Please wait a minute...
Chin. Phys. B, 2012, Vol. 21(4): 044210    DOI: 10.1088/1674-1056/21/4/044210
ELECTROMAGNETISM, OPTICS, ACOUSTICS, HEAT TRANSFER, CLASSICAL MECHANICS, AND FLUID DYNAMICS Prev   Next  

Nonclassicality of a two-variable Hermite polynomial state

Tan Guo-Bin(谭国斌), Xu Li-Juan(徐莉娟), and Ma Shan-Jun(马善钧)
College of Physics & Communication Electronics, Jiangxi Normal University, Nanchang 330022, China
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
[1] Nonclassicality of photon-modulated spin coherent states in the Holstein—Primakoff realization
Xiaoyan Zhang(张晓燕), Jisuo Wang(王继锁), Lei Wang(王磊),Xiangguo Meng(孟祥国), and Baolong Liang(梁宝龙). Chin. Phys. B, 2022, 31(5): 054205.
[2] Margolus-Levitin speed limit across quantum to classical regimes based on trace distance
Shao-Xiong Wu(武少雄), Chang-Shui Yu(于长水). Chin. Phys. B, 2020, 29(5): 050302.
[3] Quantum-classical correspondence and mechanical analysis ofa classical-quantum chaotic system
Haiyun Bi(毕海云), Guoyuan Qi(齐国元), Jianbing Hu(胡建兵), Qiliang Wu(吴启亮). Chin. Phys. B, 2020, 29(2): 020502.
[4] Nonclassicality of photon-modulated atomic coherent states in the Schwinger bosonic realization
Jisuo Wang(王继锁), Xiangguo Meng(孟祥国), and Xiaoyan Zhang(张晓燕). Chin. Phys. B, 2020, 29(12): 124213.
[5] Wigner function for squeezed negative binomial state and evolution of density operator for amplitude decay
Heng-Yun Lv(吕恒云), Ji-Suo Wang(王继锁), Xiao-Yan Zhang(张晓燕), Meng-Yan Wu(吴孟艳), Bao-Long Liang(梁宝龙), Xiang-Guo Meng(孟祥国). Chin. Phys. B, 2019, 28(9): 090302.
[6] Negativity of Wigner function and phase sensitivity of an SU(1,1) interferometer
Chun-Li Liu(刘春丽), Li-Li Guo(郭丽丽), Zhi-Ming Zhang(张智明), Ya-Fei Yu(於亚飞). Chin. Phys. B, 2019, 28(6): 060704.
[7] Analytical and numerical investigations of displaced thermal state evolutions in a laser process
Chuan-Xun Du(杜传勋), Xiang-Guo Meng(孟祥国), Ran Zhang(张冉), Ji-Suo Wang(王继锁). Chin. Phys. B, 2017, 26(12): 120301.
[8] Quantum statistical properties of photon-added spin coherent states
G Honarasa. Chin. Phys. B, 2017, 26(11): 114202.
[9] Quantum metrology with two-mode squeezed thermal state: Parity detection and phase sensitivity
Heng-Mei Li(李恒梅), Xue-Xiang Xu(徐学翔), Hong-Chun Yuan(袁洪春), Zhen Wang(王震). Chin. Phys. B, 2016, 25(10): 104203.
[10] Algebraic and group treatments to nonlinear displaced number statesand their nonclassicality features: A new approach
N Asili Firouzabadi, M K Tavassoly, M J Faghihi. Chin. Phys. B, 2015, 24(6): 064204.
[11] Comparison between photon annihilation-then-creation and photon creation-then-annihilation thermal states:Non-classical and non-Gaussian properties
Xu Xue-Xiang (徐学翔), Yuan Hong-Chun (袁洪春), Wang Yan (王燕). Chin. Phys. B, 2014, 23(7): 070301.
[12] New approach for deriving the exact time evolution of density operator for diffusive anharmonic oscillator and its Wigner distribution function
Meng Xiang-Guo (孟祥国), Wang Ji-Suo (王继锁), Liang Bao-Long (梁宝龙). Chin. Phys. B, 2013, 22(3): 030307.
[13] Nonclassicality and decoherence of coherent superposition operation of photon subtraction and photon addition on squeezed state
Xu Li-Juan (徐莉娟), Tan Guo-Bin (谭国斌), Ma Shan-Jun (马善钧), Guo Qin (郭琴). Chin. Phys. B, 2013, 22(3): 030311.
[14] A new type of photon-added squeezed coherent state and its statistical properties
Zhou Jun(周军), Fan Hong-Yi(范洪义), and Song Jun(宋军) . Chin. Phys. B, 2012, 21(7): 070301.
[15] Quantum phase distribution and the number–phase Wigner function of the generalized squeezed vacuum states associated with solvable quantum systems
G. R. Honarasa, M. K. Tavassoly, and M. Hatami . Chin. Phys. B, 2012, 21(5): 054208.
No Suggested Reading articles found!