Nonclassicality of a two-variable Hermite polynomial state

doi:10.1088/1674-1056/21/4/044210

Abstract The nonclassicality of the two-variable Hermite polynomial state is investigated. It is found that the two-variable Hermite polynomial state can be considered as a two-mode photon subtracted squeezed vacuum state. A compact expression for the Wigner function is also derived analytically by using the Weyl-ordered operator invariance under similar transformations. Especially, the nonclassicality is discussed in terms of the negativity of the Wigner function. Then violations of Bell's inequality for the two-variable Hermite polynomial state are studied.

Keywords: nonclassicality Hermite polynomial state Wigner function Bell's inequality

Received: 19 October 2011
Revised: 23 November 2011
Accepted manuscript online:

PACS:	42.50.Dv	(Quantum state engineering and measurements)
	03.65.Wj	(State reconstruction, quantum tomography)

Fund: Project supported by the National Natural Science Foundation of China (Grant No. 11047133), the Natural Science Foundation of Jiangxi Province of China (Grant No. 2010GQW0027), and the Research Foundation of the Education Department of Jiangxi Province of China (Grant No. GJJ11390).

Corresponding Authors: Ma Shan-Jun,shanjunma@126.com
E-mail: shanjunma@126.com

Cite this article:

Tan Guo-Bin(谭国斌), Xu Li-Juan(徐莉娟), and Ma Shan-Jun(马善钧) Nonclassicality of a two-variable Hermite polynomial state 2012 Chin. Phys. B 21 044210

[1]	Loudon R and Knight P L 1987 J. Mod. Opt. 34 709
[2]	Buzek V 1990 J. Mod. Opt. 37 303
[3]	Dodonov V V 2002 J. Opt. B: Quantum Semiclass. Opt. 4 R1
[4]	Schrade G, Akulin V M, Man'ko V I and Schleich W P 1993 Phys. Rev. A 48 2398
[5]	Gantsog T and Tanaś R 1991 Phys. Lett. A 152 251
[6]	Chizhov A V and Murzakhmetov B K 1993 Phys. Lett. A 176 33
[7]	Selvadoray M and Kumar M S 1997 Opt. Commun. 136 125
[8]	Hiroshima T 2001 Phys. Rev. A 63 022305
[9]	Ban M 1999 J. Opt. B: Quantum Semiclass. Opt. 1 L9
[10]	Hu L Y and Fan H Y 2008 Commun. Theor. Phys. 50 965
[11]	Ban M 2005 J. Opt. B: Quantum Semiclass. Opt. 7 L4
[12]	Schumaker B L 1986 Phys. Rep. 135 317
[13]	Abdalla M S 1992 J. Mod. Opt. 39 1067
[14]	Hu L Y and Fan H Y 2008 J. Mod. Opt. 5513 2011
[15]	Agarwal G S and Wolf E 1970 Phys. Rev. D 2 2161
[16]	Yuan H C, Li H M, Xu Y J and Fan H Y 2009 Int. J. Theor. Phys. 48 3319
[17]	Hu L Y and Fan H Y 2009 Chin. Phys. B 18 4657
[18]	Li B S, Zou X B and Guo G C 2007 Phys. Rev. A 75 045801
[19]	Hu L Y and Fan H Y 2009 Mod. Phys. Lett. A 24 2263
[20]	Xu X F and Zhu S Q 2008 Chin. Phys. Lett. 25 2762
[21]	Fan H Y, Lu H L and Fan Y 2006 Ann. Phys. 321 480
[22]	Wünsche A 1999 J. Opt. B: Quantum Semiclass. Opt. 1 R11
[23]	Hu L Y and Fan H Y 2009 Chin. Phys. B 18 902
[24]	Fan H Y and Hu L Y 2009 Chin. Phys. B 18 1061
[25]	Zhang Z M 2004 Chin. Phys. Lett. 21 5
[26]	Fan H Y and Liu S G 2007 Commun. Theor. Phys. 47 427
[27]	Xu X X, Yuan H C and Hu L Y 2010 Acta Phys. Sin. 59 4661 (in Chinese)
[28]	Fan H Y and Ye X 1993 Phys. Lett. A 175 387
[29]	Lü J F and Ma S J 2011 Acta Phys. Sin. 60 080301 (in Chinese)
[30]	Glauber R 1963 Phys. Rev. 131 2766.
[31]	Klauder J R and Skargerstam B S 1985 Coherent States (Singapore: World Scientific)
[32]	Schleich W P 2001 Quantum Optics in Phase Space (Berlin: Wiley-VCH)
[33]	Wigner E P 1932 Phys. Rev. 40 749
[34]	Agarwal G S and Wolf E 1970 Phys. Rev. D 2 2161
[35]	Fan H Y 1992 J. Phys. A: Math. Gen. 25 3443
[36]	Fan H Y and Wang J S 2005 Mod. Phys. Lett. A 20 1525
[37]	Fan H Y 2008 Ann. Phys. 323 500
[38]	Fan H Y and Zaidi H R 1987 Phys. Lett. A 124 303
[39]	Glauber R 1963 Phys. Rev. 131 2766
[40]	Wallentowitz S and Volgel W 1996 Phys. Rev. A 53 4528
[41]	Banasek K and Wodkiewicz K 1998 Phys. Rev. A 58 4345
[42]	Banasek K and Wodkiewicz K 1996 Phys. Rev. Lett. 76 4344
[43]	Clauser J F, Horne M A, Shimony A and Holt R A 1969 Phys. Rev. Lett. 23 880
[44]	Hu L Y, Xu X X, Fan H Y and Guo Q 2010 Opt. Commun. 283 5074

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