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Chin. Phys. B, 2011, Vol. 20(6): 060303    DOI: 10.1088/1674-1056/20/6/060303
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A new theorem relating quantum tomogram to the Fresnel operator

Xie Chuan-Mei (谢传梅)ab, Fan Hong-Yi (范洪义)b
a College of Physics & Material Science, Anhui University, Hefei 230039, China; b Department of Material Science and Engineering, University of Science and Technology of China, Hefei 230026, China
Abstract  According to Fan-Hu's formalism (Fan Hong-Yi and Hu Li-Yun 2009 Opt. Commun.  282 3734) that the tomogram of quantum states can be considered as the module-square of the state wave function in the intermediate coordinate-momentum representation which is just the eigenvector of the Fresnel quadrature phase, we derive a new theorem for calculating quantum tomogram of density operator, i.e., the tomogram of a density operator ρ is equal to the marginal integration of the classical Weyl correspondence function of F+ρF, where F is the Fresnel operator. Applications of this theorem to evaluating the tomogram of optical chaotic field and squeezed chaotic optical field are presented.
Keywords:  quantum tomogram      Fresnel operator      Weyl correspondence  
Received:  29 June 2010      Revised:  07 March 2011      Accepted manuscript online: 
PACS:  03.65.Wj (State reconstruction, quantum tomography)  
  42.50.-p (Quantum optics)  
  03.65.-w (Quantum mechanics)  
Fund: Project supported by the Doctoral Scientiˉc Research Startup Fund of Anhui University, China (Grant No. 33190059) and the National Natural Science Foundation of China (Grant No. 10874174).

Cite this article: 

Xie Chuan-Mei (谢传梅), Fan Hong-Yi (范洪义) A new theorem relating quantum tomogram to the Fresnel operator 2011 Chin. Phys. B 20 060303

[1] Vogel K and Risken H 1989 Phys. Rev. 40 2847 2Wünsche A 1997 J. Mod. Opt. 44 2293 3Wünsche A 1996 Phys. Rev. A 54 5291 4Wigner E 1932 Phys. Rev. 40 749 5O'Connell R F and Winger E P 1981 Phys. Lett. A 321 145 6Agawal G S and Wolf E 1972 Phys. Rev. D 2 2161 7Agawal G S and Wolf E 1972 Phys. Rev. D 2 2187 8Agawal G S and Wolf E 1972 Phys. Rev. D 2 2206 9Hillery M, O'Connell R F, Scully M O and Wigner E P 1984 Phys. Rep. 106 121 10Hu L Y and Fan H Y 2009 Chin. Phys. B 18 4657 11Yao X W, Zeng B R, Liu Q, Mu X Y, Lin X C, Yang C, Pan J and Chen Z 2010 Acta Phys. Sin. 59 6837 (in Chinese) 12Liang B L, Wang J S, Meng X G and Su J 2010 Chin. Phys. B 19 010315 13Vogel W and Schleich W P 1991 Phys. Rev. A 44 7642 14Leonhardt U 1997 Measuring the Quantum State of Light (New York: Cambridge University Press) 15Aspelmeyer M 2009 Nature Phys. 5 11 16Chuang I L and Nielson M A J 1997 Mod. Opt. 44 2455 17Schleich W P 2000 Quantum Optics in Phase Space (Berlin: Wiley-VCH) 18Mancini S, Manko V I and Tombesi P 1995 Quantum Semiclass. Opt. 7 615 19De Nicola S, Fedele R, Man'ko M A and Man'ko V I 2005 Theor. Math. Phys. 144 1206 20Man'ko V I, Marmo G, Simoni A and Ventriglia F 2009 Phys. Scr. 79 065013 21Dirac M P A 1958 The Principle of Quantum Mechanics (Oxford: Oxford University Press) 22Fan H Y and Hu L Y 2009 Opt. Commun. 282 3734 23Fan H Y and Lu H L 2006 Opt. Commun. 258 51 24Fan H Y and Lu H L 2005 Phys. Lett. A 334 132 25Fan H Y and Hu L Y 2009 Chin. Phys. B 18 611 26Chen J H and Fan H Y 2009 Chin. Phys. B 18 3714 27Fan H Y and Zaidi H R 1987 Phys. Lett. A 124 303 28Goodman J W 1972 Introduction to Fourier Optics (NewYork: McGraw-Hill) 29Weyl H 1927 Z. Phys. 46 1 30Fan H Y 2008 Ann. Phys. 323 500 31Fan H Y 1992 J. Phys. A: Math. Gen. 25 3443 32DAriano G M, Rassetti M G, Atriel J K and Solomon A I 1989 Squeezed and Nonclassical Light (New York: Plenum) 33Buzek V 1990 J. Mod. Opt. 37 303 34Loudon R and Knight P L 1987 J. Mod. Opt. 34 709 35Dodonov V V 2002 J. Opt. B: Quantum Semiclass. Opt. 4 1
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