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Advanced Photonics Nexus
Vol. 2, Issue 1, 016003 (2023)

Deterministic N-photon state generation using lithium niobate on insulator device | Article Video , On the Cover

Hua-Ying Liu^{1、2、3、†,*}, Minghao Shang^1、2、3, Xiaoyi Liu^1、3、4, Ying Wei^1、2、3, Minghao Mi^1、3、5, Lijian Zhang^1、3、5, Yan-Xiao Gong^{1、2、3、*}, Zhenda Xie^{1、3、4、*}, and Shining Zhu^{1、2、3、5}

Author Affiliations

¹Nanjing University, National Laboratory of Solid State Microstructures, Nanjing, China

²Nanjing University, School of Physics, Nanjing, China

³Nanjing University, Collaborative Innovation Center of Advanced Microstructures, Nanjing, China

⁴Nanjing University, School of Electronic Science and Engineering, Nanjing, China

⁵Nanjing University, College of Engineering and Applied Sciences, Nanjing, China

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DOI: 10.1117/1.APN.2.1.016003 Cite this Article Set citation alerts

Hua-Ying Liu, Minghao Shang, Xiaoyi Liu, Ying Wei, Minghao Mi, Lijian Zhang, Yan-Xiao Gong, Zhenda Xie, Shining Zhu. Deterministic N-photon state generation using lithium niobate on insulator device[J]. Advanced Photonics Nexus, 2023, 2(1): 016003 Copy Citation Text

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Abstract

The large-photon-number quantum state is a fundamental but nonresolved request for practical quantum information applications. We propose an N-photon state generation scheme that is feasible and scalable, using lithium niobate on insulator circuits. Such a scheme is based on the integration of a common building block called photon-number doubling unit (PDU) for deterministic single-photon parametric downconversion and upconversion. The PDU relies on a 10⁷-optical-quality-factor resonator and mW-level on-chip power, which is within the current fabrication and experimental limits. N-photon state generation schemes, with cluster and Greenberger–Horne–Zeilinger state as examples, are shown for different quantum tasks.

Keywords

deterministic parametric downconversion deterministic parametric upconversion lithium niobate on isolator microring resonator multiphoton generation

Video Introduction to the Article

\hat{H} = {\hat{H}}_{NL} + {\hat{H}}_{L} = \frac{A_{eff}}{3} \cdot (\frac{- χ^{(2)}}{ε_{0}^{2} n_{p}^{2} n_{s}^{2} n_{i}^{2}}) \int_{L} d z \frac{\partial {\hat{Λ}}_{s}}{\partial z} \frac{\partial {\hat{Λ}}_{i}}{\partial z} \frac{\partial {\hat{Λ}}_{p}}{\partial z} + \sum_{j = p, s, i} \frac{A_{j}}{2} \int_{L} d z [\frac{1}{ε_{0} n_{j}^{2}} {(\frac{\partial {\hat{Λ}}_{j}}{\partial z})}^{2} + μ_{0} {(\frac{\partial {\hat{Λ}}_{j}}{\partial t})}^{2}] .

(1)

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{\hat{Λ}}_{j} (z, t) = \int_{0}^{\infty} d k_{j} \sqrt{\frac{ℏ}{2 μ_{0} ω_{j} A_{j}}} \cdot (α_{k_{j}} {\hat{a}}_{k_{j}} e^{i k_{j} z} e^{- i ω_{j} t} + h.c.) .

(2)

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Q > \frac{ω R}{c | 1 / n_{s 0} - 1 / n_{i 0} |},

(3)

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{\hat{Λ}}_{j} (z, t) = \int_{k_{j_{0}} - Δ}^{k_{j_{0}} + Δ} d k_{j} \sqrt{\frac{ℏ}{2 μ_{0} ω_{j} A_{j}}} \cdot (α_{k_{j}} {\hat{a}}_{k_{j}} e^{i k_{j} z} e^{- i ω_{j} t} + h.c.) .

(4)

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\hat{H} = g \int_{k_{p_{0}} - Δ}^{k_{p_{0}} + Δ} d k_{p} \int_{k_{s_{0}} - Δ}^{k_{s_{0}} + Δ} d k_{s} \int_{k_{i_{0}} - Δ}^{k_{i_{0}} + Δ} d k_{i} \cdot (v (k_{p}) v^{*} (k_{s}) v^{*} (k_{i}) {\hat{a}}_{k_{s}}^{†} {\hat{a}}_{k_{i}}^{†} {\hat{a}}_{k_{p}} e^{- i (ω_{p} - ω_{s} - ω_{i}) t} + h.c.) + \sum_{j = p, s, i} \int_{k_{j 0} - Δ}^{k_{j 0} + Δ} d k_{j} \frac{ℏ c k_{j} R}{n_{j}} | v (k_{j}) |^{2} {\hat{a}}_{k_{j}}^{†} {\hat{a}}_{k_{j}},

(5)

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\frac{\hat{H}}{ℏ} = ξ ({\hat{ς}}_{s}^{†} {\hat{ς}}_{i}^{†} {\hat{ς}}_{p} + {\hat{ς}}_{p}^{†} {\hat{ς}}_{s} {\hat{ς}}_{i}) + ω_{p_{0}} {\hat{ς}}_{p}^{†} {\hat{ς}}_{p} + ω_{s_{0}} {\hat{ς}}_{s}^{†} {\hat{ς}}_{s} + ω_{i_{0}} {\hat{ς}}_{i}^{†} {\hat{ς}}_{i},

(6)

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ξ \equiv \frac{χ^{(2)}}{12} \sqrt{\frac{ℏ}{π ε_{0} R}} {(\frac{c}{n_{p_{0}} n_{s_{0}} n_{i_{0}}})}^{\frac{3}{2}} \frac{A_{eff}}{\sqrt{A_{p_{0}} A_{s_{0}} A_{i_{0}}}} \sqrt{k_{p_{0}} k_{s_{0}} k_{i_{0}}} .

(7)

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| Ψ (t_{I}) ⟩ = e^{- i ω_{p_{0}} t_{I}} [\cos (ξ t_{I}) | 1 ⟩_{p} - i \sin (ξ t_{I}) | 1,1 ⟩_{s, i}],

(8)

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η_{PDC} = \sin^{2} (\frac{2 π ξ Q}{ω}) .

(9)

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{\hat{H}}_{I} = i ℏ ι ({\hat{a}}_{s} {\hat{a}}_{p}^{†} - h.c.),

(10)

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η_{PUC} = \sin^{2} (\sqrt{κ P_{SFG 1}} l),

(11)

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| {cluster}_{4} ⟩ = \frac{1}{2} ({| \tilde{0} \tilde{0} \tilde{0} \tilde{0} ⟩}_{1234} + {| \tilde{0} \tilde{0} \tilde{1} \tilde{1} ⟩}_{1234} + | \tilde{1} \tilde{1} \tilde{0} \tilde{0} ⟩_{1234} - {| \tilde{1} \tilde{1} \tilde{1} \tilde{1} ⟩}_{1234}),

(12)

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| {GH z}_{4} ⟩ = ({| \tilde{0} ⟩}^{\otimes 4} + e^{i φ} {| \tilde{1} ⟩}^{\otimes 4}) / \sqrt{2},

(13)

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Figures&Tables (4)

References (72)

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Hua-Ying Liu, Minghao Shang, Xiaoyi Liu, Ying Wei, Minghao Mi, Lijian Zhang, Yan-Xiao Gong, Zhenda Xie, Shining Zhu. Deterministic N-photon state generation using lithium niobate on insulator device[J]. Advanced Photonics Nexus, 2023, 2(1): 016003

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