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Physical Review A

Control of harmonic orbital angular momentum in second-harmonic generation of perfect vortices

Zhi-Feng Liu, Zhi‐Cheng Ren, Yan-Chao Lou, Zi-Mo Cheng, Yu-Xiang Yang, Yongnan Li, Jianping Ding, Xi‐Lin Wang, Hui‐Tian Wang

Published Jun 27, 2022• 15 citations
Publisher

Abstract

Nonlinear interaction between orbital angular momentum (OAM) modes has interesting effects and tremendous applications in both classical and quantum realms. Here we propose a strategy of using perfect vortices, which not only overcomes the spatial mode matching problem of nondegenerate OAM modes, but also reveals the OAM-only influence on the momentum matching by tuning the OAMs of the fundamental wave. We use perfect vortices of degenerate and nondegenerate OAM modes to clearly demonstrate the flexible control of OAM modes on nonlinear interaction by carefully exploring second-harmonic generation (SHG) in periodically poled crystal. We generate second-harmonic perfect vortices with the OAM order up to 40. Based on the observed phase-matching temperature shift caused by OAMs, we also use the SHG nonlinear process to distinctly confirm the OAM-only-induced subluminal effect. Our results pave the way toward unveiling the underlying physics behind nonlinear process of OAM modes and building high-capacity quantum links between systems operating at various wavelengths. The inverse process of SHG we developed, perfect-vortex-based spontaneous parametric down-conversion, may provide a promising solution for high-dimensional OAM entangled source.

DOI
10.1103/physreva.105.063518

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Nonlinear interaction between orbital angular momentum (OAM) modes has interesting effects and tremendous applications in both classical and quantum realms. Here we propose a strategy of using perfect vortices, which not only overcomes the spatial mode matching problem of nondegenerate OAM modes, but also reveals the OAM-only influence on the momentum matching by tuning the OAMs of the fundamental wave. We use perfect vortices of degenerate and nondegenerate OAM modes to clearly demonstrate the flexible control of OAM modes on nonlinear interaction by carefully exploring second-harmonic generation (SHG) in periodically poled crystal. We generate second-harmonic perfect vortices with the OAM order up to 40. Based on the observed phase-matching temperature shift caused by OAMs, we also use the SHG nonlinear process to distinctly confirm the OAM-only-induced subluminal effect. Our results pave the way toward unveiling the underlying physics behind nonlinear process of OAM modes and building high-capacity quantum links between systems operating at various wavelengths. The inverse process of SHG we developed, perfect-vortex-based spontaneous parametric down-conversion, may provide a promising solution for high-dimensional OAM entangled source.
Using orbital angular momentum (OAM) conservation in second-order nonlinear interaction processes, we create a classical to quantum optical network link in the OAM degrees of freedom of light via sum frequency generation, followed by spontaneous parametric down-conversion. Coherent OAM-carrying beams at 1550 nm are up-converted to 525.5-nm OAM-carrying beams in the first crystal, and are used to pump a second crystal to generate non-degenerate OAM entangled photon pairs at 795 nm and 1550 nm. By switching the OAM carried by the classical part, OAM correlation in the quantum part is shifted. High-level OAM entanglements in two-dimensional subspaces are verified.
Entanglement, as a crucial feature of quantum systems, is essential for various applications of quantum technologies. High-dimensional entanglement has the potential to encode arbitrary large amount of information and enhance robustness against eavesdropping and quantum cloning. The orbital angular momentum (OAM) entanglement can achieve the high-dimensional entanglement nearly for free stems due to its discrete and theoretically infinite-dimensional Hilbert space. A stringent limitation, however, is that the phase-matching condition limits the entanglement dimension because the coincidence rate decreases significantly for high-order modes. Here we demonstrate relatively flat high-dimensional OAM entanglement based on a spontaneous parametric down conversion (SPDC) from an ultrathin nonlinear lithium niobite crystal. The difference of coincidences between the different-order OAM modes significantly decreases. To further enhance the nonlinear process, this microscale SPDC source will provide a promising and integrated method to generate optimal high-dimensional OAM entanglement.
We propose a convenient approach for managing orbital angular momentum (OAM) of second-harmonic photons generated by a quadratic nonlinear interaction under noncolinear type-I phase matching condition. Since the OAMs of two fundamental photons can be flexibly controlled by using computer-generated holograms, we were able to realize arbitrary combination of both OAMs and experimentally confirm the OAM conservation selection rule ${\ensuremath{\ell}}_{2\ensuremath{\omega}}={\ensuremath{\ell}}_{\ensuremath{\omega}}^{\ensuremath{'}}+{\ensuremath{\ell}}_{\ensuremath{\omega}}^{\ensuremath{'}\ensuremath{'}}$ in general cases. In particular, our approach could be used to generate the second-harmonic photon states with fractional and odd-order OAMs.
We experimentally demonstrate multiple copies of optical orbital angular momentum (OAM) states through quasi-phase-matched (QPM) second-harmonic (SH) generation in a 2D periodically poled LiTaO3 (PPLT) crystal. Since the QPM condition is satisfied by involving different reciprocal vectors in the 2D PPLT crystal, collinear and noncollinear SH beams carrying OAMs of l2 are simultaneously generated by the input fundamental beam with an OAM of l1. The OAM conservation law (i.e., l2 = 2l1) holds well in the experiment, which can tolerate certain phase-mismatch between the interacting waves. Our results provide an efficient way to obtain multiple copies of the wavelength-converted OAM states, which can be used to enhance the capacity in optical communications.
Nonlinear interaction between orbital angular momentum (OAM) modes provides an enticing promise for realizing high-dimensional quantum states and multimodal communications. Here, we demonstrate the inter-modal interference of OAM modes based on the nonlinear frequency conversion of perfect vortex beams, permitting the arbitrary spatial intensity and phase information to be transformed and manipulated from 778 nm input beam to 420 nm output beam. The conversion of single OAM state obeys the typical arithmetic operation. In contrast, the conversion of superposition state is predicted and revealed as the inter-modal interference of full spatial complex amplitude. For the allowed OAM modes, the probability amplitude is quantitatively analyzed by the intensity overlap of input OAM modes, which determines the degree of degradation in the intensity and phase. As a result, the output beam exhibits the nonuniform petal-shaped intensity and phase distributions under the conditions of phase matching and OAM conservation. Furthermore, the inherent transverse structure invariance of perfect vortex beams enables them to accommodate and support larger OAM values and more superposition states.
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.