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Physical Review A

Annual-ring-type quasi-phase-matching crystal for generation of narrowband high-dimensional entanglement

Yi-Lin Hua, Zong‐Quan Zhou, Xiao Liu, Tian-Shu Yang, Zongfeng Li, Pei-Yun Li, Geng Chen, Xiao-Ye Xu, Jian‐Shun Tang, Jin‐Shi Xu, Chuan‐Feng Li, Guang‐Can Guo

Published Jan 24, 2018• 4 citations
Publisher

Abstract

A photon pair can be entangled in many degrees of freedom such as polarization, time bins, and orbital angular momentum (OAM). Among them, the OAM of photons can be entangled in an infinite-dimensional Hilbert space which enhances the channel capacity of sharing information in a network. Twisted photons generated by spontaneous parametric down-conversion offer an opportunity to create this high-dimensional entanglement, but a photon pair generated by this process is typically wideband, which makes it difficult to interface with the quantum memories in a network. Here we propose an annual-ring-type quasi-phase-matching (QPM) crystal for generation of the narrowband high-dimensional entanglement. The structure of the QPM crystal is designed by tracking the geometric divergences of the OAM modes that comprise the entangled state. The dimensionality and the quality of the entanglement can be greatly enhanced with the annual-ring-type QPM crystal.

DOI
10.1103/physreva.97.013836

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A photon pair can be entangled in many degrees of freedom such as polarization, time bins, and orbital angular momentum (OAM). Among them, the OAM of photons can be entangled in an infinite-dimensional Hilbert space which enhances the channel capacity of sharing information in a network. Twisted photons generated by spontaneous parametric down-conversion offer an opportunity to create this high-dimensional entanglement, but a photon pair generated by this process is typically wideband, which makes it difficult to interface with the quantum memories in a network. Here we propose an annual-ring-type quasi-phase-matching (QPM) crystal for generation of the narrowband high-dimensional entanglement. The structure of the QPM crystal is designed by tracking the geometric divergences of the OAM modes that comprise the entangled state. The dimensionality and the quality of the entanglement can be greatly enhanced with the annual-ring-type QPM crystal.
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.
-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.
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.
A crystal superlattice structure featuring nonlinear layers with alternating orthogonal optic axes interleaved with orthogonal poling directions, is shown to generate high-quality hyperentangled photon pairs via orthogonal quasi-phase-matched spontaneous parametric downconversion. We demonstrate that orthogonal quasi-phase matching (QPM) processes in a single nonlinear domain structure correct phase and group-velocity mismatches concurrently. Compared with the conventional two-orthogonal-crystals source and the double-nonlinearity single-crystal source, the orthogonal QPM superlattice is shown to suppress the spatial and temporal distinguishability of the generated photon pairs by several orders of magnitude, depending on the number of layers. This enhanced all-over-the-cone indistinguishability enables the generation of higher fluxes of photon-pairs by means of the combined use of (a) long nonlinear crystal in noncollinear geometry, (b) low coherence-time pumping and ultra-wide-band spectral detection, and (c) focused pumping and over-the-cone detection. While each of these three features is challenging by itself, it is remarkable that the orthogonal QPM superlattice meets all of these challenges without the need for separate spatial or temporal compensation.
Cavity-enhanced spontaneous parametric down-conversion (SPDC) provides a significant way to produce ∼10 MHz narrow-band photon pairs, which matches the bandwidth of photon for quantum memory. However, the output photon pairs from the cavity are not entangled, and postselection is required to create the entanglement so far, so the direct output of cavity-enhanced narrow-band entangled photon pairs is still an open challenge. Here, we propose a solution that realizes the first postselection-free cavity-enhanced narrow-band entangled photon pairs. The entanglement is achieved in degree of freedom of orbital angular momentum (OAM) by an OAM-conservation SPDC process in an actively and precisely controlled cavity supporting degenerate high-order OAM modes. The measured linewidth and fidelity are 13.8 MHz and 0.969(3), respectively, for the directly generated OAM entangled two photons. We deterministically transfer the OAM entanglement to polarization one with almost no loss and obtain polarization entangled two photons with a fidelity of 0.948(2). Moreover, we produce narrow-band OAM-polarization hyperentangled photon pairs with a fidelity of 0.850(2), which is realized by interfering the two photons on a polarizing beam splitter (PBS) and postselecting the events of one and only one photon on each PBS port. Novel cavity may find applications in cavity-based light-matter interaction. Our results provide an efficient and promising approach to create narrow-band entangled photon sources for memory-based long-distance quantum communication and network.
Photon pairs generated from spontaneous parametric down-conversion are a well-established method to realize entangled bipartite photonic systems. Laguerre-Gaussian modes, which carry orbital angular momentum (OAM), are commonly exploited to engineer high-dimensional entangled quantum states. For Hilbert spaces with dimension d>2d>2d>2, maximally entangled states (MESs) help to improve the capacity and security of quantum communication protocols, among several other promising features. However, the direct generation of MESs in well-defined high-dimensional subspaces of the infinite OAM basis has remained a challenge. Here, we formalize how the spatial distribution of the pump beam and the nonlinear profile of the crystal can be simultaneously utilized to generate MESs without additional spatial filtering of OAM modes within a subspace. We illustrate our approach with maximally entangled qutrits (d=3)(d=3)(d=3) and ququints (d=5)(d=5)(d=5).