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In this paper, we first find out the analytic solution of the time-dependent Fokker-Planck equation of the non-degenerate optical parametric amplification (NOPA) system under the consideration of the dispersion, the loss and the pump depletion effects. Then, through the numerical calculation, we obtain the squeezing characteristic of the degenerate optical parametric amplification (DOPA) system with dispersion. the research indicates: the dispersion effect stems from the nonlinear susceptibility change from χ″ toχ″/{1+σ2/}/+2, with the increasing of the dispersion effect, the general feature of the squeezing curves beeps unchanged, and the curves contract toward left. The maximum squeezing approaches to the linear theory 1/(1+μ). Finally, we obtain the entanglement characteristic of the NOPA system with dispersion. We find out when σ is given, with the increasing of pump parameter μ, he corresponding phase makes a large change. The nonlinear susceptibility changes many times. When the polarity is positive, the system obtains the gain, when the polarity is negative, the system suffers the loss, but the gain is mainly dissipated by the loss, so the net gain is small, the squeezing is also small. The minimum variance V1 reduces gradually, and the whole curve moves to the right, approaches to the linear theory 1/(1+μ).
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Keywords:
- dispersion /
- quantum fluctuation /
- optical parametric amplification
[1] ［1］Braunstein S L, Loock P V 2005 Rev. Mod. Phys. 77 513
[2] ［2］Furusawa A, Srensen J L, Braunstein S L, Fuchs C A, Kimble H J, Polzik E S 1998 Science 282 706
[3] ［3］Li X, Pan Q, Jing J, Zhang J, Xie C, Peng K 2002 Phys. Rev. Lett. 88 047904
[4] ［4］Zhang J, Xie C D, Peng K C 2003 Europhys. Lett. 61 579
[5] ［5］Takeno Y, Yukawa M, Yonezawa H, Furusawa A 2007 Opt. Express 15 4321
[6] ［6］Vahlbruch H, Mehmet M, Chelkowski S, Hage B, Franzen A, Lastzka N, Goβler S, Danzmann K, Schnabel R 2008 Phys. Rev. Lett. 100 033602
[7] ［7］Hétet G, Glckl O, Pilypas K A, Harb C C, Buchler B C, Bachor H A, Lam P K 2007 J. Phys. B: At. Mol. Opt. Phys. 40 221
[8] ［8］Kim C, Kumar P 1994 Phys. Rev. Lett. 73 1605
[9] ［9］Hirano T, Kotani K, Ishibashi T, Okude S, Kuwamoto T 2005 Opt. Lett. 30 1722
[10] ］Eto Y, Tajima T, Zhang Y, Hirano T 2007 Opt. Lett. 32 1698
[11] ］Yu C X, Haus H A, Ippen E P 2001 Opt. Lett. 26 669
[12] ］Werner M J, Raymer M G, Beck M, Drummond P D 1995 Phys. Rev. A 52 4202
[13] ］Wenger J, Tualie-Brouri R, Grangier P 2004 Opt. Lett. 29 1267
[14] ］Takahashi Y, Soderholm J, Hirano K, Namekata N, Machida S, Mori S, Kurimura S, Komatsu S, Inoue S 2008 Phys. Rev. A 77 043801
