The Boltzmann constant. ? is the reduced

TheDoppler cooling limitThe average of the force of the absorption of photons is the scattering forceand the random kick force resulting from spontaneous emissions. However, wehave not taken into account the effect of the fluctuations in these two processes.The random nature of both the absorption and emission of photons results aheating process, this heating process will be somewhat compensated for by theLASER cooling process (equilibrium between the two) and this is how we get thefinal temperature resulting from LASER cooling.

The random addition to theaverage momentum transfer produces a random walk of the atomic momentum and anincrease in the mean square atomic momentum. This heating is countered by thecooling force opposing the atomic motion. The force is proportional to thevelocity of the atoms. The rate at which energy is removed by cooling is F.

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vwhich is proportional to v2, so the cooling rate is proportional tothe kinetic energy of the atoms. While the heating rate, proportional to thetotal photon scattering rate, is independent of atomic kinetic energy at lowvelocities. As a result, the heating and cooling come to equilibrium at acertain value of the average kinetic energy. This defines the Doppler coolinglimit to be:TDopp=??/2KB?is the rate of spontaneous emission of the excited state.?-1 is the lifetime of the excited state.

KB is the Boltzmann constant.? is the reduced Planck constant.For sodiumTDopp= 240?k.The atomswere found to be much cooler than the Doppler limit (about 40?k).

 SummaryLASER cooling and trapping refers to a number of techniques used to cool atomsdown by decelerating them using light, and bringing them to a stop usingmagnetic fields. The reason we want to cool these neutral atoms, is to helpdevelop our understanding of the atomic spectra, improve atomic clocks, createultra-cold atoms which exhibit quantum mechanical behavior, so these cold atomscan help us expand our understanding of the quantum world, and if we dig deeperand cool them even more, we create a new state of matter, the Bose-Einsteincondensate which is a remarkable discovery and could help us understand manyphenomena in the universe. Not to mention the use of trapped ions in quantumcomputing -even though my paper is on the cooling of neutral atoms, but it isworth mentioning-. 

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