Doppler cooling 2 Considerasingle 351% atom (mass 84,91 u )with kinetic energy EK = 10 ,where p is the momentum of 2m the atom. The kinetic energy of an atom reects the temperature of the system, so it is further assumed that the kinetic energy in this case is EK z kBT , where k; B is the Boltzmann constant and the temperature at the beginning is To =273 K a.) Suppose further that all motion, etc., takes place in one dimension. Solve the momentum p of the atom. b.) The momentum of an atom is very small so it is difcult to estimate its correctness. But atoms and molecules at room temperature move at a rate of the order of the speed of sound. At what speed do 85 Rb atoms move? c.) Assume that the atom moves directly toward the laser from which the wavelength of the incoming light is h A = 780,2 nm .Photons have momentum p L = , where h is the Planck constant. If the wavelength A (frequency) of the laser is appropriately resonant with the transition between the energy states of the atom, the atom can absorb the photon. How many photons are needed to stop one atom? For Doppler cooling to work, a similar laser is needed on the left side as well, with the atom between two opposite laser beams. Thus, as it moves toward the laser on the right, the atom absorbs the photons from the right, and as it moves to the left, it absorbs the photons from the left. That way the speed of the atom would slow down, no matter what direction it went. This is accomplished by utilizing the Doppler effect, as well as the quantication of the energy levels of the atom, i.e. the property that the atom can only absorb photons of a certain frequency. Assume that our 7802 nm laser above is exactly in resonance with the excitation state of some atom when the atom is at rest. If the atom is in motion, the frequency of the laser must be converted to the quantity A f . d.) Calculate the relative frequency transfer to the lasers to make the atom in the initial (thermal) state resonant. If an f atom moves to the right, how far is the equency of the laser beam coming from the left from the resonance of the atom? When the speed of an atom slows down, what needs to be done for the frequency tranfer Af