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腔增强的光学自发参量下转换是量子光学中产生量子光场的基本方法之一, 然而下转换过程往往受到非线性晶体的双折射效应的影响. 特别是在利用II类准相位匹配非线性晶体产生双光子对的过程中, 晶体的双折射效应使得信号光和闲置光不能同时起振. 本文提出并验证了一种利用1/4波片补偿信号光和闲置光的光程的方法, 在保证较小内腔损耗及良好的调节自由度的情况下, 以相对简洁的装置实现信号光和闲置光的双共振.
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关键词:
- 腔增强自发参量下转换 /
- 双折射效应 /
- 双共振 /
- 预告式单光子源
Single-photon source is an essential element in quantum information processing, and extensively used in the proof-in-principle demonstration in quantum physics, quantum imaging, quantum cryptography, etc. Considering the operating temperature and system complexity, it is a favorable option to choose spontaneous parametric down-conversion (SPDC) combined with the enhancement effect of a cavity. When generating significant single-photon source via the cavity-enhanced type-II spontaneous parametric down-conversion method, there appears inevitable birefringence effect which obviously influences the resonance condition. In order to compensate for birefringence effect, different approaches have been used such as introducing compensating crystal, placing a half-wave plate, tuning the temperature of the nonlinear crystal, customized conjoined double-cavity structure, and cluster effect. In this work, two quarter-wave plates, with an angle of 45° between the optical axis and the crystal axis, are placed in the cavity to ensure the double resonance of signal photon and idler photon. In the process, the signal photon and idler photon generated simultaneously have different polarizations perpendicular to each other through the type-II nonlinear crystal. Considering horizontally polarized photon, its polarization is changed into left circular polarization by the first quarter-wave plate and then returns as vertical polarization. After traversing a long optical path, it shifts to right circular polarization through the second quarter-wave plate. When the photon passes through the same quarter-wave plate again, the polarization state is originally converted into horizontal polarization state. Then the photon completes a round-trip. The other photon with vertical polarization experiences the same process. As a result, the signal photon and idler photon travel identical optical path. The general explanation is described by the Jones matrices, with the emphasis on the transformation of the polarizations of photons. This method can effectively compensate for birefringence effect, achieving double resonance by using a relatively simple device under the condition of smaller intra-cavity loss and more flexible for adjustment. The signal (idler) photon has a sub-natural linewidth of$1.01( 1.08 )\;{\rm{MHz}} $ , demonstrating the feasibility of the proposed technique. This introduced compensating method paves the way to the realization of single-photon quantum source applied to the research of single-photon-single-atom quantum information processing, quantum interface and quantum network node with a single cesium atom confined in the strongly coupled cavity quantum electrodynamics system.-
Keywords:
- cavity-enhanced spontaneous parametric down-conversion /
- birefringence effect /
- double resonance /
- heralded single-photon source
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图 1 置有QWPs的SPDC腔中光子的偏振变化(PZT, 压电陶瓷) (a) SPDC产生的水平偏振光子(红虚线箭头)的情况; (b) 竖直偏振光子(黑虚线箭头)的情况. 其中, 蓝实线箭头和红实线箭头分别表示波长为426 nm和852 nm的激光, R和L分别表示右旋圆偏振光和左旋圆偏振光, k, s, p分别表示光波矢(z轴)、光场垂直分量(y轴)和平行分量(x轴)
Fig. 1. Polarization transformations of photons in SPDC cavity with QWPs. Photon with an initial polarization of H (red dashed arrow) in (a) or V (black dashed arrow) in (b) generated from SPDC. Blue and red solid arrows stand for 426 nm and 852 nm laser respectively, R (L) shows right (left) circular polarization, k is wave vector (z axis), s is perpendicular part (y axis) and p represents parallel part (x axis). PZT represents piezoelectric transducer.
图 2 2个QWPs不同角度下的本征值.
${\alpha _2} = {45^ \circ }$ 并改变QWP1时本征值的振幅(a)和相位(b);${\alpha _1} = {45^ \circ }$ 并改变QWP2时本征值的振幅(c)和相位(d);${\alpha _2} = 0.23{\text{π }}$ 并改变QWP1时本征值的振幅(e)和相位(f). 其中红线和蓝线对应了2个不同的本征值Fig. 2. Eigenvalues with different degrees of two QWPs. Amplitude in (a) of eigenvalues and phase in (b) of the eigenvalues on the condition of
${\alpha _2} = {45^ \circ }$ and different degrees of QWP1; amplitude in (c) and the phase in (d) with${\alpha _1} = {45^ \circ }$ and different degrees of QWP2; amplitude in (e) and the phase in (f) with${\alpha _2} = 0.23{\text{π }}$ and different degrees of QWP1. Red line is about one of eigenvalues, while the blue line is about the other.
