By adding a large inductance in a dc-SQUID phase qubit loop, one decouples the junctions dynamics and creates a superconducting artificial atom with two internal degrees of freedom. In addition to the usual symmetric plasma mode ({it s}-mode) which gives rise to the phase qubit, an anti-symmetric mode ({it a}-mode) appears. These two modes can be described by two anharmonic oscillators with eigenstates $ket{n_{s}}$ and $ket{n_{a}}$ for the {it s} and {it a}-mode, respectively. We show that a strong nonlinear coupling between the modes leads to a large energy splitting between states $ket{0_{s},1_{a}}$ and $ket{2_{s},0_{a}}$. Finally, coherent frequency conversion is observed via free oscillations between the states $ket{0_{s},1_{a}}$ and $ket{2_{s},0_{a}}$.
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