  We analyse a nonlinear interferometer, also known as an SU(1,1)
interferometer, in the presence of internal losses and inefficient detectors.
To overcome these limitations, we consider the effect of seeding one of the
interferometer input modes with either a number state or a coherent state. We
derive analytical expressions for the interference visibility, contrast, phase
sensitivity, and signal-to-noise ratio, and show a significant enhancement in
all these quantities as a function of the seeding photon number. For example,
we predict that, even in the presence of substantial losses and highly
inefficient detectors, we can achieve the same quantum-limited phase
sensitivity of an unseeded nonlinear interferometer by seeding with a few tens
of photons. Furthermore, we observe no difference between a number or a
coherent seeding state when the interferometer operates in the low-gain regime,
which enables seeding with an attenuated laser. Our results expand the
nonlinear interferometry capabilities in the field of quantum imaging,
metrology, and spectroscopy under realistic experimental conditions.
