Unstable spinor Bose-Einstein condensates are ideal candidates to create
nonlinear three-mode interferometers. Our analysis goes beyond the standard
SU(1,1) parametric approach and therefore provides the regime of parameters
where sub shot-noise sensitivities can be reached with respect to the input
total average number of particles. Decoherence due to particle losses and
finite detection efficiency are also considered.Comment: 5 pages, 4 figure