We introduce a new technique to probe the properties of an interacting cold atomic gas that can be viewed as a dynamical compressibility measurement. We apply this technique to the study of the superfluid to Mott insulator quantum phase transition in one and three dimensions for a bosonic gas trapped in an optical lattice. Excitations of the system are detected by time-of-flight measurements. The experimental data for the one-dimensional case are in good agreement with the results of a time-dependent density matrix renormalization group calculation.
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