文档介绍：>>=ΨΨ??||Htih|Ψ1>|Ψ2>E1E2hω0= E2-E1H=H0+Hc+Hr>>=Ψ>Ψ>=Ψ?)(|e|,||i0rntEnnnnHti???hhH0|?n>=En|?n>,(n=1,2)Hc:系统与相干光场的相互作用,波函数无定态解()titiceeHωω?+??=Eμ21()teetitiωωωcos21EE=+?|Ψ > = ∑j aj(t)|Ψj>= a1(t)|Ψ1> +a2(t)|Ψ2>]ee[2*idd]ee[2idd)(i)(i12)(i)(i210000ttttataataωωωωωωωωκκ??++??+=+=hhh1202112*EEEE?===ωμκμκ旋转波近似旋转波近似((RWA)RWA)??22=(=(ωω--ωω00))22+|+|κκ||22)2sin(e*i)()]2sin()(i)2[cos(e)()(20)(102i02ittatttatt??κ??ωω?ωωωω???=??=)2(sin)()()(|)(|22*2222ttatata??κ==)2(sin)(1|)(|2221tta??κ?=-2 -1 0 1 |a2(t)|2|a1(t)|2?t/π|aj(t)|2受激辐射>吸收原子系统向相干场提供能量吸收>受激辐射相干场向原子系统提供能量2121<<?π?t2321<<π?t-1/2 1/2 3/2拉比拉比(Rabi)(Rabi)振荡振荡,拉比频率拉比频率>>=∑nnnc?Ψ||∑∑>=<=>ΨΨ>=<<,*,*||||??AAA密度矩阵密度矩阵ρρhtiEnnneac?=????????=?****22i12i211100aaeaaeaaaattωωρHHHtiρρρρ?==],[ddh)ee)((2d,)ee)((2dd,)ee)((2dd),)((21221220211122210121**********tititititititititdititieedtdiωωωωωωωωρρκρωρρρκρωρρρκρρρκρ????+?=++?=?+??=+??=titititititititiedtdiedtdieeeeeeωωωωωωωωωσσρσσρρσρσρρσσρσ12121212211221212112122112211212;*;?=?=?=====???则:令:).()1e)((2dd),()e1)((2dd],ee)[(d)(d0212112221012211221222121221121122ωωσρρκσωωσρρκσσσσσκρρωωωω?++??=??+?=?+?=???iitiitittitititivtwwutvvtuκκΔΔ?=+=?=dddddd()()( )ωωρρσσσσσσ?=Δ?=??==+==011222**********Im2Re2wivu??????????=?????????????????????ΔΔ?=??????????wvuwvuwvut?00000ddκκ二阶反对称张量Ω可写为赝矢量Ω=(-κ,0,Δ)Ω在u w平面内,随着u v w 坐标系绕着w 轴转动Bloch矢量r= (u,v,w)r?r×=tdduvw-,dd,dd122TwwvtwTvwutvTuvtueq???=?+=??=κκΔΔ纵向弛豫时间横向弛豫时间u,v,w u,v,w 的物理意义的物理意义w=ρ22-ρ11上下能级的布居差,反转(Inversion)u,v系统的总极化强度:()()()titieivueivuTrωωμμρμρμρμμ??++=+==12212**********ivuNP+∝=μ单个原子感应偶极矩的平均值::此时N个原子只有一种跃迁频率ω0!因此,u和v与原子的感应偶极矩有关Laplace变换OBE代数方程解反变换Optical Bloch EquationLaplaceLaplace变换变换[]dtetftfsst∫∞?==0)()()(LF)],([)(1stfFL?=0s/(s2+ω2)cos(ωt)30ω/(s2+ω2)sin(ωt)20C/sC1s>F(s)f(t).dd,dd,dd122TwwvtwTvwutvTuvtueq???=?+Δ=?Δ?=κκ1010202?)1(???)1(???)1(sT+=++=?++Δ?=Δ++κκLaplace);0()(])([fssdttdf?=FL微分的Laplace变换????????????????++????????++????????+????????+????????+????????+????????+