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homework4 - 1 Problem set 4 The harmonic oscillator Due Oct...

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1 Problem set 4 - The harmonic oscillator Due: Oct. 10, 2011, in class Posted on Oct. 3, 2011 1. Typical scales in harmonic oscillators. Modern cold-atoms research concentrates on trapped atoms, which are futher constrained to move in an optical lattice. (a) Consider Rb atoms (atomic mass: 85.4678amu) that are placed in a parabolic Magneto-optical well. In order to get a ground state for the atoms which is confined to length scale L 100 μm , what should be the curvature (i.e., the spring constant) of confining potential? (b) What is the gap for excitations above the ground state? Express your answer in Joules and then convert to Kelvin (using k B = 1 . 38 · 10 - 23 J/K ). (c) To simulate a lattice, the atoms are trapped into a standing wave pattern produced by a red laser with wavelength λ = 780 nm . The atoms congregate in the minima of the standing wave pattern. In order to localize each atom in a space of size of roughly 1 / 10th of the lattice periodicity, what should be the effective spring constant produced by the light field?
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