  An open question in experimental physics is the characterization of
gravitational effects in quantum regimes. We propose an experimental set-up
that uses well-tested techniques in cavity optomechanics to observe the effects
of the gravitational interaction between two micro-mechanical oscillators on
the interference of the cavity photons through the shifts in the visibility of
interfering photons. The gravitational coupling leads to a shift in the period
and magnitude of the visibility whose observability is within reach of current
technology. We discuss the feasibility of the set-up as well as the effects on
entanglement due to gravitational interaction.
