  We show that a dynamically evolving two-mode Bose-Einstein condensate (TBEC)
with an adiabatic, time-varying Raman coupling maps exactly onto a nonlinear
Ramsey interferometer that includes a nonlinear medium. Assuming a realistic
quantum state for the TBEC, namely the SU(2) coherent spin state, we find that
the measurement uncertainty of the ``path-difference'' phase shift scales as
the standard quantum limit (1/N^{1/2}) where N is the number of atoms, while
that for the interatomic scattering strength scales as 1/N^{7/5}, overcoming
the Heisenberg limit of 1/N.
