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Unformatted text preview: THEORETICAL PROBLEM 2 DOPPLER LASER COOLING AND OPTICAL MOLASSES The purpose of this problem is to develop a simple theory to understand the so-called “laser cooling” and “optical molasses” phenomena. This refers to the cooling of a beam of neutral atoms, typically alkaline, by counterpropagating laser beams with the same frequency. This is part of the Physics Nobel Prize awarded to S. Chu, P. Phillips and C. Cohen-Tannoudji in 1997. The image above shows sodium atoms (the bright spot in the center) trapped at the intersection of three orthogonal pairs of opposing laser beams. The trapping region is called “optical molasses” because the dissipative optical force resembles the viscous drag on a body moving through molasses. In this problem you will analyze the basic phenomenon of the interaction between a photon incident on an atom and the basis of the dissipative mechanism in one dimension. PART I: BASICS OF LASER COOLING Consider an atom of mass m moving in the + x direction with velocity v . For simplicity, we shall consider the problem to be one-dimensional, namely, we shall ignore the y and z directions (see figure 1). The atom has two internal energy levels. The energy of the lowest state is considered to be zero and the energy of the excited state to be h ϖ , where π 2 / h = h . The atom is initially in the lowest state. A laser beam with frequency ϖ L in the laboratory is directed in the - x direction and it is incident on the atom. Quantum mechanically the laser is composed of a large number of photons, each with energy h ϖ L and momentum - h q . A photon can be absorbed by the atom and later spontaneously emitted; this emission can occur with equal probabilities along the + x and - x directions. Since the atom moves at non-relativistic speeds, v / c << 1 (with c the speed of light) keep terms up to first order in this quantity only. Consider also 1 / << mv q h , namely, that the momentum of the atom is much larger than the momentum of a single photon. In writing your answers, keep only corrections linear in either of the above quantities....
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This note was uploaded on 11/08/2011 for the course PHYS 0000 taught by Professor Na during the Spring '11 term at Rensselaer Polytechnic Institute.
- Spring '11