  The SU(1,1) interferometer was originally conceived as a Mach-Zehnder
interferometer with the beam-splitters replaced by parametric amplifiers. The
parametric amplifiers produce states with correlations that result in enhanced
phase sensitivity. $F=1$ spinor Bose-Einstein condensates (BECs) can serve as
the parametric amplifiers for an atomic version of such an interferometer by
collisionally producing entangled pairs of $\left<F=1,m=\pm1\right|$ atoms. We
simulate the effect of single and double-sided seeding of the inputs to the
amplifier using the truncated-Wigner approximation. We find that single-sided
seeding degrades the performance of the interferometer exactly at the phase the
unseeded interferometer should operate the best. Double-sided seeding results
in a phase-sensitive amplifier, where the maximal sensitivity is a function of
the phase relationship between the input states of the amplifier. In both
single and double-sided seeding we find there exists an optimal phase shift
that achieves sensitivity beyond the standard quantum limit. Experimentally, we
demonstrate a spinor phase-sensitive amplifier using a BEC of $^{23}$Na in an
optical dipole trap. This configuration could be used as an input to such an
interferometer. We are able to control the initial phase of the double-seeded
amplifier, and demonstrate sensitivity to initial population fractions as small
as 0.1\%.
