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解析求解了包含色散、损耗和抽运吃空的含时的Fokker-Planck方程，通过数值计算首先获得了色散时简并参量放大(DOPA)系统的光压缩特性.研究结果表明：色散效应是由非线性极化率从χ″增大到χ″/{1+σ2/}/+2而引起的.随着色散效应的逐渐增大，压缩曲线的形状基本相同，且整体向左收缩，最大压缩趋近于线性理论的结果1/(1+μ).还获得了色散时非简并参量放大(NOPA)系统的光纠缠特性.研究发现：当σ给定，随着抽运参数μ的增大，相应的相位变化也增大，非线性极化率的极性发生多次变化，极性为正阶段的增益大部分被极性为负阶段的衰减所抵消，净增益不大，压缩也不大，最小均方差V1的值逐渐减小，且整体向右移动，接近于线性理论的结果1/(1+μ).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 物理学报 57 3514］
[23] ］Ye C G, Zhang J 2008 Acta Phys.Sin. 57 6962 (in Chinese) ［叶晨光、 张靖 2008 物理学报 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 物理学报 57 3514］
[23] ］Ye C G, Zhang J 2008 Acta Phys.Sin. 57 6962 (in Chinese) ［叶晨光、 张靖 2008 物理学报 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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