图 3 使用QWP补偿双折射效应的装置图. 852 nm的激光(红色)通过倍频腔(Doubler)产生腔增强的SPDC所需的426 nm (蓝色)的泵浦光. SPDC腔腔长由波长远离光子对的840 nm的辅助光(紫色)进行锁定. SPDC产生的偏振相互垂直的光子对耦合进光纤进行后续实验
Fig. 3. Experimental apparatus about birefringence compensating utilizing two QWPs. Laser with the wavelength of 852 nm in red color is sent into the doubler cavity. Generated frequency-doubling light at 426 nm (in blue color) is filtered and coupled to the SPDC cavity after lens-transforming. Length of SPDC cavity is stabilized by the 840 nm auxiliary light. Signal and idler photons generated from SPDC cavity filtered by cascaded etalons are split on a PBS and coupled to multi-fibers for further processing. Doubler, second-harmonic generation cavity.
图 4 保持QWP2的角度约
$ {45^ \circ } $ , QWP1不同角度(重合程度)下的互关联函数 (a)$ {\alpha _0} + 80' $ (72.8%); (b)$ {\alpha _0} $ (42.1%); (c)$ {\alpha _0} - 80' $ (25.0%); (d)$ {\alpha _0} - 160' $ (14.6%). 插图为相应腔内2个本征值所对应纵模的透射峰Fig. 4. Cross-correlation function with different degrees of QWP1 (overlap) on the condition of the degree of QWP2 approximately equal to
$ {45^ \circ } $ : (a)$ {\alpha _0} + 80' $ (72.8%); (b)$ {\alpha _0} $ (42.1%); (c)$ {\alpha _0} - 80' $ (25.0%); (d)$ {\alpha _0} - 160' $ (14.6%). Insets are corresponding transmission spectra for the two different orthogonal modes.
图 5 QWP1的角度固定为相对较好的
$ {\alpha _0} + 80' $ 时QWP2在不同角度(重合程度)下的互关联函数 (a)$ {\beta _0} - 40' $ (60.9%); (b)$ {\beta _0} + 40' $ (90.0%); (c)$ {\beta _0} + 80' $ (35.2%); (d)$ {\beta _0} + 120' $ (23.8%)Fig. 5. Cross-correlation function with different degrees of QWP2 (overlap) on the condition of QWP1 equal to
$ {\alpha _{\text{0}}}{\text{ + 80'}} $ : (a)$ {\beta _0} - 40' $ (60.9%); (b)$ {\beta _0} + 40' $ (90.0%); (c)$ {\beta _0} + 80' $ (35.2%); (d)$ {\beta _0} + 120' $ (23.8%).
图 6 不同时间分辨率条件下的互关联函数 (a) 100 ps; (b) 4.4 ns, 蓝色曲线(数据点)和红色曲线(数据点)分别表示信号光和闲置光的拟合曲线(数据)
Fig. 6. Cross-correlation function with different resolution time: (a) 100 ps; (b) 4.4 ns. The blue curve (points) and red curve (points) are representative fitting curves (experimental data) of signal and idler photons respectively.
