Researching | Chiral single-photon switch-assisted quantum logic gate with a nitrogen-vacancy center in a hybrid system

Journals >Photonics Research >Volume 9 >Issue 3 >Page 405 > Article

Photonics Research
Vol. 9, Issue 3, 405 (2021)

Chiral single-photon switch-assisted quantum logic gate with a nitrogen-vacancy center in a hybrid system | Editors' Pick

Yuan Zhou^1、*, Dong-Yan Lü², and Wei-You Zeng²

Author Affiliations

¹School of Science, Advanced Functional Material and Photoelectric Technology Research Institution, Hubei University of Automotive Technology, Shiyan 442002, China

²School of Science, Hubei University of Automotive Technology, Shiyan 442002, China

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DOI: 10.1364/PRJ.405246 Cite this Article Set citation alerts

Yuan Zhou, Dong-Yan Lü, Wei-You Zeng. Chiral single-photon switch-assisted quantum logic gate with a nitrogen-vacancy center in a hybrid system[J]. Photonics Research, 2021, 9(3): 405 Copy Citation Text

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Abstract

We propose what we believe is a novel proposal for realizing a quantum C-NOT logic gate, through fabricating an interesting hybrid device with a chiral photon-pulse switch, a single nitrogen-vacancy (NV) center, and an optical microcavity. Three major different practical routes on realizing a chiral photon emitter are discussed, which can implement a chiral control unit via the nonreciprocal emitter–photon interactions, so-called “propagation-direction-dependent” emission. With the assistance of dichromatic microwave driving fields, we carry out the relevant C-NOT operations by engineering the interactions on a single NV spin in a cavity. We note that this logic gate is robust against practical noise and experimental imperfection, and this attempt may evoke wide and fruitful applications in quantum information processing.

{\hat{U}}_{C - NOT} = {| - ⟩}_{C C} {⟨ - | \otimes {\hat{I}}^{s} + | + ⟩}_{C C} ⟨ + | \otimes {\hat{σ}}_{x}^{s},

(1)

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{\hat{H}}_{IP}^{(I)} = (g \hat{a} | e ⟩ ⟨ 0 | + \frac{Ω}{\sqrt{2}} | ↑ ⟩ ⟨ 0 |) e^{i Δ t} + h.c.,

(3)

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{\hat{H}}_{eff}^{(I)} ≃ Ξ_{1} | ↑ ⟩ ⟨ ↑ | + Ξ_{2} | e ⟩ ⟨ e | + Λ (\hat{a} | e ⟩ ⟨ ↑ | + h.c.),

(4)

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{\hat{H}}_{IP}^{(II)} = \frac{Ω}{2} (| - 1 ⟩ ⟨ 0 | + | + 1 ⟩ ⟨ 0 |) e^{i Δ t} + h.c.,

(6)

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{\hat{H}}_{eff}^{(II)} = \frac{Ξ_{1}}{2} (| - 1 ⟩ ⟨ + 1 | + | + 1 ⟩ ⟨ - 1 |) .

(7)

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{\hat{U}}_{C-NOT} = [\begin{matrix} 1 & 0 & 0 & 0 \\ 0 & 1 & 0 & 0 \\ 0 & 0 & 0 & 1 \\ 0 & 0 & 1 & 0 \end{matrix}],

(8)

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{\hat{U}}_{2 \times 2}^{s} = [\begin{matrix} \frac{1}{2} (1 + r) & 0 \\ 0 & \frac{1}{2} (1 + r) \end{matrix}],

(9)

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{\hat{X}}_{2 \times 2}^{s} = [\begin{matrix} - i \cos \frac{Ξ_{1} t}{2} & \sin \frac{Ξ_{1} t}{2} \\ \sin \frac{Ξ_{1} t}{2} & - i \cos \frac{Ξ_{1} t}{2} \end{matrix}],

(10)

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{\hat{U}}_{C-NOT}^{R} = [\begin{matrix} \frac{1 + r}{2} & 0 & 0 & 0 \\ 0 & \frac{1 + r}{2} & 0 & 0 \\ 0 & 0 & - i \cos \frac{Ξ_{1} t}{2} & \sin \frac{Ξ_{1} t}{2} \\ 0 & 0 & \sin \frac{Ξ_{1} t}{2} & - i \cos \frac{Ξ_{1} t}{2} \end{matrix}] .

(11)

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F (t = \frac{π}{Ξ_{1}}) = \frac{1}{4} (1 + r + 2 \sin \frac{Ξ_{1} t}{2}) ≃ 1 .

(12)

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\frac{d \hat{ρ}}{d t} = - i [{\hat{H}}_{SP}^{(I), (II)}, \hat{ρ}] + κ D [\hat{a}] \hat{ρ} + γ_{e} D [{\hat{σ}}_{e}^{-}] \hat{ρ} + γ_{g} D [{\hat{σ}}_{z}] \hat{ρ} .

(13)

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{\hat{H}}_{2}^{'} = \frac{Ω_{1}}{2} | - 1 ⟩ ⟨ 0 | e^{- i ω_{1} t} + \frac{Ω_{2}}{2} | + 1 ⟩ ⟨ 0 | e^{- i ω_{2} t} + h.c. .

(14)

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| ψ_{in} ⟩ = (\cos α | σ_{+} ⟩ + \sin α | σ_{-} ⟩) \otimes (\cos β | + 1 ⟩ + \sin β | - 1 ⟩),

(15)

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| ψ_{out} ⟩ = \cos α | σ_{+} ⟩ (\cos β | + 1 ⟩ + \sin β | - 1 ⟩) + \sin α | σ_{-} ⟩ (\cos β | - 1 ⟩ + \sin β | + 1 ⟩),

(16)

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{\hat{H}}_{IP}^{(I)} = - Δ | 0 ⟩ ⟨ 0 | + g \hat{a} | e ⟩ ⟨ 0 | + \frac{Ω}{\sqrt{2}} | ↑ ⟩ ⟨ 0 | + h.c. .

(A1)

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{\hat{H}}_{IP}^{(I)} = [\begin{matrix} 0 & Ω / \sqrt{2} & 0 \\ Ω / \sqrt{2} & - Δ & g \\ 0 & g & 0 \end{matrix}],

(A2)

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{\hat{H}}_{IP}^{(II)} = - Δ | 0 ⟩ ⟨ 0 | + \frac{Ω}{\sqrt{2}} (| ↑ ⟩ ⟨ 0 | + h.c.) .

(A3)

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{\hat{H}}_{IP}^{(II)} = [\begin{matrix} 0 & 0 & Ω / 2 \\ 0 & 0 & Ω / 2 \\ Ω / 2 & Ω / 2 & - Δ \end{matrix}] .

(A4)

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Yuan Zhou, Dong-Yan Lü, Wei-You Zeng. Chiral single-photon switch-assisted quantum logic gate with a nitrogen-vacancy center in a hybrid system[J]. Photonics Research, 2021, 9(3): 405

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