  We explore the extent to which two quantum oscillators can exchange their
quantum states efficiently through a three-level system which can be spin
levels of colored centers in solids. High transition probabilities are obtained
using Hamiltonian engineering and quantum control techniques. Starting from a
weak coupling approximation, we derive conditions on the spin-oscillator
interaction Hamiltonian that enable a high-fidelity exchange of quanta. We find
that these conditions cannot be fulfilled for arbitrary spin-oscillator
coupling. To overcome this limitation, we illustrate how a time-dependent
control field applied to the three-level system can lead to an effective
dynamic that performs the desired exchange of excitation. In the (ultra) strong
coupling regime, an important loss of fidelity is induced by the dispersion of
the excitation onto many Fock states of the oscillators. We show that this
detrimental effect can be substantially reduced by suitable control fields,
which are computed with optimal control numerical algorithms.
