侯飛雁，權(quán)潤(rùn)愛(ài)，項(xiàng)曉，靳亞晴，董瑞芳，劉濤，張首剛

基于實(shí)地光纖的雙向量子時(shí)間傳遞實(shí)驗(yàn)研究

侯飛雁1,2,3，權(quán)潤(rùn)愛(ài)1,2,3，項(xiàng)曉1,2,3，靳亞晴1,2,3，董瑞芳1,2,3，劉濤1,2,3，張首剛1,2,3

（1. 中國(guó)科學(xué)院 國(guó)家授時(shí)中心，西安 710600；2. 中國(guó)科學(xué)院 時(shí)間頻率基準(zhǔn)重點(diǎn)實(shí)驗(yàn)室，西安 710600；3. 中國(guó)科學(xué)院大學(xué) 天文與空間科學(xué)學(xué)院，北京 101048）

高精度的時(shí)間傳遞技術(shù)已經(jīng)廣泛地應(yīng)用在守時(shí)授時(shí)、導(dǎo)航定位、科學(xué)研究等各個(gè)領(lǐng)域。量子時(shí)間傳遞技術(shù)利用頻率糾纏脈沖作為時(shí)間信號(hào)的載體，結(jié)合高精度的量子測(cè)量技術(shù)可以極大地提高時(shí)間傳遞精度。由于頻率糾纏脈沖自身的高度關(guān)聯(lián)性，量子時(shí)間傳遞技術(shù)具有更高的安全性。本文在9.76km的實(shí)地光纖中開展了雙向量子時(shí)間傳遞實(shí)驗(yàn)研究，得到的時(shí)間傳遞穩(wěn)定度在平均時(shí)間是10s時(shí)為1.55ps，平均時(shí)間是20480s時(shí)為92fs。飛秒量級(jí)的雙向量子時(shí)間傳遞結(jié)合其安全性優(yōu)勢(shì)，有望在高精度的中長(zhǎng)途傳遞系統(tǒng)中獲得廣泛應(yīng)用。

量子時(shí)間傳遞；實(shí)地光纖；頻率糾纏源；色散消除

0 引言

高精度頻率參考和時(shí)間標(biāo)準(zhǔn)在科學(xué)研究、導(dǎo)航和定位等許多領(lǐng)域變得越來(lái)越重要。而精確時(shí)間標(biāo)準(zhǔn)的建立與時(shí)間傳遞的性能以及在多臺(tái)原子鐘之間的時(shí)間比對(duì)精度直接相關(guān)[1]。由于光纖具有低損耗，高可靠性和高穩(wěn)定性等優(yōu)點(diǎn)，光纖時(shí)間傳遞（TTOF）比其他基于衛(wèi)星的同類時(shí)間傳遞技術(shù)[2-3]具有更好的性能。據(jù)報(bào)道，TTOF在數(shù)百千米的光纖上，可以實(shí)現(xiàn)數(shù)十皮秒的同步精度[4-6]。通過(guò)補(bǔ)償光纖傳播延遲的波動(dòng)，雙向時(shí)間傳遞方法的穩(wěn)定度可以保持在皮秒以下，對(duì)應(yīng)的平均時(shí)間為數(shù)小時(shí)[7-15]。另一方面，在軍事用途的導(dǎo)航系統(tǒng)[16]、金融網(wǎng)絡(luò)[17]等領(lǐng)域安全時(shí)間傳遞至關(guān)重要。盡管雙向傳遞可以檢測(cè)中間人（MITM）的延遲攻擊，但是經(jīng)典技術(shù)容易受到惡意方的干擾，從而對(duì)時(shí)間傳遞性能產(chǎn)生不利影響[18]。

