky-Rosen (EPR) correlation by transferring the circular structure of the coherence of the pump beam onto that of down-converted photons. For this, we observe both anomalous ghost diffraction and normal ghost images to examine the EPR-type inequalities and showcase the transition from nonentanglement to entanglement. Our work suggests that coherence structuring can offer a new dimension to generate and control quantum entanglement.
Entangled photons produced by spontaneous parametric down-conversion have been of paramount importance for our current understanding of quantum mechanics and advances in quantum information. In this process, the quantum correlations of the down-converted photons are governed by the optical properties of the pump beam illuminating the nonlinear crystal. Extensively, the pump beam has been modeled by either coherent beams or by the well-known Gaussian-Schell model, which leads to the natural conclusion that a high degree of optical coherence is required for the generation of highly entangled states. Here, we show that when a novel class of partially coherent Gaussian pump beams is considered, a distinct type of quantum state can be generated for which the amount of entanglement increases inversely with the degree of coherence of the pump beam. This leads to highly incoherent yet highly entangled multiphoton states, which should have interesting consequences for photonic quantum information science.
We demonstrate experimental generation of spatially entangled photon pairs by spontaneous parametric down-conversion (SPDC) using a partial spatially coherent pump beam. By varying the spatial coherence of the pump, we show its influence on the down-converted photon's spatial correlations and on its degree of entanglement, in excellent agreement with theory. We then exploit this property to produce pairs of photons with a specific degree of entanglement by tailoring of the pump coherence length. This work thus unravels the fundamental transfer of coherence occurring in SPDC processes, and provides a simple experimental scheme to generate photon pairs with a well-defined degree of spatial entanglement, which may be useful for quantum communication and information processing.
The ability to engineer the properties of quantum optical states is essential for quantum information processing applications. Here, we demonstrate tunable control of spatial correlations between photon pairs produced by spontaneous parametric down-conversion. By shaping the spatial pump beam profile in a type-I collinear configuration, we tailor the spatial structure of coincidences between photon pairs entangled in high dimensions, without effect on intensity. The results highlight fundamental aspects of spatial coherence and hold potential for the development of quantum technologies based on high-dimensional spatial entanglement.
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.
The ability to engineer the properties of quantum optical states is essential for quantum information processing applications. Here, we demonstrate tunable control of spatial correlations between photon pairs produced by spontaneous parametric down-conversion, and measure them using an electron multiplying charge coupled device (EMCCD) camera. By shaping the spatial pump beam profile in a type-I collinear configuration, we tailor the spatial structure of coincidences between photon pairs entangled in high dimensions without effect on intensity. The results highlight fundamental aspects of spatial coherence and hold potential for the development of quantum technologies based on high-dimensional spatial entanglement.
We propose to generate a counter-Einstein-Podolsky-Rosen (CEPR) state which possesses a positively-correlated momentum and anticorrelated position directly from spontaneous parametric down-conversion. The general CEPR state is given under a tightly focused Gaussian pump based on type II noncritical phase matching. We analytically and numerically study how a positively-correlated momentum and anticorrelated position of a biphoton can be achieved by choosing the proper focal parameter of the pump. To verify the degree of entanglement of the CEPR state, we calculate its entanglement entropy and it shows a unique dependence on the pump's focal parameter. Suggestions for practical engineering of the state are also given. Furthermore, based on an ideal CEPR state, we deduce a type of erect quantum ghost imaging which can be applied as the entanglement criterion. This work gives applicable references to the spatial control of an entangled photon source in experiments and may stimulate the development of new types of quantum technologies.