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对相干态在通过参量转换中的演化与量子化光涡态的实现

朱开成 李绍新 郑小娟 唐慧琴

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对相干态在通过参量转换中的演化与量子化光涡态的实现

朱开成, 李绍新, 郑小娟, 唐慧琴

Pair coherent state evolutions through parametric frequency conversion and the realization of quantized vortex states

Zhu Kai-Cheng, Li Shao-Xin, Zheng Xiao-Juan, Tang Hui-Qin
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  • 本文讨论了光学参量频率转换过程中对相干态的演化问题, 获得了对相干态时间演化的解析表达式及在位形空间的波函数, 发现通过适当调节系统元件及相互作用时间, 对相干态在位形空间中的波包能呈现出量子涡态特性, 并且与这样涡态相关的波函数具有修正Bessel-Gaussian形式的结构, 即非高斯型波函数. 在相干态表象下, 这一量子化涡态是两模湮没算符平方和的本征态. 这一讨论揭示了产生量子化涡态的另一可实现方案.
    The pair coherent state evolution during a parametric frequency conversion is analyzed. And the wavefunction of the evolving pair coherent state in configuration space is obtained. It is found that the state may become a modified Bessel-Gaussian vortex state with topological charge index q which is a new non-Gaussian state. In coherent state representation such a modified Bessel-Gaussian vortex state is an eigenstate of sum of squared two-mode annihilation operators a2 + b2. The result obtained in this paper provides a new scheme for generating quantized vortex states in experiment with currently available technology.
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    [2]

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    [3]

    Bhaumik D, Bhaumik K, Dutta-Roy B 1976 J. Phys. A: Math. Gen. 9 1507

    [4]

    Agarwal G S 1986 Phys. Rev. Lett. 57 827

    [5]

    Agarwal G S 1988 J. Opt. Soc. Am. B 5 1940

    [6]

    Prakash G S, Agarwal G S 1995 Phys. Rev. A 52 2335

    [7]

    Gou S C, Steinbach J, Knight P L 1996 Phys. Rev. A 54 R1014

    [8]

    Gilchrist A, Munro W J 2000 J. Opt. B: Quantum Semiclass. Opt. 2 47

    [9]

    Meng X G, Wang J S, Fan H Y 2007 Phys. Lett. A 363 12

    [10]

    Gabris A, Agarwal G S 2007 Int. J. Quant. Inf. 5 17

    [11]

    Meng X G Wang J S 2007 Acta Phys. Sin. 56 4578 ( in Chinese) [孟祥国, 王继锁 2007 物理学报 56 4578]

    [12]

    Meng X G, Wang J S, Liang B L, Li H Q 2008 Chin. Phys. B 17 1791

    [13]

    Gerry C C, Mimih J 2010 Phys. Rev. A 82 013831

    [14]

    Chen Z H Liao C G Luo C L 2010 Acta Phys. Sin. 59 6152(in Chinese)[陈子翃, 廖长庚, 罗成立 2010 物理学报 59 6152]

    [15]

    Gerry C C, Mimih J, Birrittella R 2011 Phys. Rev. A 84 023810

    [16]

    Agarwal G S, Puri R R, Singh R P 1997 Phys. Rev. A 56 4207

    [17]

    Agarwal G S, Banerji J 2006 J. Phys. A 39 11503

    [18]

    Bandyopadhyay A, Singh R P 2011 Opt. Commun. 284 256

    [19]

    Bandyopadhyay A, Prabhakar S, Singh R P 2011 Phys. Lett. A 375 1926

    [20]

    Agarwal G S, Biswas A 2005 New J. of Phys. 7 211

    [21]

    Agarwal G S 2011 New J. of Phys. 13 073008

    [22]

    Molina-Terriza G, Torres J P, Torner L 2001 Phys. Rev. Lett. 88 013601

    [23]

    Leach J, Padgett M J, Barnett S M, Franke-Arnold S, Courtial J 2002 Phys. Rev. Lett. 88 257901

    [24]

    Allen L, Barnett S M, Padgett M J 2003 Optical Angular Momentum (Institute of Physics, Bristol)

    [25]

    Eisert J, Scheel S, Plenio M B 2002 Phys. Rev. Lett. 89 137903

    [26]

    Fiurasek J 2002 Phys. Rev. Lett. 89 137904

    [27]

    Giedke G, Cirac J I 2002 Phys. Rev. A 66 032316

    [28]

