  We study the propagation of a weak probe field through an optomechanical
system in which $N$ nearly degenerate mechanical membranes are inside a
Febry-Perot cavity, and couple dispersively to an intracavity field. We derive
a general analytical expression for the output probe field. We show that the
in-phase quadrature of the output probe field can exhibit multiple
electromagnetically induced transparency with at most $N$ narrow transparency
windows. We find that the superluminal light can be achieved with at most $N$
different negative group velocities at the transparency windows. Moreover, by
using a time-dependent strong coupling pulse, we numerically simulate the
storage and retrieval of a weak Gaussian-shaped probe pulse in an optical
cavity with two nearly degenerate mechanical resonators.

Quantum Physics