為了準(zhǔn)確而且安全地在相距甚遠(yuǎn)的時(shí)鐘間傳遞時(shí)間信息，急需開發(fā)新的時(shí)間傳遞方法。使用頻率糾纏的光子對(duì)作為時(shí)間信號(hào)的載體，結(jié)合單光子探測(cè)器能夠精確地檢測(cè)到極低功率的信號(hào)，能夠消除大多數(shù)系統(tǒng)誤差，并且可以保持?jǐn)?shù)據(jù)流量的安全性的優(yōu)勢(shì)，量子增強(qiáng)的時(shí)間傳遞技術(shù)有望進(jìn)一步提高時(shí)間傳遞精度[18,19-27]。此外，量子力學(xué)的互補(bǔ)原理保證了量子時(shí)間同步技術(shù)的安全性[28-30]。

盡管具有潛在的高精度和安全性，但是由于相對(duì)較低的光子數(shù)以及通過(guò)光纖傳播后脈沖受到色散影響會(huì)展寬，量子時(shí)間傳遞的優(yōu)越性仍未得到充分認(rèn)識(shí)。頻率糾纏光有一個(gè)突出的優(yōu)點(diǎn)：非局域色散消除特性。該特性可以消除光纖色散對(duì)量子時(shí)間傳遞的影響。該特性在1992年由Franson在理論上提出[31]，隨后在實(shí)驗(yàn)上利用局域測(cè)量的方法得到了驗(yàn)證[32-34]。作者所在研究團(tuán)隊(duì)于2019年在實(shí)驗(yàn)上利用非局域測(cè)量的方式證明了該特性[35]。信號(hào)光和閑置光分別經(jīng)過(guò)色散量相同但是符號(hào)相反的介質(zhì)傳播后，信號(hào)光由于色散引入的展寬可以被閑置光非局域地抵消，因此二階關(guān)聯(lián)函數(shù)的分布不受色散的影響，由二階關(guān)聯(lián)函數(shù)得到的時(shí)間差信號(hào)也不受色散的影響。

目前，作者所在研究團(tuán)隊(duì)已經(jīng)在20 km光纖盤上利用頻率糾纏光的非局域色散消除特性實(shí)現(xiàn)了45 fs的時(shí)間同步穩(wěn)定度，對(duì)應(yīng)的平均時(shí)間是40 960 s[27]。為了研究雙向量子時(shí)間同步技術(shù)的實(shí)際應(yīng)用，量子時(shí)間同步研究團(tuán)隊(duì)首次在9.76 km實(shí)地光纖上開展了雙向量子時(shí)間傳遞（Q-TWTTOF）實(shí)驗(yàn)研究。研究中利用頻率糾纏源的非局域色散消除特性可以提高時(shí)間傳遞穩(wěn)定性。實(shí)驗(yàn)結(jié)果表明，以時(shí)間偏差（TDEV）表示的時(shí)間傳遞穩(wěn)定性在10 s的平均時(shí)間內(nèi)達(dá)到1.55 ps，在20 480 s的平均時(shí)間內(nèi)達(dá)到92 fs。當(dāng)前，Q-TWTTOF方案的性能主要受限于糾纏光子對(duì)的損耗、事件計(jì)時(shí)器的有限數(shù)據(jù)采集速率以及單光子探測(cè)器和事件計(jì)時(shí)器的時(shí)間抖動(dòng)。Q-TWTTOF方案與類似的經(jīng)典時(shí)間同步方案相比，時(shí)間傳遞穩(wěn)定度有顯著的提高。結(jié)合固有的安全性優(yōu)勢(shì)，Q-TWTTOF方案對(duì)于在中長(zhǎng)距離上進(jìn)行高準(zhǔn)確度和安全的時(shí)間傳遞非常有用。

本文的安排如下，第1部分介紹Q-TWTTOF方案及其理論分析，第2部分介紹實(shí)驗(yàn)裝置和實(shí)驗(yàn)結(jié)果，第3部分為總結(jié)。

1 雙向量子時(shí)間傳遞理論分析及實(shí)驗(yàn)設(shè)計(jì)