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[1] Perumangatt C, Lohrmann A, Ling A 2020 Phys. Rev. A 102 012404
Google Scholar
[2] Tang J S, Tang L, Wu H D, Wu Y, Sun H, Zhang H, Li T, Lu Y Q, Xiao M, Xia K Y 2021 Phys. Rev. Appl. 15 064020
Google Scholar
[3] 杨宏恩, 韦联福 2019 物理学报 68 234202
Google Scholar
Yang H E, Wei L F 2019 Acta Phys. Sin. 68 234202
Google Scholar
[4] Wang B X, Tao M J, Ai Q, Xin T, Lambert N, Ruan D, Cheng Y C, Nori F, Deng F G, and Long G L 2018 NPJ Quantum Inf. 4 52
Google Scholar
[5] Yang B, Sun H, Ott R, Wang H Y, Zache T V, Halimeh J C, Yuan Z S, Hauke P, Pan J W 2020 Nature 587 392
Google Scholar
[6] Piro N, Rohde F, Schuck C, Almendros M, Huwer J, Ghosh J, Haase A, Hennrich M, Dubin F, and Eschner J 2011 Nat. Phys. 7 17
Google Scholar
[7] Pittman T P, Shih Y H, Strekalov D V, Sergienko A V 1995 Phys. Rev. A 52 3429
Google Scholar
[8] Zhang H, Jin X M, Yang J, Dai H N, Yang S J, Zhao T M, Rui J, He Y, Jiang X, Yang F, Pan G S, Yuan Z S, Deng Y J, Chen Z B, Bao X H, Chen S, Zhao B, Pan J W 2011 Nat. Photonics 5 628
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[9] Yin J, Cao Y, Li Y H, Liao S K, Zhang L, Ren J G, Cai W Q, Liu W Y, Li S, Dai H, Li G B, Lu Q M, Gong Y H, Xu Y, Li S L, Li F Z, Yin Y Y, Jiang Z Q, Li M, Jia J J, Ren G, He D, Zhou Y L, Zhang X X, Wang N, Chang X, Zhu Z C, Liu N L, Chen Y A, Lu C Y, Shu R, Peng C Z, Wang J Y, Pan J W 2017 Science 356 1140
Google Scholar
[10] Broome M A, Fedrizzi A, Lanyon B P, Kassal I, Guzik A A, White A G 2010 Phys. Rev. Lett. 104 153602
Google Scholar
[11] Esposito C, Barros M R, Hernandez A D, Carvacho G, Colandrea F D, Barboza R, Cardano F, Spagnolo N, Marrucci L, Sciarrino F 2022 NPJ Quantum Inf. 8 34
Google Scholar
[12] Scholz M, Koch L, Benson O 2009 Phys. Rev. Lett. 102 063603
Google Scholar
[13] Zhou Z Y, Ding D S, Li Y, Wang F Y, Shi B S 2014 J. Opt. Soc. Am. B 31 128
Google Scholar
[14] Rambach M, Nikolova A, Weinhold T J, White A G 2016 APL Photonics 1 096101
Google Scholar
[15] Niizeki K, Ikeda K, Zheng M Y, Xie X P, Okamura K, Takei N, Namekata N, Inoue S, Kosaka H, Horikiri T 2018 Appl. Phys. Express 11 042801
Google Scholar
[16] Liu J J, Liu J C, Yu P, Zhan G Q 2020 APL Photonics 5 066105
Google Scholar
[17] Moqanaki A, Maaas F, Walther P 2019 APL Photonics 4 090804
Google Scholar
[18] Tsai P J, Chen Y C 2018 Quantum Sci. Technol. 3 034005
Google Scholar
[19] Ou Z Y, Lu Y J 1999 Phys. Rev. Lett. 83 2556
Google Scholar
[20] Tian L, Li S J, Yuan H X, Wang H 2016 J. Phys. Soc. Japan 85 124403
Google Scholar
[21] Wang J, Huang Y F, Zhang C, Cui J M, Zhou Z Y, Liu B H, Zhou Z Q, Tang J S, Li C F, Guo G C 2018 Phys. Rev. Appl. 10 054036
Google Scholar
[22] Chuu C S, Yin G Y, Harris S E 2012 Appl. Phys. Lett. 101 051108
Google Scholar
[23] 吕百达 2003 激光光学(第三版) (北京: 高等教育出版社) 第422—426页
Lv B D 2003 Laser Optics (3rd Ed.) (Beijing: Higher Education Press) pp422–426 (in Chinese)
[24] Bhandari R 2008 Opt. Lett. 33 854
Google Scholar
[25] Hansch T W, Couilland B 1980 Opt. Commun. 35 441
Google Scholar
[26] 刘鑫鑫 2013 硕士学位论文 (太原: 山西大学)
Liu X X 2013 M. S. Thesis (Taiyuan: Shanxi University) (in Chinese)
[27] Scholz M, Koch L, Benson O 2009 Opt. Commun. 282 3518
Google Scholar
[28] 李岩 2016 博士学位论文 (合肥: 中国科学技术大学)
Li Y 2016 Ph. D. Dissertation (Hefei: University of Science and Technology of China) (in Chinese)
[29] Bocquillon E, Couteau C, Razavi M, Laflamme R, Weihs G 2009 Phys. Rev. A 79 035801
Google Scholar
[30] Wahl M, Rohlicke T, Rahn J H, Erdmann R, Kell G, Ahlrichs A, Kernbach M, Schell A W, Benson O 2013 Rev. Sci. Instrum. 84 043102
Google Scholar
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