量子相空间分布函数与压缩相干态表示间的变换关系
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摘要
基于Husimi算符具有压缩相干态投影子形式,首先介绍了一个新的量子算符表示,即压缩相干态表示.当高斯展宽参数κ=1时,该函数约化为通常的P函数.作为例子,研究了热态的压缩相干态表示,通过图示说明了压缩相干态表示与P函数的区别.为更好地在量子光学问题中使用该表示,我们揭示了压缩相干态表示与Wigner函数、Q函数以及Husimi函数间的积分变换关系.
A new operator representation, called squeezed coherent state representation, is introduced since Husimi operator has the form of squeezed coherent state. We fisrt introduce its specific integral expression. When κ = 1, this representation is reduced to the usual P function. As an example, we calculate the squeezed coherent state representation for thermal field to illustrate a difference between P function and the squeezed coherent state representation. Especially, in order to better apply this representation to quantum optics, we reveal the integral transformations between the squeezed coherent state representation, respectively, and the following three functions: Wigner function, Q function, and Husimi function.
A new operator representation, called squeezed coherent state representation, is introduced since Husimi operator has the form of squeezed coherent state. We fisrt introduce its specific integral expression. When κ = 1, this representation is reduced to the usual P function. As an example, we calculate the squeezed coherent state representation for thermal field to illustrate a difference between P function and the squeezed coherent state representation. Especially, in order to better apply this representation to quantum optics, we reveal the integral transformations between the squeezed coherent state representation, respectively, and the following three functions: Wigner function, Q function, and Husimi function.
引文
[1]Schleich W P 2001 Quantum Optics in Phase Space(Berlin:Wiley-VCH)
[2]Fan H Y 2014 Acta Phys.Sin.63 020302(in Chinese)[范洪义2014物理学报63 020302]
[3]Zhang X Y,Wang J S 2011 Acta Phys.Sin.60 090304(in Chinese)[张晓燕,王继锁2011物理学报60 090304]
[4]Wigner E P 1932 Phys.Rev.40 749
[5]Hillery M 1984 Phys.Rep.106 121
[6]Sudarshan E C G 1963 Phys.Rev.Lett.10 277
[7]Glauber R J 1963 Phys.Rev.Lett.10 84
[8]Meng X G,Wang J S,Liang B L 2007 Acta Phys.Sin.56 2160(in Chinese)[孟祥国,王继锁,梁宝龙2007物理学报56 2160]
[9]Wang S,Zhang B Y,Zhang Y H 2010 Acta Phys.Sin.59 1775(in Chinese)[王帅,张丙云,张运海2010物理学报59 1775]
[10]Husimi K 1940 Proc.Phys.Math.Soc.JPN 22 264
[11]Fan H Y 2008 Ann.Phys.323 500
[12]Xu Y J,Fan H Y,Liu Q Y 2010 Chin.Phys.B 19 020303
[13]Fan H Y,Yuan H C 2010 Chin.Phys.B 19 070301
[14]Xu X X,Yuan H C,Hu L Y 2010 Acta Phys.Sin.594661(in Chinese)[徐学翔,袁洪春,胡利云2010物理学报59 4661]
[15]Fan H Y,Guo Q 2006 Phys.Lett.A 358 203
[16]Yuan H C,Xu X X 2012 Acta Phys.Sin.61 064205(in Chinese)[袁洪春,徐学翔2012物理学报61 064205]
[17]Scully M O 1997 Quantum Optics(England,Cambridge:Cambridge University Press)
[18]Mehta C L 1967 Phys.Rev.Lett.18 752
[19]Korennoy Y A,Man’ko V I 2011 Phys.Rev.A 83 053817
[20]Benichi H,Furusawa A 2011 Phys.Rev.A 84 032104
[21]Filippov S N,Man’ko V I 2011 Phys.Rev.A 84 033827
[22]Xie C M,Fan H Y 2011 Chin.Phys.B 20 060303
[23]Xie C M,Fan H Y 2012 Chin.Phys.B 21 010302
[2]Fan H Y 2014 Acta Phys.Sin.63 020302(in Chinese)[范洪义2014物理学报63 020302]
[3]Zhang X Y,Wang J S 2011 Acta Phys.Sin.60 090304(in Chinese)[张晓燕,王继锁2011物理学报60 090304]
[4]Wigner E P 1932 Phys.Rev.40 749
[5]Hillery M 1984 Phys.Rep.106 121
[6]Sudarshan E C G 1963 Phys.Rev.Lett.10 277
[7]Glauber R J 1963 Phys.Rev.Lett.10 84
[8]Meng X G,Wang J S,Liang B L 2007 Acta Phys.Sin.56 2160(in Chinese)[孟祥国,王继锁,梁宝龙2007物理学报56 2160]
[9]Wang S,Zhang B Y,Zhang Y H 2010 Acta Phys.Sin.59 1775(in Chinese)[王帅,张丙云,张运海2010物理学报59 1775]
[10]Husimi K 1940 Proc.Phys.Math.Soc.JPN 22 264
[11]Fan H Y 2008 Ann.Phys.323 500
[12]Xu Y J,Fan H Y,Liu Q Y 2010 Chin.Phys.B 19 020303
[13]Fan H Y,Yuan H C 2010 Chin.Phys.B 19 070301
[14]Xu X X,Yuan H C,Hu L Y 2010 Acta Phys.Sin.594661(in Chinese)[徐学翔,袁洪春,胡利云2010物理学报59 4661]
[15]Fan H Y,Guo Q 2006 Phys.Lett.A 358 203
[16]Yuan H C,Xu X X 2012 Acta Phys.Sin.61 064205(in Chinese)[袁洪春,徐学翔2012物理学报61 064205]
[17]Scully M O 1997 Quantum Optics(England,Cambridge:Cambridge University Press)
[18]Mehta C L 1967 Phys.Rev.Lett.18 752
[19]Korennoy Y A,Man’ko V I 2011 Phys.Rev.A 83 053817
[20]Benichi H,Furusawa A 2011 Phys.Rev.A 84 032104
[21]Filippov S N,Man’ko V I 2011 Phys.Rev.A 84 033827
[22]Xie C M,Fan H Y 2011 Chin.Phys.B 20 060303
[23]Xie C M,Fan H Y 2012 Chin.Phys.B 21 010302