# Theo2_Answer - THEORETICAL PROBLEM 2 SOLUTION DOPPLER LASER...

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THEORETICAL PROBLEM 2 SOLUTION DOPPLER LASER COOLING AND OPTICAL MOLASSES The key to this problem is the Doppler effect (to be precise, the longitudinal Doppler effect): The frequency of a monochromatic beam of light detected by an observer depends on its state of motion relative to the emitter, i.e. the observed frequency is c v c v c v 1 / 1 / 1 where v is the relative speed of emitter and observer and the frequency of the emitter. The upper-lower signs correspond, respectively, when source and observer move towards or away from each other. The second equality holds in the limit of low velocities (non-relativistic limit). The frequency of the laser in the lab is L ; 0 is the transition frequency of the atom; the atom moves with speed v towards the incident direction of the laser: It is important to point out that the results must be given to first significant order in v / c or mv q / . PART I: BASICS OF LASER COOLING 1. Absorption. 1a Write down the resonance condition for the absorption of the photon. c v L 1 0 0.2 1b Write down the momentum p at of the atom after absorption, as seen in the laboratory c mv q p p L at 0.2 1c Write down the energy at of the atom after absorption, as seen in the laboratory L at at mv m p 2 2 2 0 2 0.2

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2. Spontaneous emission in the x direction. First, one calculates the energy of the emitted photon, as seen in the lab reference frame. One must be careful to keep the correct order; this is because the velocity of the atom changes after the absorption, however, this is second order correction for the emitted frequency: m q v v c v ph with 1 0 thus, L L L L ph c v mv q mc q mc q c v c v mc q c v 1
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Theo2_Answer - THEORETICAL PROBLEM 2 SOLUTION DOPPLER LASER...

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