  Interferometers measure a wide variety of dynamic processes by converting a
phase change into an intensity change. Nonlinear interferometers, making use of
nonlinear media in lieu of beamsplitters, promise substantial improvement in
the quest to reach the ultimate sensitivity limits. Here we demonstrate a new
nonlinear interferometer utilizing a single parametric amplifier for mode
mixing---conceptually, a nonlinear version of the conventional Michelson
interferometer with its arms collapsed together. We observe up to 99.9\%
interference visibility and find evidence for noise reduction based on
phase-sensitive gain. Our configuration utilizes fewer components than previous
demonstrations and requires no active stabilization, offering new capabilities
for practical nonlinear interferometric-based sensors.
