Abstract
Interacting particles in a harmonic trap are known to possess a radial collective oscillation---the breathing mode (BM). We show that a quantum system has two BMs and analyze their properties by exactly solving the time-dependent Schr\"odinger equation. We report that the frequency of one BM changes with system dimensionality, the particle spin and the strength of the pair interaction and propose a scheme that gives direct access to key properties of trapped particles, including their many-body effects.
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