[15] ］Golubeva T, Ivanov D, Golubev Yu 2008 Phys. Rev. A 77 052316
[16] ］Zhao C Y, Tan W H 2006 J. Mod. Opt. 53 1965
[17] ］Zhao C Y, Tan W H 2006 J. Opt. Soc. Am. B 23 2174
[18] ］Zhao C Y, Tan W H 2007 J. Mod. Opt. 54 97
[19] ］Zhao C Y, Tan W H 2007 Chin. Phys. 16 1009
[20] ］Walls D F, Milburn G J 1994 Quantum Opt. (2nd Ed.) (NewYork: Springer) p178
[21] ］Reid M D, Drummond P D 1989 Phys. Rev. A 40 4493
[22] ］Shang Y N, Wang D, Yan Z H, Wang W Z,Jia X J, Peng K C 2008 Acta Phys.Sin. 57 3514 (in Chinese) ［商娅娜、 王东、 闫智辉、 王文哲、 贾晓军、 彭堃墀 2008 57 3514］
[23] ］Ye C G, Zhang J 2008 Acta Phys.Sin. 57 6962 (in Chinese) ［叶晨光、 张靖 2008 57 6962］
[24] ］Kuang M H, Ma S J, Liu D M, Wang S J 2009 Chin. Phys. B 18 1065
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[1] ［1］Braunstein S L, Loock P V 2005 Rev. Mod. Phys. 77 513
[2] ［2］Furusawa A, Srensen J L, Braunstein S L, Fuchs C A, Kimble H J, Polzik E S 1998 Science 282 706
[3] ［3］Li X, Pan Q, Jing J, Zhang J, Xie C, Peng K 2002 Phys. Rev. Lett. 88 047904
[4] ［4］Zhang J, Xie C D, Peng K C 2003 Europhys. Lett. 61 579
[5] ［5］Takeno Y, Yukawa M, Yonezawa H, Furusawa A 2007 Opt. Express 15 4321
[6] ［6］Vahlbruch H, Mehmet M, Chelkowski S, Hage B, Franzen A, Lastzka N, Goβler S, Danzmann K, Schnabel R 2008 Phys. Rev. Lett. 100 033602
[7] ［7］Hétet G, Glckl O, Pilypas K A, Harb C C, Buchler B C, Bachor H A, Lam P K 2007 J. Phys. B: At. Mol. Opt. Phys. 40 221
[8] ［8］Kim C, Kumar P 1994 Phys. Rev. Lett. 73 1605
[9] ［9］Hirano T, Kotani K, Ishibashi T, Okude S, Kuwamoto T 2005 Opt. Lett. 30 1722
[10] ］Eto Y, Tajima T, Zhang Y, Hirano T 2007 Opt. Lett. 32 1698
[11] ］Yu C X, Haus H A, Ippen E P 2001 Opt. Lett. 26 669
[12] ］Werner M J, Raymer M G, Beck M, Drummond P D 1995 Phys. Rev. A 52 4202
[13] ］Wenger J, Tualie-Brouri R, Grangier P 2004 Opt. Lett. 29 1267
[14] ］Takahashi Y, Soderholm J, Hirano K, Namekata N, Machida S, Mori S, Kurimura S, Komatsu S, Inoue S 2008 Phys. Rev. A 77 043801
[15] ］Golubeva T, Ivanov D, Golubev Yu 2008 Phys. Rev. A 77 052316
[16] ］Zhao C Y, Tan W H 2006 J. Mod. Opt. 53 1965
[17] ］Zhao C Y, Tan W H 2006 J. Opt. Soc. Am. B 23 2174
[18] ］Zhao C Y, Tan W H 2007 J. Mod. Opt. 54 97
[19] ］Zhao C Y, Tan W H 2007 Chin. Phys. 16 1009
[20] ］Walls D F, Milburn G J 1994 Quantum Opt. (2nd Ed.) (NewYork: Springer) p178
[21] ］Reid M D, Drummond P D 1989 Phys. Rev. A 40 4493
[22] ］Shang Y N, Wang D, Yan Z H, Wang W Z,Jia X J, Peng K C 2008 Acta Phys.Sin. 57 3514 (in Chinese) ［商娅娜、 王东、 闫智辉、 王文哲、 贾晓军、 彭堃墀 2008 57 3514］
[23] ］Ye C G, Zhang J 2008 Acta Phys.Sin. 57 6962 (in Chinese) ［叶晨光、 张靖 2008 57 6962］
[24] ］Kuang M H, Ma S J, Liu D M, Wang S J 2009 Chin. Phys. B 18 1065
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