Efficient two-mode interferometers with spinor Bose-Einstein condensates

We consider general three-mode interferometers using a spin-1 atomic Bose-Einstein condensate with macroscopic magnetization. We show that these interferometers, combined with the measurement of the number of particles in each output port, provide an ultra-high phase sensitivity. We construct effective two-mode interferometers which involve two Zeeman modes showing that they also provide an ultra-high phase sensitivity but of a bit reduced factor in the corresponding Fisher information. A special case of zero magnetization is shown to persist the efficiency of the two-mode interferometry.