  Stimulated Raman adiabatic passage (STIRAP) describes adiabatic population
transfer between two states coherently coupled via a mediating state that
remains unoccupied. This renders STIRAP robust against loss in the mediating
state, leading to profound applications in atomic- and molecular-beam research,
trapped-ion physics, superconducting circuits, other solid-state systems,
optics, in entanglement generation and qubit operations. STIRAP in
optomechanics has been considered for optical frequency conversion where a
mechanical mode provides the mediating state. Given the advances of
optomechanical devices with exceptionally high mechanical-quality factors,
STIRAP between mechanical modes has the prospect of generating macroscopic
quantum superposition and of supporting quantum information protocols. An
optical cavity mode can mediate the coupling between mechanical modes, without
detrimental effects of optical losses. We demonstrate STIRAP between two
mechanical modes of a phononic membrane-in-the-middle system with an efficiency
of 86% and immune against photon loss through the mediating optical cavity.
