探测器对量子增强马赫-曾德尔干涉仪相位测量灵敏度的影响

李诗宇; 田剑锋; 杨晨; 左冠华; 张玉驰; 张天才

doi:10.7498/aps.67.20181193

摘要

研究了强度差测量方案下，探测器量子效率对光子数态、关联数态、压缩真空态三种量子光源注入的马赫-曾德尔干涉仪相位测量灵敏度的影响.获得了相位测量灵敏度与效率的定量关系，比较了探测效率对不同量子态注入的干涉仪相位灵敏度的影响.研究表明：光子数态注入时，相位测量灵敏度始终不能超越标准量子极限；关联数态注入时，无论多大的光子数，要获得相位测量的量子增强，探测效率不得小于75%；对于压缩真空态，只要有压缩存在就可以获得一定的相位测量的量子增强；关联数态、压缩真空态的注入，相位灵敏度皆随探测效率的增大而不同程度的提高，且压缩真空态比关联数态具有更好的量子增强效果.给出了在量子增强的精密测量实验中对探测效率的要求，并结合实际应用说明了探测效率的提高有助于提高干涉仪探测的灵敏度.

关键词:

Abstract

Three kinds of quantum light sources:Fock state, correlated Fock-state and squeezed vacuum state, which serve as the injection end of Mach-Zehnder interferometer (MZI) are investigated. The effect of detection quantum efficiency on the sensitivity of phase measurement in MZI is analyzed by using the intensity difference detection scheme. By analyzing the MZI system, the quantitative relationship between the sensitivity of phase measurement and the detection efficiency is obtained. It is found that the phase sensitivity cannot go beyond the standard quantum limit in any case when the Fock state is injected into interferometer, that is, the Fock state does not realize quantum enhanced measurement (QEM). And the injection of correlated Fock-state or squeezed vacuum state of light can go beyond the standard quantum limit, but the conditions for realizing quantum enhancement are different, quantum enhancement can only be achieved when the detection efficiency is greater than 75% for correlated Fock-state, or the squeezed vacuum state of light is injected into interferometer. There is no limitation of the minimum detection efficiency for realizing quantum enhancement on squeezed vacuum state. In principle, quantum enhancement can be achieved as long as the squeezed vacuum state is injected. The influence of detection efficiency on the phase sensitivity is investigated when the correlated Fock-state and the squeezed vacuum state are injected into the MZI. It is found that the phase sensitivity or quantum enhancement becomes better as the quantum efficiency of the detection system turns higher. And it is the squeezed vacuum state injected into the interferometer that has better quantum enhancement effect than the correlated Fock-state. In this study, the requirements for the detection efficiency for realizing QEM in experiment are given, which is of great significance for studying the QEM, when taking the real experimental system into account. In addition, the conclusions obtained from the MZI model discussed can also be used to analyze the sensitivity of detecting the gravitational wave, it explains that the improvement of detector efficiency can indeed improve the sensitivity to gravitational wave detection, which will play an important role in exploring gravitational waves and understanding the time and space to reveal the mystery of the universe in the future.

Keywords:

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, 极端光学协同创新中心, 太原 030006;

2. 山西大学物理电子工程学院, 太原 030006

基金项目: 国家重点研发计划（批准号：2017YFA0304502）和国家自然科学基金（批准号：11634008，11674203，11574187，61227902）资助的课题.

Authors and contacts

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

2. College of Physics and Electronic Engineering, Shanxi University, Taiyuan 030006, China

Funds: Project supported by the National Key Research and Development Program of China (Grant No. 2017YFA0304502) and the National Natural Science Foundation of China (Grants Nos. 11634008, 11674203, 11574187, 61227902).

参考文献

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[2]	LIGO Scientific Collaboration and Virgo Collaboration 2016 Phys. Rev. Lett. 116 241103
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[4]	Xiao M, Wu L A, Kimble H J 1987 Phys. Rev. Lett. 59 278
[5]	Holland M J, Burnett K 1993 Phys. Rev. Lett. 71 1355
[6]	Kim T, Shin J, Ha Y, Kim H, Park G, Noh T G, Hong C K 1998 Opt. Commun. 156 37
[7]	Campos R A, Gerry C C, Benmoussa A 2003 Phys. Rev. A 68 023810
[8]	Higgins B L, Berry D W, Bartlett S D, Wiseman H M, Pryde G J 2007 Nature 450 393
[9]	Anisimov P M, Raterman G M, Chiruvelli A, Plick W N, Huver S D, Lee H, Dowling J P 2010 Phys. Rev. Lett. 104 103602
[10]	Seshadreesan K P, Anisimov P M, Lee H, Dowling J P 2011 New J. Phys. 13 083026
[11]	Li W F, Du J J, Wen R J, Li G, Zhang T C 2014 J. Appl. Phys. 115 123106
[12]	Bollinger J J, Itano W M, Wineland D J, Heinzen D J 1996 Phys. Rev. A 54 R4649
[13]	Nagata T, Okamoto R, O'Brien J L, Sasaki K, Takeuchi S 2007 Science 316 726
[14]	Gerry C C, Mimih J 2010 Phys. Rev. A 82 013831
[15]	Joo J, Munro W J, Spiller T P 2011 Phys. Rev. Lett. 107 083601
[16]	Kim T, Ha Y, Shin J, Kim H, Park G, Kim K, Noh T G, Hong C K 1999 Phys. Rev. A 60 708
[17]	Gilbert G, Hamrick M, Weinstein Y S 2008 J. Opt. Soc. Am. B 25 1336
[18]	Genoni M G, Olivares S, Paris M G A 2011 Phys. Rev. Lett. 106 153603
[19]	Genoni M G, Olivares S, Brivio D, Cialdi S, Cipriani D, Santamato A, Vezzoli S, Paris M G A 2012 Phys. Rev. A 85 043817
[20]	Datta A, Zhang L J, Thomas-Peter N, Dorner U, Smith B J, Walmsley I A 2011 Phys. Rev. A 83 063836
[21]	Xie D, Peng J Y 2013 Sci. China: Phys. Mech. Astron. 56 593
[22]	Xin J, Wang H L, Jing J T 2016 Appl. Phys. Lett. 109 051107
[23]	Xie D, Chen H F 2017 J. Korean Phys. Soc. 70 1016
[24]	Ben-Aryeh Y 2012 J. Opt. Soc. Am. B 29 2754
[25]	Yurke B, McCall S L, Klauder J R 1986 Phys. Rev. A 33 4033
[26]	Yurke B 1986 Phys. Rev. Lett. 56 1515
[27]	Yurke B 1985 Phys. Rev. A 32 311
[28]	Ou Z Y 1996 Phys. Rev. Lett. 77 2352
[29]	Demkowicz-Dobrzanski R, Banaszek K, Schnabel R 2013 Phys. Rev. A 88 041802
[30]	The LIGO Scientific Collaboration 2011 Nat. Phys. 7 962
[31]	Goda K, Miyakawa O, Mikhailov E E, Saraf S, Adhikari R, McKenzie K, Ward R, Vass S, Weinstein A J, Mavalvala N 2008 Nat. Phys. 4 472

