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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.
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Keywords:
- squeezed coherent state /
- Wigner function /
- P function
[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 63 020302]
[3] Zhang X Y, Wang J S 2011 Acta Phys. Sin. 60 090304 (in Chinese) [张晓燕, 王继锁 2011 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 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 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. 59 4661 (in Chinese) [徐学翔, 袁洪春, 胡利云 2010 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 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
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[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 63 020302]
[3] Zhang X Y, Wang J S 2011 Acta Phys. Sin. 60 090304 (in Chinese) [张晓燕, 王继锁 2011 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 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 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. 59 4661 (in Chinese) [徐学翔, 袁洪春, 胡利云 2010 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 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
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