Optical Cooling by Resonance Photon Recoil

Assume a single two-level atom moving through a laser beam with a frequency 0) tuned into resonance with the atomic transition Ej. During its transit time T through the laser beam the atom may absorb and reradiate a photon many times before it leaves the interaction zone. For sufficiently strong laser intensities the number n of absorption-emission cycles may reach the limit n = T/t set by the spontaenous lifetime t of the upper level Ej.  

Since the emission of spontaneous photons occurs randomly distributed over all directions, the average momentum experienced by the atom due to recoil of the spontaneously emitted photons approaches zero for n The recoil due to absorption of photons, however, does not average to zero but accumulates for successive absorptions, since the absorbed photons all come from the same direction (Fig.13.9). 

If the initial velocity v of the atom is opposite to the light propagationk (v ii 0), y decreases for each absorption by an amount 

1) For a sodium atom with M = 23 AMU which absorbs photons on the 3S 3P transition with Ho) 2 eV, (13.18) yields av = 3 cm/s. This implies that 

2) For magnesium atoms absorbing photons on the singlet resonance line at 

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