Phase sensitivity of two nonlinear interferometers with inputting entangled coherent states

We investigate the phase sensitivity of the SU（1,1） interfereometer [SU（1,1）I] and the modified Mach-Zehnder in- terferometer （MMZI） with the entangled coherent states （ECS） as inputs. We consider the ideal case and the situations in which the photon losses are taken into account. We find that, under ideal conditions, the phase sensitivity of both the MMZI and the SU（1,1）I can beat the shot-noise limit （SNL） and approach the Heisenberg limit （HL）. In the presence of photon losses, the ECS can beat the coherent and squeezed states as inputs in the SU（1,1）I, and the MMZI is more robust against internal photon losses than the SU（1,1）I.