施引文献

[1]	Caves C M 1981 Phys. Rev. D 23 1693
[2]	LIGO Scientific Collaboration and Virgo Collaboration 2016 Phys. Rev. Lett. 116 241103
[3]	Grangier P, Slusher R E, Yurke B, Laporta A 1987 Phys. Rev. Lett. 59 2153
[4]	Xiao M, Wu L A, Kimble H J 1987 Phys. Rev. Lett. 59 278
[5]	Holland M J, Burnett K 1993 Phys. Rev. Lett. 71 1355
[6]	Kim T, Shin J, Ha Y, Kim H, Park G, Noh T G, Hong C K 1998 Opt. Commun. 156 37
[7]	Campos R A, Gerry C C, Benmoussa A 2003 Phys. Rev. A 68 023810
[8]	Higgins B L, Berry D W, Bartlett S D, Wiseman H M, Pryde G J 2007 Nature 450 393
[9]	Anisimov P M, Raterman G M, Chiruvelli A, Plick W N, Huver S D, Lee H, Dowling J P 2010 Phys. Rev. Lett. 104 103602
[10]	Seshadreesan K P, Anisimov P M, Lee H, Dowling J P 2011 New J. Phys. 13 083026
[11]	Li W F, Du J J, Wen R J, Li G, Zhang T C 2014 J. Appl. Phys. 115 123106
[12]	Bollinger J J, Itano W M, Wineland D J, Heinzen D J 1996 Phys. Rev. A 54 R4649
[13]	Nagata T, Okamoto R, O'Brien J L, Sasaki K, Takeuchi S 2007 Science 316 726
[14]	Gerry C C, Mimih J 2010 Phys. Rev. A 82 013831
[15]	Joo J, Munro W J, Spiller T P 2011 Phys. Rev. Lett. 107 083601
[16]	Kim T, Ha Y, Shin J, Kim H, Park G, Kim K, Noh T G, Hong C K 1999 Phys. Rev. A 60 708
[17]	Gilbert G, Hamrick M, Weinstein Y S 2008 J. Opt. Soc. Am. B 25 1336
[18]	Genoni M G, Olivares S, Paris M G A 2011 Phys. Rev. Lett. 106 153603
[19]	Genoni M G, Olivares S, Brivio D, Cialdi S, Cipriani D, Santamato A, Vezzoli S, Paris M G A 2012 Phys. Rev. A 85 043817
[20]	Datta A, Zhang L J, Thomas-Peter N, Dorner U, Smith B J, Walmsley I A 2011 Phys. Rev. A 83 063836
[21]	Xie D, Peng J Y 2013 Sci. China: Phys. Mech. Astron. 56 593
[22]	Xin J, Wang H L, Jing J T 2016 Appl. Phys. Lett. 109 051107
[23]	Xie D, Chen H F 2017 J. Korean Phys. Soc. 70 1016
[24]	Ben-Aryeh Y 2012 J. Opt. Soc. Am. B 29 2754
[25]	Yurke B, McCall S L, Klauder J R 1986 Phys. Rev. A 33 4033
[26]	Yurke B 1986 Phys. Rev. Lett. 56 1515
[27]	Yurke B 1985 Phys. Rev. A 32 311
[28]	Ou Z Y 1996 Phys. Rev. Lett. 77 2352
[29]	Demkowicz-Dobrzanski R, Banaszek K, Schnabel R 2013 Phys. Rev. A 88 041802
[30]	The LIGO Scientific Collaboration 2011 Nat. Phys. 7 962
[31]	Goda K, Miyakawa O, Mikhailov E E, Saraf S, Adhikari R, McKenzie K, Ward R, Vass S, Weinstein A J, Mavalvala N 2008 Nat. Phys. 4 472

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