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We investigate the nonclassicality and decoherence of a photon-subtraction-addition coherent state (a++a)m|a in a thermal environment. Its nonclassicality is discussed by deriving analytically Mandel's Q parameter, photon number distribution, and Wigner function. It is shown that if the condition |2z*+ -*|2 1 is satisfied, the Wigner function always presents the negativity for the one-order photon-subtraction-addition coherent state (m=1). Based on the evolution formula of Wigner function, we derive a compact expression for Wigner function in the thermal environment. It is found that when t(1/2)ln[(2N+2)/(2N+1)] there is no negativity for the case of m=1. In addition, the evolution of nonclassicality is discussed in terms of the negative volume of Wigner function.
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Keywords:
- photon-subtraction-addition operation /
- Q-parameter /
- Wigner function /
- decoherence
[1] Loudon R, Knight P L 1987 J. Mod. Opt. 34 709
[2] Xu X X, Yuan H C, Hu L Y 2010 Acta Phys. Sin. 59 4661 (in Chinese) [徐学翔, 袁洪春, 胡利云 2010 59 4661]
[3] Short R, Mandel L 1983 Phys. Rev. Lett. 51 384
[4] Hillery M, O'Connell R F, Scully M O, Wigner E P 1984 Phys. Rep. 106 121
[5] Kenfack A, Życzkowski K 2004 J. Opt. B: Quantum Semiclass. Opt. 6 396
[6] Hu L Y, Fan H Y 2008 J. Opt. Soc. Am. B 25 1955
[7] Stobińska M, Milburn G J, Wódkiewicz K 2008 Phys. Rev. A 78 013810
[8] Hu L Y, Zhang Z M 2012 J. Opt. Soc. Am. B 29 529
[9] Hu L Y, Jia F, Zhang Z M 2012 J. Opt. Soc. Am. B 29 1456
[10] Agarwal G S, Tara K 1991 Phys. Rev. A 43 492
[11] Kalamidas D, Gerry C C, Benmoussa A 2008 Phys. Lett. A 372 1937
[12] Xu X X, Yuan H C, Fan H Y 2011 Chin. Phys. B 20 024203
[13] Hu L Y, Xu X X, Wang Z S, Xu X F 2010 Phys. Rev. A 82 043842
[14] Lee S Y, Park J, Ji S W, Ooi C H R, Lee H W 2009 J. Opt. Soc. Am. B 26 1532
[15] Yang Y, Li F L 2009 J. Opt. Soc. Am. B 26 830
[16] Lee S Y, Nha H, 2010 Phys. Rev. A 82 053812
[17] Lee S Y, Ji S W, Kim H J, Nha H 2011 Phys. Rev. A 84 012302
[18] Li H M, Xu X F 2012 Chin. Phys. B 21 024202
[19] Fan H Y 1997 Representation and Transformation Theory in Quantum Mechanics (Shanghai: Shanghai Scientific & Technical Press) (in Chinese) [范洪义 1997 量子力学表 象与变换论–-狄拉克符号法进展(上海: 上海科学技术出版社)]
[20] Agarwal G S, Tara K 1992 Phys. Rev. A 46 485
[21] Fan H Y 1987 Phys. Lett. A 124 303
[22] Gardner C W, Zoller P 2000 Quantum Noise (Berlin: Springer)
[23] Hu L Y, Fan H Y 2009 Opt. Commun. 282 4379
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[1] Loudon R, Knight P L 1987 J. Mod. Opt. 34 709
[2] Xu X X, Yuan H C, Hu L Y 2010 Acta Phys. Sin. 59 4661 (in Chinese) [徐学翔, 袁洪春, 胡利云 2010 59 4661]
[3] Short R, Mandel L 1983 Phys. Rev. Lett. 51 384
[4] Hillery M, O'Connell R F, Scully M O, Wigner E P 1984 Phys. Rep. 106 121
[5] Kenfack A, Życzkowski K 2004 J. Opt. B: Quantum Semiclass. Opt. 6 396
[6] Hu L Y, Fan H Y 2008 J. Opt. Soc. Am. B 25 1955
[7] Stobińska M, Milburn G J, Wódkiewicz K 2008 Phys. Rev. A 78 013810
[8] Hu L Y, Zhang Z M 2012 J. Opt. Soc. Am. B 29 529
[9] Hu L Y, Jia F, Zhang Z M 2012 J. Opt. Soc. Am. B 29 1456
[10] Agarwal G S, Tara K 1991 Phys. Rev. A 43 492
[11] Kalamidas D, Gerry C C, Benmoussa A 2008 Phys. Lett. A 372 1937
[12] Xu X X, Yuan H C, Fan H Y 2011 Chin. Phys. B 20 024203
[13] Hu L Y, Xu X X, Wang Z S, Xu X F 2010 Phys. Rev. A 82 043842
[14] Lee S Y, Park J, Ji S W, Ooi C H R, Lee H W 2009 J. Opt. Soc. Am. B 26 1532
[15] Yang Y, Li F L 2009 J. Opt. Soc. Am. B 26 830
[16] Lee S Y, Nha H, 2010 Phys. Rev. A 82 053812
[17] Lee S Y, Ji S W, Kim H J, Nha H 2011 Phys. Rev. A 84 012302
[18] Li H M, Xu X F 2012 Chin. Phys. B 21 024202
[19] Fan H Y 1997 Representation and Transformation Theory in Quantum Mechanics (Shanghai: Shanghai Scientific & Technical Press) (in Chinese) [范洪义 1997 量子力学表 象与变换论–-狄拉克符号法进展(上海: 上海科学技术出版社)]
[20] Agarwal G S, Tara K 1992 Phys. Rev. A 46 485
[21] Fan H Y 1987 Phys. Lett. A 124 303
[22] Gardner C W, Zoller P 2000 Quantum Noise (Berlin: Springer)
[23] Hu L Y, Fan H Y 2009 Opt. Commun. 282 4379
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