高灵敏度的量子迈克耳孙干涉仪

左小杰; 孙颍榕; 闫智辉; 贾晓军

doi:10.7498/aps.67.20172563

摘要

迈克耳孙干涉仪不仅可以用来研究物理学的基本问题，而且能够用于精密测量，比如引力波信号的测量.因此，构建高灵敏度的迈克耳孙干涉仪是实现微弱信号测量的关键.目前，人们利用压缩态可以降低迈克耳孙干涉仪的噪声；通过光学四波混频过程能够放大马赫曾德尔干涉仪中的相位信号，从而提高干涉仪的信噪比和灵敏度.本文研究了一种用于高灵敏度相位测量的量子迈克耳孙干涉仪.在迈克耳孙干涉仪中，利用非简并光学参量放大器取代干涉仪中的线性光学分束器；并且将压缩态注入干涉仪的真空通道，可以得到高信噪比和高灵敏度的干涉仪.由于存在不可避免的光学损耗，分析了迈克耳孙干涉仪内部和外部的损耗对相位测量灵敏度的影响.通过理论计算研究了干涉仪的相位测量灵敏度随系统参数的变化关系，得到了高灵敏度的相位测量量子迈克耳孙干涉仪的实现条件，为用于精密测量的干涉仪的设计提供了直接参考.

关键词:

Abstract

Michelson interferometer can be applied to not only the building block of the fundamental research of physics, but also the precise measurement, such as the direct observation of gravity wave signal. Therefore, high performance Michelson interferometer is the key step towards the implementation of direct observation of weak gravity wave signal. Recently, the vacuum noise was reduced by injecting squeezed vacuum into the unused port of Michelson interferomter, and the phase signal optical field in Mach-Zender interferometer is amplified based on the four-wave mixing in hot Rubidium atom. Here we study high sensitivity quantum Michelson interferometer. In the Michelson interferometer, the linear optical beam splitter is replaced by a non-degenerated optical parametric amplifier to realize the splitting and combining of optical fields, and the squeezed vacuum is also injected into the unused port of interferomter, so that the high signal-to-noise ratio and high sensitivity of phase measurement can be realized. Due to the inevitable optical losses, the losses inside and outside the Michelson interferometer are considered in our theoretical model. We investigate the influences of the losses inside and outside the Michelson interferometer on the sensitivity of phase measurement. By theoretical calculation, we analyze the dependence of sensitivity of phase measurement on system parameters, such as intensity of optical fields for phase sensing, gain factor of non-degenerated optical parametric amplifier, the losses inside and outside the Michelson interferometer, and the squeezing parameter of input squeezed vacuum, and thus the condition of high sensitivity nonlinear Michelson interferometer can be obtained. In a broad system parametric range, the quantum Michaleson interferometer can surpass standard quantum limit, and the nonlinear Michaleson interferometer with squeezed state injection can provide the optimal sensitivity for phase measurement. The nonlinear Michelson interferometer with squeezed state is suitable for weak signal measurement. While the gain factor of non-degenerated optical parametric amplifier is large enough, the nonlinear Michelson interferometer without injecting the squeezed vacuum can still reach the optimal sensitivity, which reduces the use of quantum resources. When the phase sensing optical field is strong, the linear Michelson interferometer with injecting the squeezed vacuum can also reach the optimal sensitivity, and the sensitivity is robust for both losses inside and outside the interferometer. All the kinds of interferometers are more sensitive to the loss inside the interferometer than outside the interferometer, and the sensitivity of phase measurement can be improved by reducing the loss inside the interferometer. Our result provides direct reference of experimental implementation of high performance interferometer for high precision quantum metrology.

Keywords:

Michelson interferometer /
squeezed state /
non-degenerated optical parametric amplifier /
sensitivity

作者及机构信息

1.
山西大学光电研究所, 量子光学与光量子器件国家重点实验室, 太原 030006;

2.
山西大学, 极端光学协同创新中心, 太原 030006

通信作者: 闫智辉, zhyan@sxu.edu.cn

基金项目: 国家重点研发计划（批准号：2016YFA0301402）、国家自然科学基金（批准号：61775127，11474190，11654002）、山西青年三晋学者项目、山西省回国留学人员科研资助项目和山西省1331工程重点学科建设计划资助的课题.