    Louisell W H, Yariv A, Semjonov A E 1961 Phys. Rev. 124 1646

    [29]

    Tucker J, Walls D F 1969 Ann. Phys. NY 52 1

    [30]

    Perina J 1987 Quantum Statistics of Linear and Nolinear Optical Phenomena (D. Reidel, Dordrecht-Boston) p217

    [31]

    Dodonov A V, Dodonov V V, Mizrahi S S 2005 J. Phys. A: Math. Gen. 38 683

    [32]

    Korenev B G 2002 Bessel functions and their applications (Taylor & Francis) p23

  • [1]

    Braunstein S L, Pati A K 2003 Quantum Information with Continuous Variables (Kluwer Academic, Dordrecht)

    [2]

    Braunstein S L, von Loock P 2005 Rev. Mod. Phys. 77 513

    [3]

    Bhaumik D, Bhaumik K, Dutta-Roy B 1976 J. Phys. A: Math. Gen. 9 1507

    [4]

    Agarwal G S 1986 Phys. Rev. Lett. 57 827

    [5]

    Agarwal G S 1988 J. Opt. Soc. Am. B 5 1940

    [6]

    Prakash G S, Agarwal G S 1995 Phys. Rev. A 52 2335

    [7]

    Gou S C, Steinbach J, Knight P L 1996 Phys. Rev. A 54 R1014

    [8]

    Gilchrist A, Munro W J 2000 J. Opt. B: Quantum Semiclass. Opt. 2 47

    [9]

    Meng X G, Wang J S, Fan H Y 2007 Phys. Lett. A 363 12

    [10]

    Gabris A, Agarwal G S 2007 Int. J. Quant. Inf. 5 17

    [11]

    Meng X G Wang J S 2007 Acta Phys. Sin. 56 4578 ( in Chinese) [孟祥国, 王继锁 2007 物理学报 56 4578]

    [12]

    Meng X G, Wang J S, Liang B L, Li H Q 2008 Chin. Phys. B 17 1791

    [13]

    Gerry C C, Mimih J 2010 Phys. Rev. A 82 013831

    [14]

    Chen Z H Liao C G Luo C L 2010 Acta Phys. Sin. 59 6152(in Chinese)[陈子翃, 廖长庚, 罗成立 2010 物理学报 59 6152]

    [15]

    Gerry C C, Mimih J, Birrittella R 2011 Phys. Rev. A 84 023810

    [16]

    Agarwal G S, Puri R R, Singh R P 1997 Phys. Rev. A 56 4207

    [17]

    Agarwal G S, Banerji J 2006 J. Phys. A 39 11503

    [18]

    Bandyopadhyay A, Singh R P 2011 Opt. Commun. 284 256

    [19]

    Bandyopadhyay A, Prabhakar S, Singh R P 2011 Phys. Lett. A 375 1926

    [20]

    Agarwal G S, Biswas A 2005 New J. of Phys. 7 211

    [21]

    Agarwal G S 2011 New J. of Phys. 13 073008

    [22]

    Molina-Terriza G, Torres J P, Torner L 2001 Phys. Rev. Lett. 88 013601

    [23]

    Leach J, Padgett M J, Barnett S M, Franke-Arnold S, Courtial J 2002 Phys. Rev. Lett. 88 257901

    [24]

    Allen L, Barnett S M, Padgett M J 2003 Optical Angular Momentum (Institute of Physics, Bristol)

    [25]

    Eisert J, Scheel S, Plenio M B 2002 Phys. Rev. Lett. 89 137903

    [26]

    Fiurasek J 2002 Phys. Rev. Lett. 89 137904

    [27]

    Giedke G, Cirac J I 2002 Phys. Rev. A 66 032316

    [28]

    Louisell W H, Yariv A, Semjonov A E 1961 Phys. Rev. 124 1646

    [29]

    Tucker J, Walls D F 1969 Ann. Phys. NY 52 1

    [30]

    Perina J 1987 Quantum Statistics of Linear and Nolinear Optical Phenomena (D. Reidel, Dordrecht-Boston) p217

    [31]

    Dodonov A V, Dodonov V V, Mizrahi S S 2005 J. Phys. A: Math. Gen. 38 683

    [32]

    Korenev B G 2002 Bessel functions and their applications (Taylor & Francis) p23

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出版历程
  • 收稿日期:  2011-12-27
  • 修回日期:  2012-03-01

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