李銀海 許昭懷 王雙 許立新?周志遠(yuǎn)? 史保森

1)(中國科學(xué)技術(shù)大學(xué)光學(xué)與光學(xué)工程系,合肥 230026)

2)(中國科學(xué)技術(shù)大學(xué),中國科學(xué)院量子信息重點(diǎn)實(shí)驗(yàn)室,合肥 230026)

3)(中國科學(xué)技術(shù)大學(xué),量子信息和量子物理協(xié)作創(chuàng)新中心,合肥 230026)

兩個(gè)獨(dú)立全光纖多通道光子糾纏源的Hong-Ou-Mandel干涉?

李銀海1)許昭懷1)王雙2)3)許立新1)?周志遠(yuǎn)2)3)?史保森2)3)

1)(中國科學(xué)技術(shù)大學(xué)光學(xué)與光學(xué)工程系,合肥 230026)

2)(中國科學(xué)技術(shù)大學(xué),中國科學(xué)院量子信息重點(diǎn)實(shí)驗(yàn)室,合肥 230026)

3)(中國科學(xué)技術(shù)大學(xué),量子信息和量子物理協(xié)作創(chuàng)新中心,合肥 230026)

(2017年2月21日收到;2017年3月29日收到修改稿)

獨(dú)立光子源的干涉是實(shí)現(xiàn)復(fù)雜量子體系應(yīng)用(比如多光子糾纏態(tài)產(chǎn)生和量子隱形傳態(tài)等)的核心技術(shù).利用100 GHz密集波分復(fù)用技術(shù),實(shí)現(xiàn)了1.55μm全光纖多通道獨(dú)立糾纏光子源的Hong-Ou-Mandel干涉,在不去除暗符合(隨機(jī)符合計(jì)數(shù))的情況下,可見度為53.2%±8.4%,去除暗符合可見度可達(dá)到82.9%±5.3%.給出了關(guān)于色散位移光纖中基于自發(fā)四波混頻過程產(chǎn)生的單光子光譜純度嚴(yán)格的理論描述,模擬了抽運(yùn)脈沖寬度和濾波器帶寬對單光子光譜純度的影響,并給出了理論上的最佳條件(最佳的抽運(yùn)脈沖寬度為8 ps,高斯濾波器帶寬為40 GHz及以下).在測量Hong-Ou-Mandel干涉之前,先測量了液氮冷卻狀態(tài)下的色散位移光纖關(guān)聯(lián)光子源的符合和隨機(jī)符合比率,在抽運(yùn)功率為23μW的情況下,最大比率可以達(dá)到131.Hong-Ou-Mandel干涉在高精度光學(xué)測量、測量裝置無關(guān)的量子密鑰分配等應(yīng)用中扮演著極為重要的角色.

密集波分復(fù)用,Hong-Ou-Mandel干涉,色散位移光纖

1 引 言

獨(dú)立光子源之間的Hong-Ou-Mandel干涉(HOMI)是實(shí)現(xiàn)高精度光學(xué)測量[1]、復(fù)雜的多光子GHz態(tài)和團(tuán)簇態(tài)產(chǎn)生、量子密鑰分配和光子NOON態(tài)測量[2?7]的核心技術(shù),而這些技術(shù)正是量子科學(xué)的基石,因此獨(dú)立源之間的HOMI已被廣泛研究.最早在可見光波段的研究,是利用非線性晶體中的自發(fā)參量下轉(zhuǎn)換過程[8?13]或者是光子晶體光纖中的自發(fā)四波混頻過程展開[14?16];后來對通信波段的研究是利用非線性晶體中的自發(fā)參量下轉(zhuǎn)換過程展開[17].從這些工作中,我們了解到提高干涉可見度的關(guān)鍵是提高光子源的單光子光譜純度(簡記為純度),可采用的手段為管理色散、控制相位匹配條件和盡量減小濾波器帶寬.

當(dāng)今基于波導(dǎo)的平臺(tái)(比如光纖和硅基波導(dǎo))相較于傳統(tǒng)的空間光學(xué)系統(tǒng)表現(xiàn)出了巨大的潛力:低成本、高集成和光纖通信系統(tǒng)無縫連接等.許多科研工作者將精力集中到基于色散位移光纖(dispersion shifted fi ber,DSF)[18?23]和硅波導(dǎo)[24?26]的糾纏光子源產(chǎn)生和量子態(tài)管理中.為了在DSF中產(chǎn)生更復(fù)雜的量子態(tài),獨(dú)立源的HOMI勢在必行.