Authors and contacts

1.
Institute of Opto-Electronics, State Key Laboratory of Quantum Optics and Quantum Optics Devices, Shanxi University, Taiyuan 030006, China;

2.
Collaborative Innovation Center of Extreme Optics, Shanxi University, Taiyuan 030006, China

Corresponding author: Yan Zhi-Hui, zhyan@sxu.edu.cn

Funds: Project supported by National Key RD Program of China (Grant No. 2016YFA0301402), the National Natural Science Foundation of China (Grant Nos. 61775127, 11474190, 11654002), the Program for Sanjin Scholars of Shanxi Province, Shanxi Scholarship Council of China, and the Fund for Shanxi 1331Project Key Subjects Construction, China.

参考文献

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[2]	Sathyaprakash B S, Schutz B F 2009 Living Rev. Relativ. 2 1
[3]	Hinderer T J, Lackey B D, Lang R N, Read J S 2010 Phys. Rev. D 81 123016
[4]	Vines J, Flanagan E E, Hinderer T J 2011 Phys. Rev. D 83 084051
[5]	Bauswein A, Janka H T 2012 Phys. Rev. Lett. 108 011101
[6]	Abramovici A, Althouse W E, Drever R W P, Grsel Y, Kawamura S, Raab F J, Shoemaker D, Sievers L, Spero R E, Thorne K S, Vogt R E, Weiss R, Whitcomb S E, Zucker M E 1992 Science 256 5055
[7]	Aasi J, Abbott B P, Abbott R, et al. 2015 Class. Quant. Grav. 32 074001
[8]	Grote H 2010 Class. Quant. Grav. 27 084003
[9]	Acernese F, Agathos M, Agatsuma K, et al. 2015 Class. Quant. Grav. 32 024001
[10]	Arai K, Takahashi R, Tastumi D, et al. 2009 Class. Quant. Grav. 26 204020
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[14]	Abbott B P, Abbott R, Abbott T D, et al. 2017 Phys. Rev. Lett. 119 161101
[15]	Hou Z B, Zhu H J, Xiang G Y, Li C F, Guo G C 2016 npj Quantum Information 2 16001
[16]	Liu F, Zhou Y Y, Yu J, Guo J L, Wu Y, Xiao S X, Wei D, Zhang Y, Jia X J, Xiao M 2017 Appl. Phys. Lett. 110 021106
[17]	Walls D F 1983 Nature 306 141
[18]	Zhang M Z 2015 Quantum Optics (Beijing: Science Press) pp72-75 (in Chinese) 张智明 2015 量子光学 (北京:科学出版社) 第7275页
[19]	Caves C M 1980 Phys. Rev. Lett. 45 75
[20]	Caves C M 1981 Phys. Rev. D 23 1693
[21]	Sun H X, Liu K, Zhang J X, Gao J R 2015 Acta Phys. Sin. 64 234210 (in Chinese) [孙恒信, 刘奎, 张俊香, 郜江瑞 2015 64 234210]
[22]	Slusher R E, Hollberg L W, Yurke B, Mertz J C, Valley J F 1985 Phys. Rev. Lett. 55 2409
[23]	Wu L A, Kimble H J, Hall J L, Wu H F 1986 Phys. Rev. Lett. 57 2520
