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研究了由光子增减叠加操作作用于相干态而得量子态的非经典性及其在热环境中的退相干问题. 通过解析导出了Mandel's Q参数, 光子数分布, Wigner函数等讨论其非经典性. 研究表明一阶光子增减相干叠加相干态在相空间总是取负值, 只要满足条件|2z* +-*|21. 基于 Wigner函数的演化积分公式, 解析地推导出了在热环境中Wigner函数的简洁表达式. 研究首次表明: 如果满足t(1/2)ln[(2N+2)/(2N+1)] 得以满足, 一阶光子增减相干叠加相干态在相空间最小值点处Wigner函数分布总存在负部. 此外, 根据 Wigner函数负部体积讨论了其非经典特性.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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