  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 $\ket{2_{s},0_{a}}$.