[24]	Henning V, Moritz M, Karsten D, Schnabel R 2016 Phys. Rev. Lett. 117 110801
[25]	Wan Z J, Feng J X, Sun Z N, Yao L T, Zhang K S 2014 Acta Sin. Quantum Opt. 20 271 (in Chinese) [万振菊, 冯晋霞, 孙志妮, 要立婷, 张宽收 2014 量子光学学报 20 271]
[26]	Sun Z N, Feng J X, Wan Z J, Zhang K S 2016 Acta Phys. Sin. 65 044203 (in Chinese) [孙志妮, 冯晋霞, 万振菊, 张宽收 2016 65 044203]
[27]	McKenzie K, Grosse N, Bowen W P, Whitcomb S E, Gray M B, McClelland D E, Lam P K 2004 Phys. Rev. Lett. 93 161105
[28]	Vahlbruch H, Chelkowski S, Hage B, Franzen A, Danzmann K, Schnabel R 2006 Phys. Rev. Lett. 97 011101
[29]	Yan Z H, Sun H X, Cai C X, Ma L, Liu K, Gao J R 2017 Acta Phys. Sin. 66 114205 (in Chinese) [闫子华, 孙恒信, 蔡春晓, 马龙, 刘奎, 郜江瑞 2017 66 114205]
[30]	Goda K, Miyakawa O, Mikhailov E E, Saraf S, Adhikari R, McKenzie K, Ward R, Vass S, Weinstein A J, Mavalvala N 2008 Nature Phys. 4 472
[31]	Schnabel R, Mavalvala N, McClelland D E, Lam P K 2010 Nature Commun. 1 121
[32]	Abadie J, Abbott B P, Abbott R, et al. 2011 Nature Phys. 7 962
[33]	Aasi J, Abadie J, Zweizi J, et al. 2013 Nature Photon. 7 613
[34]	Liu Y C, Xiao Y F, Chen Y L, Yu X C, Gong Q H 2013 Phys. Rev. Lett. 111 083601
[35]	Wang X L, Chen L K, Li W, Huang H L, Liu C, Chen C, Luo Y H, Su Z E, Wu D, Li Z D, Lu H, Hu Y, Jiang X, Peng C Z, Li L, Liu N L, Chen Y A, Lu C Y, Pan J W 2016 Phys. Rev. Lett. 117 210502
[36]	Deng X W, Xiang Y, Tian C X, Adesso G, He Q Y, Gong Q H, Su X L, Xie C D, Peng K C 2017 Phys. Rev. Lett. 118 230501
[37]	Yurke B, McCall S L, Klauder J R 1986 Phys. Rev. A 33 4033
[38]	Plick W N, Dowling J P, Agarwal 2010 New J. Phys. 12 083014
[39]	Ou Z Y 1997 Phys. Rev. A 55 2598
[40]	Tian X D, Liu Y M, Cui C L, Wu J H 2015 Phys. Rev. A 92 063411
[41]	Ding D S, Zhang W, Zhou Z Y, Shi S, Shi B S, Guo G C 2015 Nature Photon. 9 332
[42]	Xin J, Jian Q, Jing J T 2017 Opt. Lett. 42 366
[43]	Jing J T, Liu C J, Zhou Z F, Ou Z Y, Zhang W P 2011 Appl. Phys. Lett. 99 011110
[44]	Hudelist F, Kong J, Liu C J, Jing J T, Zhou Z F, Ou Z Y, Zhang W P 2014 Nature Commun. 5 3049
[45]	Xin J, Liu J M, Jing J T 2017 Opt. Express 25 1350
[46]	Xin J, Wang H L, Jing J T 2016 Appl. Phys. Lett. 109 051107
[47]	Wang H L, Marino A M, Jing J T 2015 Appl. Phys. Lett. 107 121106
[48]	Kong J, Jing J T, Wang H L, Hudelist F, Liu C J, Zhang W P 2013 Appl. Phys. Lett. 102 011130
[49]	Liu S S, Jin J T 2017 Opt. Express 25 15854

