Researching | Quantum information transfer between photonic and quantum-dot spin qubits

Journals >Chinese Optics Letters >Volume 14 >Issue 6 >Page 062701 > Article

Chinese Optics Letters
Vol. 14, Issue 6, 062701 (2016)

Quantum information transfer between photonic and quantum-dot spin qubits

Ruitong Zhao and Ruisheng Liang^*

Author Affiliations

Laboratory of Nanophotonic Functional Materials and Devices, School for Information and Optoelectronic Science and Engineering, South China Normal University, Guangzhou 510006, China

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DOI: 10.3788/COL201614.062701 Cite this Article Set citation alerts

Ruitong Zhao, Ruisheng Liang. Quantum information transfer between photonic and quantum-dot spin qubits[J]. Chinese Optics Letters, 2016, 14(6): 062701 Copy Citation Text

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Abstract

We propose schemes for the efficient information transfer between a propagating photon and a quantum-dot (QD) spin qubit in an optical microcavity that have no auxiliary particles required. With these methods, the information transfer between two photons or two QD spins can also be achieved. All of our proposals can work with high fidelity, even with a high leakage rate. What is more, each information transfer process above can also be seen as a controlled-NOT (CNOT) operation. It is found that the information transfer can be equivalent to a CNOT gate. These proposals will promote more efficient quantum information networks and quantum computation.

\frac{d \hat{a}}{d t} = - [i (ω_{c} - ω) + \frac{κ}{2} + \frac{κ_{s}}{2}] \hat{a} - g {\hat{σ}}_{-} - \sqrt{κ} {\hat{a}}_{in}, \frac{d {\hat{σ}}_{-}}{d t} = - [i (ω_{X^{-}} - ω) + \frac{γ}{2}] {\hat{σ}}_{-} - g {\hat{σ}}_{z} \hat{a}, {\hat{a}}_{out} = {\hat{a}}_{in} + \sqrt{κ} \hat{a},

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r_{h} (ω) = 1 - \frac{κ [i (ω_{X^{-}} - ω) + \frac{γ}{2}]}{[i (ω_{X^{-}} - ω) + \frac{γ}{2}] [i (ω_{c} - ω) + \frac{κ}{2} + \frac{κ_{s}}{2}] + g^{2}} .

(2)

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r_{0} (ω) = \frac{i (ω_{c} - ω) - \frac{κ}{2} + \frac{κ_{s}}{2}}{i (ω_{c} - ω) + \frac{κ}{2} + \frac{κ_{s}}{2}} .

(3)

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\frac{1}{2} (| R 〉 + | L 〉) \otimes (| ↑ 〉 + | ↓ 〉) \to \frac{1}{2} e^{i φ_{0}} [(| R 〉 + e^{i Δ φ} | L 〉) | ↑ 〉 + (e^{i Δ φ} | R 〉 + | L 〉) | ↓ 〉],

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\frac{1}{\sqrt{2}} [(α + β) {| R 〉}_{a} + i (α - β) {| L 〉}_{a}] .

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\frac{1}{2} [(α + β) {| R 〉}_{a} {| ↑ 〉}_{s} + i (α + β) {| R 〉}_{a} {| ↓ 〉}_{s} - (α - β) {| L 〉}_{a} {| ↑ 〉}_{s} + i (α - β) {| R 〉}_{a} {| ↓ 〉}_{s}] .

(6)

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\frac{1}{\sqrt{2}} [(β {| ↑ 〉}_{s} + i α {| ↓ 〉}_{s}) {| R 〉}_{a} + (α {| ↑ 〉}_{s} + i β {| ↓ 〉}_{s}) {| L 〉}_{a}] .

(7)

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\frac{1}{\sqrt{2}} [(α {| ↓ 〉}_{s} + β {| ↑ 〉}_{s}) {| R 〉}_{a} + (α {| ↑ 〉}_{s} + β {| ↓ 〉}_{s}) {| L 〉}_{a}] .

(8)

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{| Ψ 〉}_{a} {| Ψ 〉}_{s} = (α {| R 〉}_{a} + β {| L 〉}_{a}) \otimes \frac{1}{\sqrt{2}} ({| ↑ 〉}_{s} + {| ↓ 〉}_{s}) \to \frac{1}{\sqrt{2}} [(α {| L 〉}_{a} + β {| R 〉}_{a}) {| ↑ 〉}_{s} + (α {| R 〉}_{a} + β {| L 〉}_{a}) {| ↓ 〉}_{s}] .

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{\hat{U}}_{1} = \frac{1}{\sqrt{2}} (\begin{matrix} 1 & 1 \\ i & - i \end{matrix}) .

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\frac{1}{2} [(α + β) {| R 〉}_{a} {| ↑ 〉}_{s} - (α - β) {| R 〉}_{a} {| ↓ 〉}_{s} + i (α + β) {| L 〉}_{a} {| ↑ 〉}_{s} + i (α - β) {| L 〉}_{a} {| ↓ 〉}_{s}] .