對于DSF中的HOMI,Takesue[27]利用100 MHz重復(fù)頻率,脈沖寬度小于1 ps的鎖模激光器(波長1551.1 nm)和25 GHz的濾波器實(shí)現(xiàn)了53%的干涉可見度.在本文的工作中,首先詳細(xì)給出了DSF中關(guān)聯(lián)光子光譜純度的理論描述,并給出了理論上的最佳實(shí)驗(yàn)條件;然后利用基于密集波分復(fù)用(DWDM)技術(shù)在DSF中產(chǎn)生的多通道關(guān)聯(lián)光子源[28],理論上實(shí)現(xiàn)了多通道的HOMI.

2 基于DSF中自發(fā)四波混頻過程的關(guān)聯(lián)光子光譜純度理論

2.1 理論模型

首先我們給出了基于DSF中自發(fā)四波混頻產(chǎn)生光子對的理論描述.產(chǎn)生光子對的量子態(tài)可以表述為[9,12,29]

每個(gè)模式都有一個(gè)由施密特?cái)?shù)gn[29]決定的權(quán)重.施密特分解告訴我們,如果一個(gè)光子位于態(tài)則預(yù)示了對應(yīng)的其余光子的態(tài)為對應(yīng)的純度定義為而且純度由聯(lián)合譜振幅(joint spectral amplitude,JSA)f(ωs,ωi)[30]的分解因式?jīng)Q定. 雖然施密特分解不能解析地實(shí)現(xiàn),但是我們可以數(shù)值模擬并計(jì)算奇異值.純度由奇異值的平方求和給出,與施密特量[31]相等.因此,一個(gè)必要條件是在單個(gè)光譜模式下,我們將f(ωs,ωi)分解為f(ωs,ωi)=fs(ωs)fi(ωi).

在DSF中產(chǎn)生的光子對的JSA決定于抽運(yùn)包絡(luò)ε(ωs+ ωi)和光纖相位匹配條件Γ(ωs,ωi),因此f(ωs,ωi)= ε(ωs+ ωi)Γ(ωs,ωi). 假設(shè)抽運(yùn)激光是高斯模式,帶寬為σp,則|ε(ωs+ ωi)|2=exp{?2[(ωs+ ωi? ωp)/σp]2}, 相較于非線性晶體中的自發(fā)參量下轉(zhuǎn)換過程,有一個(gè)因數(shù)2的不同,這是由于自發(fā)四波混頻產(chǎn)生信號光和閑頻光的過程不同[32].DSF中自發(fā)四波混頻的相位匹配條件可以寫成|Γ(ωs,ωi)|2=[sinc(?kL/2)]2,其中?k=2kp?ks?ki+2γP是相位失配,kp,ks,ki分別為抽運(yùn)光、信號光和閑頻光的波數(shù),γ=2.6 km?1·W?1為DSF的三階非線性系數(shù),P為抽運(yùn)功率.我們用高斯函數(shù)來逼近這個(gè)位相匹配條件|Γ(ωs,ωi)|2∝ exp(?2α2?k2L2), 其中α=0.220.在抽運(yùn)光、信號光和閑頻光的中心頻率對相位失配展開,聯(lián)合譜強(qiáng)度(joint spectral intensity,JSI)可以寫成

2.2 模擬結(jié)果

結(jié)合實(shí)驗(yàn)條件,我們數(shù)字模擬了抽運(yùn)光的寬度和濾波器帶寬對JSI和光子源純度的影響,結(jié)果參見圖1.圖1(a)—(d)為相位匹配函數(shù)、抽運(yùn)包絡(luò)函數(shù)、JSI不加40 GHz濾波器和加40 GHz濾波器的結(jié)果,圖中橫坐標(biāo)和縱坐標(biāo)為信號光和閑頻光分別相對其中心頻率的頻率偏移量,圖形表示了強(qiáng)度分布和頻率失諧量的關(guān)系.模擬的參數(shù)為其中Td=25 ps為抽運(yùn)激光的脈沖寬度;L=300 m為光纖長度,理論上,不加濾波器時(shí)單光子純度為0.5693,加上100 GHz DWDM(等效高斯濾波帶寬約為40 GHz)濾波之后為0.8765.圖1(e)為不加濾波器的情況下抽運(yùn)脈沖寬度對純度的影響,我們得到最佳的抽運(yùn)脈沖寬度為8 ps.圖1(f)為高斯濾波對純度的影響,對應(yīng)濾波器帶寬的降低,光子純度增加(抽運(yùn)脈沖寬度固定為25 ps,和我們實(shí)際使用的激光器的脈沖寬度一致).

