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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.
[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 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 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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[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 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 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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