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{\hat{U}}_{2} = \frac{1}{\sqrt{2}} (\begin{matrix} 1 & 1 \\ 1 & - 1 \end{matrix})

(12)

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\frac{1}{\sqrt{2}} [(β {| R 〉}_{a} + i α {| L 〉}_{a}) {| ↑ 〉}_{s} + (α {| R 〉}_{a} + i β {| L 〉}_{a}) {| ↓ 〉}_{s}],

(13)

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\frac{1}{\sqrt{2}} [(β {| R 〉}_{a} + α {| L 〉}_{a}) {| ↑ 〉}_{s} + (α {| R 〉}_{a} + β {| L 〉}_{a}) {| ↓ 〉}_{s}] .

(14)

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| Ψ 〉_{s}^{'} | Ψ 〉_{a}^{'} = (α {| ↑ 〉}_{s} + β {| ↓ 〉}_{s}) \otimes \frac{1}{\sqrt{2}} ({| R 〉}_{a} + {| L 〉}_{a}) \to \frac{1}{\sqrt{2}} [(α {| ↓ 〉}_{s} + β {| ↑ 〉}_{s}) {| R 〉}_{a} + (α {| ↑ 〉}_{s} + β {| ↓ 〉}_{s}) {| L 〉}_{a}] .

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\frac{1}{2} (α {| ↑ 〉}_{s_{1}} + β {| ↓ 〉}_{s_{1}}) \otimes ({| ↑ 〉}_{s_{2}} + {| ↓ 〉}_{s_{2}}) \otimes {(| R 〉 + | L 〉)}_{a} .

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\frac{1}{2} [(α {| ↓ 〉}_{s_{1}} + β {| ↑ 〉}_{s_{1}})_{1} {| R 〉}_{a} + i (α {| ↑ 〉}_{s_{1}} + β {| ↓ 〉}_{s_{1}}) {| L 〉}_{a}] ({| ↑ 〉}_{s_{2}} + {| ↓ 〉}_{s_{2}}) .

(17)

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\frac{1}{2} [i {| ↑ 〉}_{s_{1}} {| R 〉}_{a} (α {| ↑ 〉}_{s_{2}} + β {| ↓ 〉}_{s_{2}}) + {| ↑ 〉}_{s_{1}} {| L 〉}_{a} (β {| ↑ 〉}_{s_{2}} - α {| ↓ 〉}_{s_{2}}) + i {| ↓ 〉}_{s_{1}} {| R 〉}_{a} (α {| ↓ 〉}_{s_{2}} + β {| ↑ 〉}_{s_{2}}) + {| ↓ 〉}_{s_{1}} {| L 〉}_{a} (α {| ↑ 〉}_{s_{2}} - β {| ↓ 〉}_{s_{2}})] .

(18)

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\frac{1}{2} {i [{| ↑ 〉}_{s_{2}} (α {| ↑ 〉}_{s_{1}} + β {| ↓ 〉}_{s_{1}}) + {| ↓ 〉}_{s_{2}} (α {| ↓ 〉}_{s_{1}} + β {| ↑ 〉}_{s_{1}})] {| R 〉}_{a} + [{| ↑ 〉}_{s_{2}} (α {| ↓ 〉}_{s_{1}} + β {| ↑ 〉}_{s_{1}}) - {| ↓ 〉}_{s_{2}} (α {| ↑ 〉}_{s_{1}} + β {| ↓ 〉}_{s_{1}})] {| L 〉}_{a}} .

(19)

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\frac{1}{2} {(α | R 〉 + β | L 〉)}_{a_{1}} \otimes {(| R 〉 + | L 〉)}_{a_{2}} \otimes {(| ↑ 〉 + | ↓ 〉)}_{s}

(20)

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\frac{1}{2} [{(α | L 〉 + β | R 〉)}_{a_{1}} {| ↑ 〉}_{s} + i {(α | R 〉 + β | L 〉)}_{a_{1}} {| ↓ 〉}_{s}] {(| R 〉 + | L 〉)}_{a_{2}} .

(21)

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\frac{1}{2} [i {| ↑ 〉}_{s} {| R 〉}_{a_{1}} {(α | R 〉 + β | L 〉)}_{a_{2}} + i {| ↑ 〉}_{s} {| L 〉}_{a_{1}} {(α | L 〉 + β | R 〉)}_{a_{2}} + {| ↓ 〉}_{s} {| R 〉}_{a_{1}} {(β | R 〉 - α | L 〉)}_{a_{2}} + {| ↓ 〉}_{s} {| L 〉}_{a_{1}} {(α | R 〉 - β | L 〉)}_{a_{2}} .

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\frac{1}{2} {i [{(α | R 〉 + β | L 〉)}_{a_{1}} {| R 〉}_{a_{2}} + {(α | L 〉 + β | R 〉)}_{a_{1}} {| L 〉}_{a_{2}}] {| ↑ 〉}_{s} + [{(α | L 〉 + β | R 〉)}_{a_{1}} {| R 〉}_{a_{2}} - {(α | R 〉 + β | L 〉)}_{a_{1}} {| L 〉}_{a_{2}}] {| ↓ 〉}_{s}} .

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F_{1} = \frac{{(ς + ξ)}^{2}}{2 (ς^{2} + ξ^{2})}, F_{2} = \frac{{(ς + ξ)}^{4} + {(ς - ξ)}^{4}}{{({(ς + ξ)}^{2} + {(ς - ξ)}^{2})}^{2}},

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Ruitong Zhao, Ruisheng Liang. Quantum information transfer between photonic and quantum-dot spin qubits[J]. Chinese Optics Letters, 2016, 14(6): 062701

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