圖1 (網(wǎng)刊彩色)(a)相位匹配函數(shù)數(shù)學(xué)模擬;(b)抽運(yùn)函數(shù);(c)不加濾波器的JSI;(d)加40 GHz高斯濾波器的JSI;(e)光子純度和抽運(yùn)脈沖寬度的關(guān)系;(f)光子純度和濾波器帶寬的關(guān)系Fig.1.(color online)(a)Numerical simulations of phase matching function;(b)pump functions;(c)JSI without spectral fi ltering;(d)JSI fi ltered with 40 GHz Gaussian fi lters;(e)single photon spectral purity against pump pulse width;(f)single photon spectral purity against fi lter bandwidth of the photon pairs.

3 實(shí)驗(yàn)系統(tǒng)及測量結(jié)果

實(shí)驗(yàn)裝置如圖2所示.我們用一個(gè)自制的脈寬25 ps、重復(fù)頻率27.9 MHz的鎖模激光器作為抽運(yùn)光,然后用可調(diào)衰減器(TA)來調(diào)節(jié)光子源的抽運(yùn)功率,利用級聯(lián)的100 GHz的DWDM濾波器來過濾抽運(yùn)光.然后用50:50分束器將濾波后的抽運(yùn)光分成兩路分別抽運(yùn)兩段液氮冷卻的300 m長DSF光纖來產(chǎn)生兩個(gè)獨(dú)立的光子源.經(jīng)過DSF之后,使用兩組級聯(lián)的200 GHz的DWDM濾波器以及光纖偏振旋轉(zhuǎn)器和偏振片過濾掉抽運(yùn)光及其正交偏振方向的拉曼散射.然后兩個(gè)32通道的100 GHz DWDM器件被用來將對應(yīng)通道的關(guān)聯(lián)光子對分開(選用信道C31和C37,對應(yīng)中心波長1552.52 nm和1547.72 nm).兩個(gè)獨(dú)立源之間的延遲用可調(diào)光纖延遲線來調(diào)整.從這兩個(gè)32通道的DWDM器件相同信道出射的光子被引入同一個(gè)50:50耦合器進(jìn)行干涉,另外兩路光子被用作觸發(fā)信號,用兩個(gè)連續(xù)觸發(fā)InGaAs單光子探測器(APD1,APD4,ID Quanta,ID220,20%探測效率,3μs死時(shí)間,暗計(jì)數(shù)率4k cps),它們輸出的電信號用來觸發(fā)兩個(gè)門觸發(fā)模式的單光子探測器(APD2,APD3,Qasky,合肥,中國,100 MHz,20%探測效率,每個(gè)門暗計(jì)數(shù)4×10?5)來做光子符合測量.APD2和APD3探測的光子信號輸出到我們的符合計(jì)數(shù)設(shè)備(Pico quanta,TimeHarp 260,1.6 ns符合窗口)來進(jìn)行四光子符合測量.

圖2 兩個(gè)基于300 m DSF中自發(fā)四波混頻的獨(dú)立光子源的HOMI實(shí)驗(yàn)裝置(DSF,色散位移光纖;APD1-4,雪崩光電二極管單光子探測器;PFR&P,光纖偏振旋轉(zhuǎn)器和檢偏器;PC1(2),偏振控制器)Fig.2.Experiment setup for HOMI between two independent photon sources generated by spontaneous four-wave mixing in two 300 m DSFs(DSF,dispersion shifted fi ber;APD1-4,avalanched photon detector;FPR and P, fi ber polarization rotator and polarizer;PC1(2),polarization controller).

4 討 論

圖3 (a)CAR和抽運(yùn)功率的關(guān)系;(b)符合時(shí)間為1000 s,四光子符合和兩個(gè)單光子源的相對延遲的關(guān)系Fig.3.(a)CAR as a function of pump power;(b)four-fold coincidences in 1000 s as a function of the relative delay between the two single photon sources.

