Effects of dipolar interactions on the sensitivity of nonlinear spinor-BEC interterometry

We consider the effects of dipole-dipole interactions on a nonlinear interferometer with spin-1 Bose-Einstein condensates. Compared with the traditional atomic SU(1,1) interferometer, the shot-noise phase sensitivity can be beaten with respect to the input total average number of particles; and the improved sensitivity depends on the effective strength of the dipolar interaction via modifying the trapping geometry. It indicates that the best performance of the interferometer is achieved with highly oblate trap potential. The Bayesian phase estimation strategy is explored to extract the phase information. We show that the Cramér-Rao phase uncertainly bound can saturate, when the ideal dis-entangle scheme is applied. The phase average of the phase sensitivity is also discussed.