Coherent frequency conversion in a superconducting artificial atom with two internal degrees of freedom

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