Abstract
We construct the exact time dependent density profile for a superposition of the ground and singly excited states of a harmonically trapped one dimensional Bose gas in the limit of strongly interacting particles, the Tonks-Girardeau gas. We obtain analytic results that allows one to determine the number of particles in the gas, as well as the quantum amplitudes in the superposition, from measurement results in an off-resonant light scattering experiment.
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