在測量兩個(gè)獨(dú)立單光子源的HOMI之前,我們首先測量了單光子源的符合和隨機(jī)符合比率(coincidence to accidental coincidence ratio,CAR)關(guān)于抽運(yùn)功率的關(guān)系,結(jié)果見圖3(a).對于相對較低的抽運(yùn)功率,CAR受限于由單光子探測器暗計(jì)數(shù)導(dǎo)致的暗符合,隨著抽運(yùn)功率的上升,CAR隨之升高;在抽運(yùn)功率為23μW時(shí)達(dá)到最大,CAR為131.抽運(yùn)功率繼續(xù)升高,多光子效應(yīng)開始出現(xiàn)并限制CAR的提高,所以CAR開始下降.然后我們進(jìn)行了HOMI測量過程,濾波后的抽運(yùn)功率為0.25 mW,每段DSF的抽運(yùn)功率是0.12 mW.采用相對較高的功率可以縮短測量時(shí)間,但是相對較大的多光子效應(yīng)會(huì)導(dǎo)致較低的干涉可見度.不去除暗符合,可見度為53.2%±8.4%,去除暗符合之后,為82.9%±5.3%,去除暗符合之后可見度的值非常接近我們理論計(jì)算的結(jié)果0.8765,分束器的分束比誤差和兩段DSF的不完全一致導(dǎo)致了和理論值的微小差異.通過斷開耦合器的一臂進(jìn)行測量,我們可以得到暗符合的值.單光子探測器較高的暗計(jì)數(shù)和多光子效應(yīng)導(dǎo)致的暗符合嚴(yán)重降低了HOMI的可見度.最大可見度可以表示為

5 結(jié) 論

我們給出了兩個(gè)獨(dú)立的多通道全光纖光子源的HOMI的理論研究和實(shí)驗(yàn)結(jié)果,詳細(xì)討論了在DSF中抽運(yùn)脈沖寬度和濾波器帶寬對單光子純度的影響,并給出了理論上最佳的實(shí)驗(yàn)條件.需要進(jìn)一步說明的是:1)我們的光子源抽運(yùn)脈沖寬度并沒有處在理論最佳的實(shí)驗(yàn)位置;2)試驗(yàn)中使用的單光子探測器探測效率相對較低,暗計(jì)數(shù)相對較高,這是影響實(shí)驗(yàn)結(jié)果的重要因素,如果能提高探測效率,降低暗計(jì)數(shù),四光子符合實(shí)驗(yàn)結(jié)果將能大大提高;3)在實(shí)驗(yàn)中我們用了相對較高的抽運(yùn)功率(0.12 mW)來大幅縮短測量時(shí)間(符合測量時(shí)間為1000 s),而在抽運(yùn)功率為23μW時(shí),DSF單光子源的CAR最佳可以達(dá)到131;4)我們在實(shí)驗(yàn)中采用了32通道DWDM的一對信道(C31-C37),根據(jù)之前實(shí)現(xiàn)的多通道全光纖糾纏光子源,我們有理由相信可以采用其他信道(比如C30-C38,C32-C36)來拓展在量子通信任務(wù)中的信道容量.

總之,兩個(gè)獨(dú)立光子源的HOMI是光子對在多光子態(tài)操作、量子隱形傳態(tài)和測量裝置無關(guān)量子密鑰分配等應(yīng)用中的關(guān)鍵技術(shù),我們實(shí)現(xiàn)了兩個(gè)獨(dú)立的多通道全光纖糾纏光子源的HOMI.基于光纖的糾纏光子系統(tǒng)在未來的量子信息技術(shù)中扮演著極為重要的角色.

感謝中國科學(xué)技術(shù)大學(xué)的李海鷗博士提供了液氮、陳巍博士提供了單光子探測器以及武漢工程大學(xué)的金銳博博士提供給予的建議和幫助.

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PACS:03.67.Hk,42.79.Sz,42.81.UvDOI:10.7498/aps.66.120302

Hong-Ou-Mandel interference between two independent all- fi ber multiplexed photon sources?

