Photon pair generation from lithium niobate metasurface with tunable spatial entanglement

Quantum entanglement is a key fundamental concept and an enabling feature for various quantum technologies, as recognized in particular by the Nobel Prize in Physics in 2022. When we say two particles are entangled, it means that certain properties of them remain linked, even when they are far apart, a phenomenon that Einstein thought implausible, dubbing it "spooky action at a distance." The photons, quasi-particles of light, can possess entanglement in different degrees of freedom such as frequency, spatial position, and propagation direction. Photon pairs that are entangled in the spatial degrees of freedom represent an essential resource for a broad range of quantum applications, including imaging, communications, and computations. Therefore, photon sources with tunable spatial entanglement are pivotal in quantum photonic technologies. The most common way to generate spatially entangled photon pairs is based on a process called spontaneous parametric down-conversion (SPDC), where a pump photon goes through a quadratically nonlinear material and spontaneously splits into two lower-energy photons that are emitted in different directions. Conventional SPDC sources rely on nonlinear crystals, which are bulky, with a typical thickness on the scale of millimeters to centimeters. In such thick crystals, the emission directions are limited to a certain predefined angle range, making it challenging to flexibly tune the spatial pattern and entanglement of the photon pairs while maintaining the generation efficiency.

Recently, it was shown that strong spatial entanglement can be achieved when reducing the thickness of nonlinear crystals to a few microns, less than one-tenth the diameter of a human hair. However, the generation efficiency became much weaker due to the reduced light-matter interaction length, and the spatial entanglement property is fixed. Thereby, it remained a challenge how to efficiently generate tunable spatially entangled photon pairs at a tiny scale. One way to boost the nonlinear SPDC efficiency is to pattern the nonlinear film into nanostructures, thereby creating a so-called metasurface that supports optical resonances and can enhance nonlinear processes.

The research group led by Prof. Andrey Sukhorukov from the ARC Centre of Excellence for Transformative Meta-Optical Systems (TMOS) at the Australian National University recently demonstrated experimentally a spatially entangled photon-pair source from a metasurface using lithium niobate (LiNbO₃), a commonly used quadratically nonlinear material in photonic devices. In an invited paper published in the Special Issue on Optical Metasurfaces: Fundamentals and Applications in Chinese Optics Letters, Volume 21, Issue 1 (J. Zhang et al., Photon pair generation from lithium niobate metasurface with tunable spatial entanglement), the group went one step further and developed a new method to tune spatial entanglement of the generated photon pairs from the metasurface, which incorporates a 200-nanometer thick silica grating on top of a 300-nanometer thick film of lithium niobate, as shown in figure 1.

This metasurface offers important advantages. Firstly, it doesn't need nanofabrication on the LiNbO₃ so we can maximize the nonlinear material volume and avoid its possible damage in the nanopatterning process. Secondly, the grating can couple free-space light into the waveguide modes supported by the LiNbO₃ film and excite the so-called guided mode resonance. This kind of nonlocal resonance has a high quality factor, meaning that the optical field can stay in the LiNbO3 layer for a long time and build up a strong field intensity, thereby boosting the SPDC efficiency. Furthermore, the resonance features a strong angular dispersion, that is, the resonant wavelength is dependent on the propagation direction of light. The latter property is the key to realizing tunable spatial entanglement.

In this work, the authors provided a full theoretical description of the two-photon state wavefunction generated from metasurfaces. It was found that the emission pattern and wavelength of the photon pairs can be varied continuously over a broad range by simply changing the wavelength or beam size of the pump laser. This is achieved by leveraging the strong angular dispersion of metasurface resonances. The photons are generated with near-degenerate wavelengths around double the pump wavelength, and the degree of their spatial entanglement is quantified by the so-called Schmidt number. It is shown that entanglement can be tuned between a weakly entangled state with Schmidt number close to one and strongly entangled states with an order-of-magnitude larger Schmidt numbers. A unique advantage of such a metasurface-based quantum source is that there is no need to tune its temperature or physical orientation, in contrast to traditional sources based on thick crystals that require careful temperature control to operate at different wavelengths.

"Controlling the temperature is inconvenient in everyday devices – mobile phones for example need to operate in a range of environments," said Dr Jihua Zhang who is the leading author of the paper.

"This type of light source with efficient control of the quantum entanglement can benefit free-space quantum communications and quantum imaging", said Dr. Jinyong Ma who is working on the quantum imaging application.

In the future, the metasurface platform is promising for the realization of hyperentanglement simultaneously in several degrees of freedom including spectrum, polarization, and orbital angular momentum, further broadening the application prospects.

