  We consider a cavity optomechanical cooling configuration consisting of a
mechanical resonator (denoted as resonator b) and an electromagnetic resonator
(denoted as resonator a), which are coupled in such a way that the effective
resonance frequency of resonator a depends linearly on the displacement of
resonator b. We study whether back-reaction effects in such a configuration can
be efficiently employed for suppression of decoherence. To that end, we
consider the case where the mechanical resonator is prepared in a superposition
of two coherent states and evaluate the rate of decoherence. We find that no
significant suppression of decoherence is achievable when resonator a is
assumed to have a linear response. On the other hand, when resonator a exhibits
Kerr nonlinearity and/or nonlinear damping the decoherence rate can be made
much smaller than the equilibrium value provided that the parameters that
characterize these nonlinearities can be tuned close to some specified optimum
values.
