  We describe how electromagnetically induced transparency can arise in
quadratically coupled optomechanical systems. Due to quadratic coupling the
underlying optical process involves a two phonon process in optomechanical
system and this two phonon process makes the mean amplitude, which plays the
role of atomic coherence in traditional EIT, zero. We show how the fluctuation
in displacement can play a role similar to atomic coherence and can lead to
EIT-like effects in quadratically coupled optomechanical systems. We show how
such effects can be studied using the existing optomechanical systems.
