Threedimensional Cooling of Atoms Optical Mollasses

For a Lorentzian absorption profile with FHWM y, the frequency dependence of the absorption rate is (Fig. 14.13) 

An atom moving within the overlap region of the six running laser waves therefore experiences a force F/(u/) = —avi i =x,y z) that damps its velocity. From the relation du/dr = F/m = Av/v = —aim At we obtain the time-dependent velocity 

The velocity decreases exponentially with a damping time tY = mla, 

The dotted curve shows the absorption profiles by a single atom moving with Vx = //A for a single laser beam propagating into the jc-direction 

Note These optical trapping methods reduce the velocity components (vx. Vy,Vz) to a small interval around u = 0. However, they do not compress the atoms into a spatial volume, except if the dispersion force for the field gradients V/ 7 0 is sufficiently strong. 

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