  Homodyne detection is often used for interferometers based on nonlinear
optical gain media. For the configuration of a seeded, 'truncated SU(1,1)'
interferometer Anderson et al. (Phys. Rev. A 95, 063843 (2017)) showed how to
optimize the homodyne detection scheme and demonstrated theoretically that it
can saturate the quantum Cramer-Rao bound for phase estimation. In this work we
extend those results by taking into account loss in the truncated SU(1,1)
interferometer and determining the optimized homodyne detection scheme for
phase measurement. Further, we build a truncated SU(1,1) interferometer and
experimentally demonstrate that this optimized scheme achieves a reduction in
noise level, corresponding to an enhanced potential phase sensitivity, compared
to a typical homodyne detection scheme for a two-mode squeezed state. In doing
so, we also demonstrate an improvement in the degree to which we can beat the
standard quantum limit with this device.
