Heisenberg-limited Kerr phase estimation with coherent and squeezed vacuum states

Two-path interferometry with coherent and squeezed vacuum states is a feasible approach for estimating linear phase shifts. In view of excellent performance demonstrated previously, it is expected to be applied to the next generation of gravitational wave detection. In this paper, we extend this configuration to nonlinear Kerr phase estimation. We analytically investigate the phase sensitivity and the optimal input ratio of such states. It is shown that the optimal phase sensitivity surpasses the Kerr-type Heisenberg limit by a factor greater than 2. We also study the effects of photon losses on the phase sensitivity. The phase sensitivity can outperform the shot-noise limit when the lossy rate is less than 2/3. It turns out that our scheme has the advantages of high precision and strong loss tolerance.