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• Photonics Research
• Vol. 10, Issue 2, 02000389 (2022)
Yunning Lu1、2, Zeyang Liao1、3、*, Fu-Li Li2, and Xue-Hua Wang1、4、*
Author Affiliations
• 1State Key Laboratory of Optoelectronic Materials and Technologies, School of Physics, Sun Yat-sen University, Guangzhou 510275, China
• 2Shaanxi Province Key Laboratory of Quantum Information and Quantum Optoelectronic Devices, School of Physics, Xi’an Jiaotong University, Xi’an 710049, China
• 3e-mail: liaozy7@mail.sysu.edu.cn
• 4e-mail: wangxueh@mail.sysu.edu.cn
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Abstract

Generation of multi-photon entangled states with high efficiency in integrated photonic quantum systems is still a big challenge. The usual three-photon generation efficiency based on the third-order nonlinear effect is extremely low. Here, we propose a scheme to generate three-photon correlated states, which are entangled states in frequency space and bound states in real space, with high efficiency. This method relies on two crucial processes. On one hand, by employing a Sagnac interferometer, an incident photon can be transformed into a symmetric superposition of the clockwise and counterclockwise modes of the Sagnac loop, which can then be perfectly absorbed by the emitter. On the other hand, the coupling strengths of the two transition paths of the emitter to the Sagnac loop are set to be equal, under which the absorbed photon can be emitted completely from the cascaded transition path due to quantum interference. By adjusting the coupling strengths among the three transition paths of the emitter and the waveguide modes, we can control the spectral entanglement and spatial separation among the three photons. Our proposal can be used to generate three-photon entangled states on demand, and the efficiency can be higher than 90% with some practical parameters, which can find important applications in integrated quantum information processing.

1. INTRODUCTION

Quantum entanglement, “spooky action at a distance,” is one of the most intriguing phenomena in quantum mechanics. The generation of entangled photon states plays a crucial role in quantum information, quantum computation, and quantum metrology [17]. Two-photon entangled states, the simplest multi-photon entangled states, can be prepared based on second-order parametric downconversion in nonlinear media [815], but the generation efficiency is usually very low. For example, in beta-barium borate crystals, only one in every $1012$ pumped photons can be transformed into a two-photon state. The efficiency can be significantly improved by embedding semiconductor quantum dots in broadband photonic nanostructures [16], and the quantum states of a single photon can be on-demand controlled [17,18]. In comparison to the two-photon entangled pair, the efficiency to generate three-photon entangled states is even lower because the third-order nonlinear coefficient $χ(3)$ is usually extremely small, typically ranging from $10−21 m2/V2$ to $10−19 m2/V2$ [19]. For example, for the type-I process in $TiO2$, the effective cubic susceptibility is $χ(3)=2.1×10−20 m2/V2$. When a $TiO2$ crystal with a length of 5 mm is pumped by a continuous wave with power $100 mW$ (about $1017$ photons per second), only a few three-photon states can be obtained per hour [20]. Generation of three-photon entangled states with high efficiency is still a big challenge.