Li Yin-Hai1)Xu Zhao-Huai1)Wang Shuang2)3)Xu Li-Xin1)?Zhou Zhi-Yuan2)3)?Shi Bao-Sen2)3)

1)(Department of Optics and Optical Engineering,University of Science and Technology of China,Hefei 230026,China)
2)(Key Laboratory of Quantum Information,University of Science and Technology of China,Hefei 230026,China)
3)(Synergetic Innovation Center of Quantum Information and Quantum Physics,University of Science and Technology of China,Hefei 230026,China)

21 February 2017;revised manuscript

29 March 2017)

Interference between independent photon sources is the key technique to realize complex quantum systems for more sophisticated applications such as multi-photon entanglement generation and quantum teleportation.Here,we report Hong-Ou-Mandel interference(HOMI)between two independent 1.55μm all- fi ber photon pair sources over two 100 GHz dense wave division multiplexing(DWDM)channels,whose visibility reaches 53.2%±8.4%(82.9%±5.3%)without(with)back ground counts subtracted.In addition,we theoretically describe in detail the single photon spectral purity of the photon source generated in dispersion shifted fi ber(DSF),simulate the in fl uences of the pulse width and fi lter bandwidth on the purity,and obtain the optimized condition.The optimized pump pulse width is 8 ps and fi lter bandwidth is about 40 GHz or less.A home-made 1550.1 nm mode-locked fi ber laser source,whose pulse width and repetition rate are 25 ps and 27.9 MHz respectively,acts as a pump of photon source.A tunable attenuator is used to adjust the pump power of the photon source,and the broad band background fl uorescence photons are fi ltered out by cascade 100 GHz DWDM fi lters.The clean pump beam is divided into two equal parts by the 50:50 optical coupler to pump two 300 m DSFs(cooled by liquid nitrogen)to generate independent photon sources.Then the strong pump beam and noise photon from Raman scattering in orthogonal polarization are removed by 2 groups of 200 GHz DWDM fi lters and fi ber polarization rotator and polarizer.Then two 100 GHz DWDMs are used for separating photons at correlated channel pairs.The relative delay between the two independent photons is adjusted by tunable fi ber delay line.Photons from the same channels are combined in a second beam splitter for interference,and the other two photons are used as trigger signals.The two triggered photons are detected by two free running InGaAs avalanched single photon detectors(APD1,APD4,ID Quanta,ID220,20%detection efficiency,3μs dead time,dark count rate 4k cps),and the outputs of detectors APD1 and APD4 are used to trigger two single-photon detectors running in the gated mode(APD2,APD3,Qasky,Hefei,China,100 MHz,free gating single photon detectors,20%detection efficiency,dark count probability 4×10?5per gate)for twophoton coincidence measurement.Detection output signals from APD2 and APD3 are sent to our coincidence count device(Pico quanta,TimeHarp 260,1.6 ns coincidence window)for four-photon coincidence measurement.Before measuring the HOMI,we obtain a maximum-coincidence-to-accidental-coincidence ratio(CAR)of 131 by cooling the fi ber in liquid nitrogen when the pump power is 23μW.There are a few remarks we want to point out.Firstly,the photon sources are not operated at the optimized pump pulse width for pure single photon generation,but narrow band 100 GHz fi lters are used in the experiments to increase the purity of the sources.Secondly,single photon detectors used in our experiment have lower detection efficiency and much higher dark counts than nano-wire single photon detectors,if we have high-performance nano-wire single photon detector,experimental results will be greatly improved due to the four-fold coincidences and dark coincidences scaling quadruplicate with the detection efficiency and dark count probability of a single detector.Thirdly,we use relatively high pump power for each DSF(0.12 mW)to reduce measurement time for photon coincidence,which will lead to a very poor raw visibility certainly.Finally,though only a 100 GHz channel pair is used in our experiment,we can use other channels for multiplexing such interference processes to improve the channel capacity in future quantum communication tasks theoretically.Our study shows greatly promising integrated optical elements for future scalable quantum information processing.

dense wave division multiplexing,Hong-Ou-Mandel interference,dispersion shifted fi ber

10.7498/aps.66.120302

?國家自然科學(xué)基金(批準(zhǔn)號:11174271,61275115,61435011,61525504)和中央高?；究蒲袠I(yè)務(wù)費(fèi)專項(xiàng)資金(批準(zhǔn)號:WK2030380009)資助的課題.

?通信作者.E-mail:xulixin@ustc.edu.cn

?通信作者.E-mail:zyzhouphy@ustc.edu.cn

?2017中國物理學(xué)會(huì)Chinese Physical Society

http://wulixb.iphy.ac.cn

*Project supported by the National Natural Science Foundation of China(Grant Nos.11174271,61275115,61435011,61525504)and the Fundamental Research Funds for the Central Universities,China(Grant No.WK2030380009).

?Corresponding author.E-mail:xulixin@ustc.edu.cn

?Corresponding author.E-mail:zyzhouphy@ustc.edu.cn