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Physical Review A

Manipulating the orbital-angular-momentum correlation of entangled two-photon states in three-dimensional nonlinear photonic crystals

Chuan Xu, Songtao Huang, Qian Yu, Dunzhao Wei, Pengcheng Chen, Saiwei Nie, Yong Zhang, Min Xiao

Published Dec 27, 2021• 20 citations
Publisher

Abstract

Three-dimensional (3D) nonlinear photonic crystal (NPC) has recently been realized in experiment, which provides a powerful platform for quantum-state engineering. Here, we propose a fork-grating 3D NPC scheme to manipulate orbital-angular-momentum (OAM) correlations of entangled two-photon pairs. The spiral spectra, bandwidths, and generation rates of counterpropagating and copropagating photon pairs are theoretically analyzed. Our results show that 3D NPC is of practical significance to generate high-dimensional OAM entanglement for quantum precision measurement, quantum computing, and quantum communication.

DOI
10.1103/physreva.104.063716

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•Dec 1, 2014•0 citations
Three-dimensional (3D) nonlinear photonic crystal (NPC) has recently been realized in experiment, which provides a powerful platform for quantum-state engineering. Here, we propose a fork-grating 3D NPC scheme to manipulate orbital-angular-momentum (OAM) correlations of entangled two-photon pairs. The spiral spectra, bandwidths, and generation rates of counterpropagating and copropagating photon pairs are theoretically analyzed. Our results show that 3D NPC is of practical significance to generate high-dimensional OAM entanglement for quantum precision measurement, quantum computing, and quantum communication.
-modulation in this crystal is designed for fulfilling a tilted quasi-phase-matching geometry to ensure the efficient generation of entangled photons as well as for transferring of topological charge of the crystal to the photon pairs. Numerical results show that the OAM of photon pair is anti-correlated and the degree of OAM entanglement can be enhanced by modulating the topological charge of crystal, which indicates a feasible extension to high-dimensional OAM entanglement. These studies suggest that the fork-poling nonlinear photonic crystal a unique platform for compact generation and manipulation of high-dimensional and high-order OAM entanglement, which may have potential applications in quantum communication, quantum cryptography and quantum remote sensing.
Maximally entangled photon pairs with a spatial degree of freedom is a potential way for realizing high-capacity quantum computing and communication. However, methods to generate such entangled states with high quality, high brightness, and good controllability are needed. Here, a scheme is experimentally demonstrated that generates spatially maximally entangled photon pairs with an orbital angular momentum degree of freedom via spontaneous parametric down-conversion in a nonlinear crystal. Compared with existing methods using postselection, the technique can directly modulate the spatial spectrum of down-converted photon pairs by engineering the input pump beam. In addition, the relative phase between spatially entangled photon pairs can be easily manipulated by preparing the relative phase of input pump states.
We investigate wavefront engineering of photon pairs generated through spontaneous parametric down conversion in lithium niobate-based nonlinear photonic crystals (NPCs). Due to the complexity of domain structures, it is more convenient to describe photon interaction based on the nonlinear Huygens-Fresnel principle than conventional quasiphase matching regime. Analytical expressions are obtained to describe the transverse properties of down-converted photon states. The convenience of domain engineering in LiNbO3crystals provides a potential platform for flexible wavefront manipulation of multiphoton states. The generation of N00N state with orbital angular momentum in a twisted NPC is studied utilizing this method. The obtained state is of great value in quantum cryptography, metrology, and lithography applications.
The bandwidth of any communication system, classical or quantum, is limited by the number of orthogonal states in which the information can be encoded. Quantum key distribution systems available commercially rely on the two-dimensional polarisation state of photons. Quantum computation has also been largely designed on the basis of qubits. However, a photon is endowed with other degrees of freedom, such as orbital angular momentum (OAM). OAM is an attractive basis to be used for quantum information because it is discrete and theoretically infinite-dimensional. This promises a higher information capacity per photon which can lead to more complex quantum computation protocols and more security and robustness for quantum cryptography. Entanglement of OAM naturally arises from spontaneous parametric down-conversion (SPDC). However, any practical experiment utilising the innately high-dimensional entanglement of the orbital angular momentum (OAM) state space of photons is subject to the modal capacity of the detection system. Only a finite subset of this space is accessible experimentally. Given such a constraint, we show that the number of measured, entangled OAM modes in photon pairs generated by SPDC can be increased by tuning the phase-matching conditions in the SPDC process. We achieve this by tuning the orientation angle of the nonlinear crystal generating the entangled photons.
ENGLISH ABSTRACT: High-dimensional quantum entanglement offers an increase in information capacity per photon; a highly desirable property for quantum information processes such as quantum communication, computation and teleportation. As the orbital angular momentum (OAM) modes of light span an infinite-dimensional Hilbert space, they have become frontrunners in achieving entanglement in higher dimensions. In light of this, we investigate the potential of OAM entanglement of photons by controlling the parameters in both the generation and measurement systems. We show the experimental procedures and apparatus involved in generating and measuring entangled photons in two-dimensions. We verify important quantum tests such as the Einstein, Podolsky and Rosen (EPR) paradox using OAM and angle correlations, as well as a violation of a Bell-type inequality. By performing a full state tomography, we characterise our quantum state and show we have a pure, highly entangled quantum state. We demonstrate that this method can be extended to higher dimensions. The experimental techniques used to generate and measure OAM entanglement place an upper bound on the number of accessible OAM modes. As such, we investigate new methods in which to increase the spiral bandwidth of our generated quantum state. We alter the shape of the pump beam in spontaneous parametric down-conversion and demonstrate an effect on both OAM and angle correlations. We also made changes to the measurement scheme by projecting the photon pairs into the Bessel-Gaussian (BG) basis and demonstrate entanglement in this basis. We show that this method allows the measured spiral bandwidth to be optimised by simply varying the continuous radial parameter of the BG modes. We demonstrate that BG modes can be entangled in higher dimensions compared with the commonly used helical modes by calculating and comparing the linear entropy and fidelity for both modes. We also show that quantum entanglement can be accurately simulated using classical light using back-projection, which allows the study of projective measurements and predicts the strength of the coincidence correlations in an entanglement experiment. Finally, we make use of each of the techniques to demonstrate the effect of a perturbation on OAM entanglement measured in the BG basis. We investigate the self-healing property of BG beams and show that the classical property is translated to the quantum regime. By calculating the concurrence, we see that measured entanglement recovers after encountering an obstruction.