- Photonics Research
- Vol. 10, Issue 2, 02000389 (2022)

Abstract

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 [1–7]. Two-photon entangled states, the simplest multi-photon entangled states, can be prepared based on second-order parametric downconversion in nonlinear media [8–15], but the generation efficiency is usually very low. For example, in beta-barium borate crystals, only one in every ${10}^{12}$ 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 ${\chi}^{(3)}$ is usually extremely small, typically ranging from ${10}^{-21}\text{\hspace{0.17em}\hspace{0.17em}}{\mathrm{m}}^{2}/{\mathrm{V}}^{2}$ to ${10}^{-19}\text{\hspace{0.17em}\hspace{0.17em}}{\mathrm{m}}^{2}/{\mathrm{V}}^{2}$ [19]. For example, for the type-I process in ${\mathrm{TiO}}_{2}$, the effective cubic susceptibility is ${\chi}^{(3)}=2.1\times {10}^{-20}\text{\hspace{0.17em}\hspace{0.17em}}{\mathrm{m}}^{2}/{\mathrm{V}}^{2}$. When a ${\mathrm{TiO}}_{2}$ crystal with a length of 5 mm is pumped by a continuous wave with power $100\text{\hspace{0.17em}\hspace{0.17em}}\mathrm{mW}$ (about ${10}^{17}$ 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.

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