  In a recent publication [Y.D. Wang and A.A. Clerk, Phys. Rev. Lett. 108,
153603 (2012)], we demonstrated that one can use interference to significantly
increase the fidelity of state transfer between two electromagnetic cavities
coupled to a common mechanical resonator over a naive sequential-transfer
scheme based on two swap operations. This involved making use of a delocalized
electromagnetic mode which is decoupled from the mechanical resonator, a
so-called "mechanically-dark" mode. Here, we demonstrate the existence of a new
"hybrid" state transfer scheme which incorporates the best elements of the
dark-mode scheme (protection against mechanical dissipation) and the
double-swap scheme (fast operation time). Importantly, this new scheme also
does not require the mechanical resonator to be prepared initially in its
ground state. We also provide additional details on the previously-described
interference-enhanced transfer schemes, and provide an enhanced discussion of
how the interference physics here is intimately related to the optomechanical
analogue of electromagnetically-induced transparency (EIT). We also compare the
various transfer schemes over a wide range of relevant experimental parameters,
producing a "phase diagram" showing the the optimal transfer scheme for
different points in parameter space.

Mesoscale and Nanoscale Physics;Quantum Physics