Adiabatic transfer of energy fluctuations between membranes inside an optical cavity

A scheme is presented for the adiabatic transfer of average fluctuations in the phonon number between two membranes in an optical cavity. We show that by driving the cavity modes with external time-delayed pulses, one can obtain an effect analogous to stimulated Raman adiabatic passage in the atomic systems. The adiabatic transfer of fluctuations from one membrane to the other is attained through a ``dark'' mode, which is robust against decay of the mediating cavity mode. The results are supported with analytical and numerical calculations with experimentally feasible parameters.