明 瑩

( 延邊大學(xué)理學(xué)院 物理系, 吉林 延吉 133002 )

參量頻率轉(zhuǎn)換能夠產(chǎn)生可調(diào)諧的相干輻射和壓縮光[1]，因此被廣泛應(yīng)用于干涉測量、精確測量和光譜學(xué)等方面，并成為量子網(wǎng)絡(luò)的重要組成部分[2].在量子網(wǎng)絡(luò)中， 實(shí)現(xiàn)量子態(tài)的單位轉(zhuǎn)換的方法有很多，例如可以通過粒子湮滅或產(chǎn)生來實(shí)現(xiàn)，也可以通過參量頻率上轉(zhuǎn)換來實(shí)現(xiàn)，等等.由于參量頻率上轉(zhuǎn)換能夠顯著提高轉(zhuǎn)換效率[3]，因此被認(rèn)為是目前解決量子態(tài)轉(zhuǎn)換的最佳方法，但在所知文獻(xiàn)中其轉(zhuǎn)換效率均低于50%.研究[4-5]表明，在共振腔內(nèi)進(jìn)行頻率轉(zhuǎn)換可以有效增強(qiáng)轉(zhuǎn)換效率.基于文獻(xiàn)[5]，本文提出了在光學(xué)參量振蕩腔中的量子態(tài)頻率上轉(zhuǎn)換的方案.

1 理論模型

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圖1 實(shí)驗(yàn)裝置圖

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用振幅和位相正交量定義X=a+a+和Y=-i(a-a+), 獲得輸出場諧波模的起伏為:

經(jīng)過傅里葉變換后可得到：

δX0(Ω)=-1/{Ω2(iΩ+γ0+μ0)(γ+μ)+2Ω(Ω-iμ0-2iγ0σ2)(γ+μ)2+

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δY0(Ω)=1/{-Ω2(iΩ+γ0+μ0)(γ+μ)+2Ω(-Ω+iμ0+2iγ0σ2)(γ+μ)2+

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其中：

R1=Ω2(iΩ+γ0+μ0)(γ+μ)+2Ω(Ω-iμ0-2iγ0σ2)(γ+μ)2+4γ0(1-σ2)(γ+μ)3,

2Ω(Ω-iμ0-2iγ0σ2)(γ+μ)2-4γ0(1-σ2)(γ+μ)3,

R2=-Ω2(iΩ+γ0+μ0)(γ+μ)+2Ω(-Ω+iμ0+2iγ0σ2)(γ+μ)2+4γ0σ2(γ+μ)3,

2Ω(-Ω+iμ0+2iγ0σ2)(γ+μ)2-4γ0σ2(γ+μ)3,

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2 結(jié)果與討論

圖2 信號傳遞效率TX、TY和轉(zhuǎn)換效率η隨泵浦參數(shù)σ的變化曲線

參考文獻(xiàn)：

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[2] Cirac J I, Zoller P, Kimble H J, et al. Quantum state transfer and entanglement distribution among distant nodes in a quantum network[J]. Phys Rev Lett, 1997,78(16):3221-3224.

[3] Giorgi G, Mataloni P, Marini F D. Frequency hoppping in quantum interferometry: efficient up-down conversion for qubits and ebits[J]. Phys Rev Lett, 2003,90(2):027902.

[4] Bosenberg W R, Guyer D R. Broadly tunable, single-frequency optical parametric frequency-conversion system[J]. J Opt Soc Am B, 1993,10(9):1716-1722.

[5] Bai Y F, Zhai S Q, Gao J R, et al. Noise-free frequency conversion of quantum states[J]. Chin Phys B, 2011,20(3):034207.

[6] Jen H H, Kennedy T A B. Efficiency of light-frequency conversion in an atomic ensemble[J]. Phys Rev A, 2010,82(2):023815.

[7] Pooser R C, Marino A M, Boyer V, et al. Low-noise amplification of a continuous-variable quantum state[J]. Phys Rev Lett, 2009,103(1):010501.

[8] Gardiner C W, Collett M J. Input and output in damped quantum systems: quantum stochastic differential equations and the master equation[J]. Phys Rev A, 1985,31(6):3761-3774.

[9] Reynaud S, Fabre C, Giaocobino E. Quantum fluctuations in a two-mode parametric oscillator[J]. J Opt Soc Am B, 1987,4(10):1520-1524.

[10] Collett M J, Gardiner C W. Squeezing of intracavity and traveling-wave light fields produced in parametric amplification[J]. Phys Rev A, 1984,30(3):1386-1391.