注：FC為光纖環(huán)行器；D1~D 4為單光子探測(cè)器。待同步的時(shí)鐘A和B分別位于A、B兩地，A、B兩地分別有一個(gè)頻率糾纏源、一對(duì)超導(dǎo)單光子探測(cè)器、一個(gè)事件計(jì)時(shí)器與時(shí)鐘同步。糾纏源產(chǎn)生的閑置光經(jīng)過(guò)長(zhǎng)度為l’的色散補(bǔ)償光纖由本地的單光子探測(cè)器探測(cè)，事件計(jì)時(shí)器記錄其到達(dá)時(shí)間，信號(hào)光經(jīng)過(guò)長(zhǎng)度為l的傳遞光纖傳到對(duì)端由對(duì)端的單光子探測(cè)器探測(cè)，對(duì)端的事件計(jì)時(shí)器記錄其到達(dá)時(shí)間。

第個(gè)探測(cè)器處的湮滅算符可以表示為：

把式（2）至式（5）代入式（1），四階關(guān)聯(lián)函數(shù)可以表示為[31-32]

式（10）中，

2 實(shí)驗(yàn)裝置和實(shí)驗(yàn)結(jié)果

注：圖中實(shí)直線為光路，實(shí)曲線為光纖，虛線為電纜。780 nm激光由BS分成兩束分別泵浦兩個(gè)PPKTP晶體，產(chǎn)生的頻率糾纏光耦合進(jìn)FPBS，兩糾纏源的信號(hào)光和分別經(jīng)過(guò)FC和9.76 km光纖到達(dá)對(duì)端，由探測(cè)器D2和D4探測(cè)。閑置光和分別經(jīng)過(guò)DCF由D1和D3探測(cè)。事件計(jì)時(shí)器A和B分別記錄探測(cè)器D1、D4和D2、D3探測(cè)的光子到達(dá)時(shí)間。時(shí)鐘A和B共用國(guó)家授時(shí)中心（NTSC）氫鐘信號(hào)并為事件計(jì)時(shí)器A和B提供秒脈沖信號(hào)（PPS）和10 MHz信號(hào)。

圖3 經(jīng)過(guò)實(shí)地光纖傳遞后的頻率糾纏源二階關(guān)聯(lián)函數(shù)分布

圖4 實(shí)地光纖雙向時(shí)間傳遞時(shí)間穩(wěn)定度

除了傳遞鏈路的損耗外，限制目前雙向量子時(shí)間傳遞穩(wěn)定度的因素主要包括：?jiǎn)喂庾犹綔y(cè)器和事件計(jì)時(shí)器的抖動(dòng)以及事件計(jì)時(shí)器的數(shù)據(jù)流量限制。本文中使用的單光子探測(cè)器和事件計(jì)時(shí)器的總抖動(dòng)約為70 ps，因此測(cè)量到的糾纏光子對(duì)二階關(guān)聯(lián)函數(shù)的寬度的最小也只能達(dá)到70 ps左右，如果采用抖動(dòng)更低的單光子探測(cè)器和事件計(jì)時(shí)器，可以有效地降低二階關(guān)聯(lián)函數(shù)測(cè)量的寬度，進(jìn)而優(yōu)化時(shí)間傳遞穩(wěn)定度。本文中采用的事件計(jì)時(shí)器兩個(gè)數(shù)據(jù)輸入端口的數(shù)據(jù)流量之和不能超過(guò)12 kHz，因此為了避免數(shù)據(jù)流量過(guò)大，實(shí)驗(yàn)中將下轉(zhuǎn)換晶體前的780 nm激光的功率衰減到了10 mW左右，這也限制了糾纏光的亮度，如果采用不限制數(shù)據(jù)流量的事件計(jì)時(shí)器則可以提高糾纏光源的亮度，進(jìn)而優(yōu)化時(shí)間傳遞穩(wěn)定度。因此下一步我們擬采用時(shí)間抖動(dòng)小的單光子探測(cè)器和亞皮秒精度的不限制數(shù)據(jù)流量的事件計(jì)時(shí)器來(lái)優(yōu)化時(shí)間傳遞穩(wěn)定度。