施引文献

[1]	Einstein A 1916 Ann. Phys. 49 769
[2]	Sathyaprakash B S, Schutz B F 2009 Living Rev. Relativ. 2 1
[3]	Hinderer T J, Lackey B D, Lang R N, Read J S 2010 Phys. Rev. D 81 123016
[4]	Vines J, Flanagan E E, Hinderer T J 2011 Phys. Rev. D 83 084051
[5]	Bauswein A, Janka H T 2012 Phys. Rev. Lett. 108 011101
[6]	Abramovici A, Althouse W E, Drever R W P, Grsel Y, Kawamura S, Raab F J, Shoemaker D, Sievers L, Spero R E, Thorne K S, Vogt R E, Weiss R, Whitcomb S E, Zucker M E 1992 Science 256 5055
[7]	Aasi J, Abbott B P, Abbott R, et al. 2015 Class. Quant. Grav. 32 074001
[8]	Grote H 2010 Class. Quant. Grav. 27 084003
[9]	Acernese F, Agathos M, Agatsuma K, et al. 2015 Class. Quant. Grav. 32 024001
[10]	Arai K, Takahashi R, Tastumi D, et al. 2009 Class. Quant. Grav. 26 204020
[11]	Barriga P, Blair G D, Coward D, et al. 2010 Class. Quant. Grav. 27 084005
[12]	Punturo M, Abernathy M, Acernese F, et al. 2010 Class. Quant. Grav. 27 084007
[13]	Abbott B P, Abbott R, Abbott T D, et al. 2016 Phys. Rev. Lett. 116 061102
[14]	Abbott B P, Abbott R, Abbott T D, et al. 2017 Phys. Rev. Lett. 119 161101
[15]	Hou Z B, Zhu H J, Xiang G Y, Li C F, Guo G C 2016 npj Quantum Information 2 16001
[16]	Liu F, Zhou Y Y, Yu J, Guo J L, Wu Y, Xiao S X, Wei D, Zhang Y, Jia X J, Xiao M 2017 Appl. Phys. Lett. 110 021106
[17]	Walls D F 1983 Nature 306 141
[18]	Zhang M Z 2015 Quantum Optics (Beijing: Science Press) pp72-75 (in Chinese) 张智明 2015 量子光学 (北京:科学出版社) 第7275页
[19]	Caves C M 1980 Phys. Rev. Lett. 45 75
[20]	Caves C M 1981 Phys. Rev. D 23 1693
[21]	Sun H X, Liu K, Zhang J X, Gao J R 2015 Acta Phys. Sin. 64 234210 (in Chinese) [孙恒信, 刘奎, 张俊香, 郜江瑞 2015 64 234210]
[22]	Slusher R E, Hollberg L W, Yurke B, Mertz J C, Valley J F 1985 Phys. Rev. Lett. 55 2409
[23]	Wu L A, Kimble H J, Hall J L, Wu H F 1986 Phys. Rev. Lett. 57 2520
[24]	Henning V, Moritz M, Karsten D, Schnabel R 2016 Phys. Rev. Lett. 117 110801
[25]	Wan Z J, Feng J X, Sun Z N, Yao L T, Zhang K S 2014 Acta Sin. Quantum Opt. 20 271 (in Chinese) [万振菊, 冯晋霞, 孙志妮, 要立婷, 张宽收 2014 量子光学学报 20 271]
[26]	Sun Z N, Feng J X, Wan Z J, Zhang K S 2016 Acta Phys. Sin. 65 044203 (in Chinese) [孙志妮, 冯晋霞, 万振菊, 张宽收 2016 65 044203]
[27]	McKenzie K, Grosse N, Bowen W P, Whitcomb S E, Gray M B, McClelland D E, Lam P K 2004 Phys. Rev. Lett. 93 161105
[28]	Vahlbruch H, Chelkowski S, Hage B, Franzen A, Danzmann K, Schnabel R 2006 Phys. Rev. Lett. 97 011101
[29]	Yan Z H, Sun H X, Cai C X, Ma L, Liu K, Gao J R 2017 Acta Phys. Sin. 66 114205 (in Chinese) [闫子华, 孙恒信, 蔡春晓, 马龙, 刘奎, 郜江瑞 2017 66 114205]
[30]	Goda K, Miyakawa O, Mikhailov E E, Saraf S, Adhikari R, McKenzie K, Ward R, Vass S, Weinstein A J, Mavalvala N 2008 Nature Phys. 4 472
[31]	Schnabel R, Mavalvala N, McClelland D E, Lam P K 2010 Nature Commun. 1 121
[32]	Abadie J, Abbott B P, Abbott R, et al. 2011 Nature Phys. 7 962
[33]	Aasi J, Abadie J, Zweizi J, et al. 2013 Nature Photon. 7 613
[34]	Liu Y C, Xiao Y F, Chen Y L, Yu X C, Gong Q H 2013 Phys. Rev. Lett. 111 083601
[35]	Wang X L, Chen L K, Li W, Huang H L, Liu C, Chen C, Luo Y H, Su Z E, Wu D, Li Z D, Lu H, Hu Y, Jiang X, Peng C Z, Li L, Liu N L, Chen Y A, Lu C Y, Pan J W 2016 Phys. Rev. Lett. 117 210502
[36]	Deng X W, Xiang Y, Tian C X, Adesso G, He Q Y, Gong Q H, Su X L, Xie C D, Peng K C 2017 Phys. Rev. Lett. 118 230501
[37]	Yurke B, McCall S L, Klauder J R 1986 Phys. Rev. A 33 4033
[38]	Plick W N, Dowling J P, Agarwal 2010 New J. Phys. 12 083014
[39]	Ou Z Y 1997 Phys. Rev. A 55 2598
[40]	Tian X D, Liu Y M, Cui C L, Wu J H 2015 Phys. Rev. A 92 063411
[41]	Ding D S, Zhang W, Zhou Z Y, Shi S, Shi B S, Guo G C 2015 Nature Photon. 9 332
[42]	Xin J, Jian Q, Jing J T 2017 Opt. Lett. 42 366
[43]	Jing J T, Liu C J, Zhou Z F, Ou Z Y, Zhang W P 2011 Appl. Phys. Lett. 99 011110
[44]	Hudelist F, Kong J, Liu C J, Jing J T, Zhou Z F, Ou Z Y, Zhang W P 2014 Nature Commun. 5 3049
[45]	Xin J, Liu J M, Jing J T 2017 Opt. Express 25 1350
[46]	Xin J, Wang H L, Jing J T 2016 Appl. Phys. Lett. 109 051107
[47]	Wang H L, Marino A M, Jing J T 2015 Appl. Phys. Lett. 107 121106
[48]	Kong J, Jing J T, Wang H L, Hudelist F, Liu C J, Zhang W P 2013 Appl. Phys. Lett. 102 011130
[49]	Liu S S, Jin J T 2017 Opt. Express 25 15854

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