Phase sensitivity of a three-mode nonlinear interferometer

In this paper, we construct the input–output relationships of a three-mode nonlinear beam splitter (TNBS) mathematically, and a set of special solutions for the input–output equations are given. By combining two TNBSs and a phase shifter, we propose a scheme for a three-mode nonlinear interferometer (TNI) and give the input–output expression of the whole TNI. Then, we study the phase sensitivity of the TNI by giving input states and detection scheme. In addition, we also calculate the phase sensitivity of a Mach–Zehnder interferometer (MZI), SU(1,1) interferometer (SU(1,1)I) and modified Mach–Zehnder interferometer (MMZI), and we discuss the relationships of phase sensitivity between the MZI, SU(1,1)I, MMZI and TNI. Finally, in the presence of photon losses, we discuss the phase sensitivity of the four different interferometers and make detailed comparisons. It is shown that the TNI has the best robustness against photon losses under certain conditions with the same parameters.