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The theory of interaction between light and a cold atomic gas
Interaction processes between light and a condensate Dipole potential Light induced atom-atom interaction Atom density Refraction index of the condensate Local field effect Ight propagation
Interaction processes between light and a condensate Dipole potential Light induced atom-atom interaction Refraction index of the condensate Light propagation Atom density Local field effect
PHYSICAL REVIEW A VOLUME 59. NUMBER 2 FEBRUARY 1999 Local-field approach to the interaction of an ultracold dense bose gas with a light field (2+)的-的2一+6( (+)一”-一时-△++ (A+iy/2)r 方 (2m1+1-M+(2+Gx =ej(-+12-kd的 (△+p/2)dt'+ i(△+iy/2) -i(△+iy/2) v 当时间足够长,括号中第二项可忽略 (1-e4+p/2 i(△+iy/2) 得到通常的绝热近似结果 在上述近似基础上,采用迭代计算,可以证明余下的误差 (△+iy/2 可见在大失谐的情况下,余项可抛, 绝热近似成立与否与快光/慢光无关!
( ) ( ) ( ) ( ) 2 2 /2 /2 ' /2 /2 ' 2 ? ( ) 2 2 1 1 2 1 2 0 0 ˆ ˆ ˆ ˆ ˆ ' ( ) ' ˆ 2 2 t t i i t i i t i i t i i t e V kd e dt e G e dt m + − + + − + + = − + − + − + ( ) ( ) ( ) ( ) ( ) 1 2 ( ) 2 2 1 2 /2 /2 ' /2 /2 ' 2 ? 2 2 1 1 2 0 0 ˆ ˆ 2 ˆ ˆ ˆ ˆ 2 ' ( ) ' (1 ) ' ˆ ˆ 2 ( / 2) ( / 2) t t i i t i i t i i t i i t d G G dt e V kd e dt e e dt m i i i i + + + − + + − + − + − + = − + − + − − − + − + ( ) 1 2 ( /2) 2 ˆ ˆ ˆ 2 (1 ) ( / 2) i i t G e i i + + − + − − + 在上述近似基础上，采用迭代计算，可以证明余下的误差 2 1 ~ ( / 2) + i 当时间足够长，括号中第二项可忽略， 得到通常的绝热近似结果 可见在大失谐的情况下，余项可抛， 绝热近似成立与否与快光/慢光无关！ 1 ˆ 𝜙 2
PHYSICAL REVIEW A VOLUME 59, NUMBER 2 FEBRUARY 1999 Local-field approach to the interaction of an ultracold dense bose gas with a light field +1)1-2-02-22921+G1( t=(-2+)2-1-22-h(△+的12+(2 绝数消去 h22 r)2「h P(r, t)=x(r, tEmae(r, t) xii(rn), (r. v,(rn) avi(r,t)v1(r,t) X(r,t)= dr,)1(r,n) V×V×E(r,) 8丌 1aE(r,)4丌a2p(r,t) +3a的h 4丌 a vy
绝热消去
The light induced interaction between atoms have been emphasized in early research It's now widely accepeted that back influence of atomic density modification on the light propagation can be neglected in free space So far, two approaches have been applied to enhance the back influence effect One approach is to Another approach is to increase the density put an atomic gas in a cavity Sn Threee statistics and quantum tlucnntns an i Collect ve Atom kernel L ase CARLI gennum epee ef a Hose- nstein condensate chapped to a quantized light tel Cavity Opto- Mechanics with a Bose-Einstein Condensate Ferdinand Brennecke, Stephan Ritter, Tobias Donner, and Tilman Eswlinger
The light induced interaction between atoms have been emphasized in early research. It’s now widely accepeted that back influence of atomic density modification on the light propagation can be neglected in free space! 2 n So far, two approaches have been applied to enhance the back influence effect. One approach is to increase the density Another approach is to put an atomic gas in a cavity