铌酸锂超构表面，光子对“心灵感应”的调节器

量子纠缠

量子纠缠在2022年诺贝尔物理学奖后走入大众视野，但一直以来，科学家对量子纠缠的探索从未停止。当两个粒子相互纠缠，意味着它们的某种特性是相互关联的，不管它们相距多远，当其中一个量子状态发生改变，另一个的状态会瞬时发生相应改变，可谓量子间的“心灵感应”。爱因斯坦曾经认为这是一种难以置信的现象并称之为“鬼魅般的超距作用”。

调控纠缠度的一大挑战

光子作为准粒子，可以在各种不同的自由度上产生纠缠，包括频率、空间、偏振和时间等。其中，在空间自由度纠缠的光子对在很多量子光学应用中发挥重要作用，比如量子成像、通信和计算，因此可调控的空间纠缠光源在量子光学中具有举足轻重的作用。产生空间纠缠光子对最常用的方式是基于自发参量下转换（SPDC）过程，即一个泵浦光子通过一个二阶非线性材料后分裂成两个沿不同方向出射的低能量光子，一个叫信号光子，另一个叫闲频光子。但是传统的基于非线性晶体的SPDC光源通常比较厚，一般在毫米到几厘米的量级。在此厚度下，产生的光子对只能沿着某些特定的方向出射，这使得在不损失光子对产生效率的情况下有效地调节空间纠缠特性成为挑战。

高效调节纠缠度光子对

研究表明，当把非线性晶体的厚度降低到比头发丝的直径还要小十多倍的微米尺度的薄膜时，其可以产生空间纠缠的光子对，但非线性相互作用距离的大大缩短使得光子对的产生速率极大降低。另外，在薄膜中产生光子对的空间纠缠特性也是固定的。因此，如何在很小的尺度下产生具有可调空间纠缠特性的光子对任然是一项重大挑战。一个高效的方法是把薄膜加工成微纳结构，形成超构表面，然后利用微纳结构支持的光学共振效应增强非线性光学效率。

澳大利亚国立大学TMOS卓越中心Andrey Sukhorukov教授研究团队发展了在铌酸锂超表面上产生空间纠缠度可调谐的光子对，相关研究成果发表在Chinese Optics Letters第21卷第1期Optical Metasurfaces: Fundamentals and Applications专题中，并被选为当期封面（Jihua Zhang, et al. Photon pair generation from lithium niobate metasurface with tunable spatial entanglement[Invited]）。

封面展示了光子对产生的过程：一个泵浦光子通过超构表面后分裂成两个在出射方向上相互纠缠的光子。

整个超构表面包含下层厚300 nm的铌酸锂薄膜和上层厚200 nm的二氧化硅光栅，如图1所示。该超构表面优势显著：第一，其制备过程不需要在铌酸锂上加工微纳结构，从而最大化地利用了非线性材料的空间体积，同时避免了在微纳加工过程中对非线性材料的损伤；第二，上层的光栅能把自由空间传输的光耦合到铌酸锂薄膜中支持的波导模式，从而激发导模共振。并且此非局域共振模式有很高的品质因子，能够延长光场在铌酸锂薄膜中的持续时间从而增强光场强度和非线性效应。更重要的是，这种共振模式拥有很强的角度色散，即共振波长随着入射角度变化，这一特性是实现可调谐空间纠缠度的关键。

研究小组首先提出了一种理论去描述在超构表面上产生双光子态的波函数。通过研究此波函数，发现只需简单改变泵浦光的波长或光斑尺寸就可以在较大范围内连续调控光子对的波长和出射方向，这正是利用了超构表面的角度色散。产生光子对的波长接近简并，是泵浦波长的两倍，其空间纠缠度是通过计算波函数的施密特数来表征。研究表明空间波函数可以在一个施密特数接近一的弱纠缠态和一个施密特数高一个数量级的强纠缠态之间可调。

同时，此超构表面空间纠缠光源的一个独特优势在于不需要调节温度或空间朝向，而传统的非线性晶体量子光源通常需要精确地温度控制来产生不同波长的光子对。这对于在类似手机这种需要在不同的环境下使用的日常设备中，调节温度是很不方便的。

未来展望

这种可以有效调节纠缠度的量子光源将有利于自由空间的量子成像和通信。在未来，基于此超构表面平台有望实现多个自由度之间的超纠缠，包括光谱、偏振和轨道角动量等，将进一步扩展其应用范围。