Abstract
We explore the behavior of the phonon number distribution in an heterogeneous linear ion crystal. The presence of ion species with different masses changes dramatically the transverse energy spectrum, in such a way that two eigenfrequencies become non-analytic functions of the mass ratio in the form of a sharp cusp. This non-analyticity induces a quantum phase transition between condensed and conducting phase of the transverse local phonons. In order to continuously vary the mass ratio we adiabatically modify a locally applied laser field, exerting optical dipole forces which reduces the effective mass.
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