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 $|F=1,m=\pm 1⟩$ 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 ${}^{23}\mathrm{Na}$ 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%.

• Atom interferometry
• Entanglement in quantum gases
• Spinor Bose-Einstein condensates
• Quantum Monte Carlo