  The precise estimation of the gravitational acceleration is important for
various disciplines. We consider making such an estimation using quantum
optics. A Mach-Zehnder interferometer in an "optical fountain" type arrangement
is considered and used to define a standard quantum limit for estimating the
gravitational acceleration. We use an approach based on quantum field theory on
a curved, Schwarzschild metric background to calculate the coupling between the
gravitational field and the optical signal. The analysis is extended to include
the injection of a squeezed vacuum to the Mach-Zehnder arrangement and also to
consider an active, two-mode SU(1,1) interferometer in a similar arrangement.
When detection loss is larger than $8\%$, the SU(1,1) interferometer shows an
advantage over the MZ interferometer with single-mode squeezing input. The
proposed system is based on current technology and could be used to examine the
intersection of quantum theory and general relativity as well as for possible
applications.
