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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.
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Keywords:
- detection efficiency /
- quantum enhanced measurement /
- Mach-Zehnder interferometer /
- phase sensitivity
[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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[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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