In laser cooling and trapping, a beam of atoms traveling

Chapter , Problem 21

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In laser cooling and trapping, a beam of atoms traveling in one direction is slowed by interaction with an intense laser beam in the opposite direction. The photons scatter off the atoms by resonance absorption, a process by which the incident photon is absorbed by the atom, and a short time later a photon of equal energy is emitted in a random direction. The net result of a single such scattering event is a transfer of momentum to the atom in a direction opposite to the motion of the atom, followed by a second transfer of momentum to the atom in a random direction. Thus, during photon absorption the atom loses speed, but during photon emission the change in speed of the atom is, on average, zero (because the directions of the emitted photons are random). An analogy often made to this process is that of slowing down a bowling ball by bouncing ping-pong balls off of it. (a) Given that the typical photon energy used in these experiments is about 1 eV, and that the typical kinetic energy of an atom in the beam is the typical kinetic energy of the atoms in a gas that has a temperature of about 500 K (a typical temperature for an oven that produces an atomic beam), estimate the number of photonatom collisions that are required to bring an atom to rest. (The average kinetic energy of an atom is equal to where is the Boltzmann constant and T is the temperature. Use this to estimate the speed of the atoms.) (b) Compare the Part (a) result with the number of ping-pong ballbowling ball collisions that are required to bring the bowling ball to rest. (Assume the typical speed of the incident ping-pong balls are all equal to the initial speed of the bowling ball.) (c) is a type of atom often used during cooling experiments. The wavelength of the light resonant with the cooling transition of the atoms is Estimate the number of photons needed to slow down an atom from a typical thermal velocity of to a stop.