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Chin. Phys. B, 2016, Vol. 25(10): 104203    DOI: 10.1088/1674-1056/25/10/104203

Quantum metrology with two-mode squeezed thermal state: Parity detection and phase sensitivity

Heng-Mei Li(李恒梅)1, Xue-Xiang Xu(徐学翔)2, Hong-Chun Yuan(袁洪春)3,4, Zhen Wang(王震)1
1 College of Mathematical Physics and Chemical Engineering, Changzhou Institute of Technology, Changzhou 213002, China;
2 College of Physics and Communication Electronics, Jiangxi Normal University, Nanchang 330022, China;
3 College of Electrical and Optoelectronic Engineering, Changzhou Institute of Technology, Changzhou 213002, China;
4 Changzhou Institute of Modern Optoelectronic Technology, Changzhou 213002, China
Abstract  Based on the Wigner-function method, we investigate the parity detection and phase sensitivity in a Mach-Zehnder interferometer (MZI) with two-mode squeezed thermal state (TMSTS). Using the classical transformation relation of the MZI, we derive the input-output Wigner functions and then obtain the explicit expressions of parity and phase sensitivity. The results from the numerical calculation show that supersensitivity can be reached only if the input TMSTS have a large number photons.
Keywords:  Mach-Zenhder interferometer      two-mode squeezed thermal state      Wigner function      phase sensitivity     
Received:  20 March 2016      Published:  05 October 2016
PACS:  42.50.St (Nonclassical interferometry, subwavelength lithography)  
  42.50.Dv (Quantum state engineering and measurements)  
  42.50.Lc (Quantum fluctuations, quantum noise, and quantum jumps)  
Fund: Project supported by the National Natural Science Foundation of China (Grant No. 11447002), the Research Foundation of the Education Department of Jiangxi Province of China (Grant No. GJJ150338), and the Research Foundation for Changzhou Institute of Modern Optoelectronic Technology (Grant No. CZGY15).
Corresponding Authors:  Heng-Mei Li     E-mail:

Cite this article: 

Heng-Mei Li(李恒梅), Xue-Xiang Xu(徐学翔), Hong-Chun Yuan(袁洪春), Zhen Wang(王震) Quantum metrology with two-mode squeezed thermal state: Parity detection and phase sensitivity 2016 Chin. Phys. B 25 104203

[1] Hariharan P 2003 Optical Interferometry (Amsterdam: Elsevier)
[2] Helstrom C W 1976 Quantum Detection and Estimation Theory, Mathematics in Science and Engineering (New York: Elsevier Science)
[3] Escher B M, de Matos Filho R L and Davidovich L 2011 Nat. Phys. 7 406
[4] Giovannetti V, Lloyd S and Maccone L 2011 Nat. Photon. 5 222
[5] Yurke B, McCall S L and Klauder J R 1986 Phys. Rev. A 33 4033
[6] Boixo S, Datta A, Davis M J, Flammia S T, Shaji A and Caves C M 2008 Phys. Rev. Lett. 101 040403
[7] Holland M J and Burnett K 1993 Phys. Rev. Lett. 71 1355
[8] Caves C M 1981 Phys. Rev. D 23 1693
[9] Pezzé L and Smerzi A 2008 Phys. Rev. Lett. 100 073601
[10] Seshadreesan K P, Anisimov P M, Lee H and Dowling J P 2011 New J. Phys. 13 083026
[11] Boto A N, Kok P, Abrams D S, et al. 2000 Phys. Rev. Lett. 85 2733
[12] Dowling J P 2008 Contemp. Phys. 49 125
[13] Hu L Y, Wei C P, Huang J H and Liu C J 2014 Opt. Commun. 323 68
[14] Lee S Y, Lee C W, Nha H and Kaszlikowski D 2015 J. Opt. Soc. Am. B 32 1186
[15] Giovannetti V, Lloyd S and Maccone L 2006 Phys. Rev. Lett. 96 010401
[16] Anisimov P M, Raterman G M, Chiruvelli A, Plick W N, Huver S D, Lee H and Dowling J P 2010 Phys. Rev. Lett. 104 103602
[17] Zhang Y M, Li X W and Jin G R 2013 Chin. Phys. B 22 114206
[18] Ekert A K and Knight P L 1991 Phys. Rev. A 43 3934
[19] Suda M 2006 Quantum Interferometry in Phase Space (Berlin Heidelberg: Springer-Verlag)
[20] Schleich W P 2001 Quantum Optics in Phase space (Berlin: Verlag)
[21] Xu X X, Jia F, Hu L Y, Duan Z L, Guo Q and Ma S J 2012 J. Mod. Opt. 59 1624
[22] Xu X X and Yuan H C 2015 Quantum Inf. Process. 14 411
[23] Hu L Y, Wang S and Zhang Z M 2012 Chin. Phys. B 21 064207
[24] Hu L Y, Fan H Y and Zhang Z M 2013 Chin. Phys. B 22 034202
[25] Fan H Y, Lu H L and Fan Y 2006 Ann. Phys. 321 480
[26] Fan H Y, Lu H L, Gao W B and Xu X F 2006 Ann. Phys. 321 2116
[27] Meng X G, Wang J S and Liang B L 2009 Chin. Phys. B 18 1534
[28] Meng X G, Wang Z, Fan H Y, Wang J S and Yang Z S 2012 J. Opt. Soc. Am. B 29 1844
[29] Campos R A, Gerry C C and Benmoussa A 2003 Phys. Rev. A 68 023810
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