3 總結(jié)

我們利用頻率糾纏光的非局域色散消除的特性，在9.76 km實(shí)地光纖中實(shí)現(xiàn)了高精度的量子時(shí)間同步，得到的時(shí)間同步穩(wěn)定度在平均時(shí)間是10 s時(shí)為1.55 ps，20 480 s時(shí)為92 fs。系統(tǒng)的時(shí)間同步穩(wěn)定性為：平均時(shí)間是10 s時(shí)為344 fs，平均時(shí)間是20 480 s時(shí)，穩(wěn)定度為30 fs。下一步我們將對(duì)傳遞光纖的色散進(jìn)行精確補(bǔ)償，使二階關(guān)聯(lián)函數(shù)的寬度降低，同時(shí)提高符合計(jì)數(shù)，并且采用亞皮秒精度的事件計(jì)時(shí)器，數(shù)據(jù)的采集率將不受限制，同時(shí)采用低抖動(dòng)的超導(dǎo)單光子探測(cè)器，時(shí)間同步的結(jié)果還可以進(jìn)一步改善。

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Experimental research on two-way quantum time transfer based on solid fiber

HOU Fei-yan1,2,3, QUAN Run-ai1,2,3, XIANG Xiao1,2,3, JIN Ya-qing1,2,3, DONG Rui-fang1,2,3, LIU Tao1,2,3, ZHANG Shou-gang1,2,3

(1. National Time Service Center, Chinese Academy of Sciences, Xi’an 710600, China;2. Key Laboratory of Time and Frequency Primary Standards, Chinese Academy of Sciences, Xi’an 710600, China;3. School of Astronomy and Space Science, University of Chinese Academy of Sciences, Beijing 101048, China)

High-precision time transfer technology has been widely applied in a variety of fields, such as punctual timing, navigation and positioning, scientific research, and so on. Quantum time transfer technology, which uses frequency entangled pulse as the carrier of time signals, and combined with high-precision quantum measurement technologies, can greatly improve the time transfer accuracy. Due to the high correlation of the frequency entangled pulse itself, quantum time transfer technology has higher security. We carry out the two-way quantum time transfer experiment in a 9.76 km solid fiber. The time transfer stability is 1.55 ps over 10 s, and 92 fs over 20 480 s. The femtosecond-scale two-way quantum time transfer is expected to be widely used in high-precision medium and long distant transmission system.

quantum time transfer; solid fiber; frequency entangled source; dispersion cancellation

10.13875/j.issn.1674-0637.2020-04-0253-09

侯飛雁, 權(quán)潤(rùn)愛(ài), 項(xiàng)曉, 等. 基于實(shí)地光纖的雙向量子時(shí)間傳遞實(shí)驗(yàn)研究[J]. 時(shí)間頻率學(xué)報(bào), 2020, 43(4): 253-261.

2020-04-23；

2020-05-15

國(guó)家自然科學(xué)基金資助項(xiàng)目（12033007；61875205；61801458；91836301）；中國(guó)科學(xué)院前沿科學(xué)重點(diǎn)研究資助項(xiàng)目（QYZDB-SSWSLH007）；中國(guó)科學(xué)院“西部之光”人才培養(yǎng)計(jì)劃“西部青年學(xué)者”B類資助項(xiàng)目（XAB2019B15；XAB2019B17）；中國(guó)科學(xué)院戰(zhàn)略性先導(dǎo)科技專項(xiàng)C類資助項(xiàng)目（XDC07020200）；中國(guó)科學(xué)院重點(diǎn)資助項(xiàng)目（ZDRW-KT-2019-1-0103）；廣東省重點(diǎn)研發(fā)資助項(xiàng)目（2018B030325001）