Phase sensitivity of a Mach-Zehnder interferometer with single-intensity and difference-intensity detection

Interferometry is a widely used technique for precision measurements in both classical and quantum contexts. One way to increase the precision of phase measurements, for example, in a Mach-Zehnder interferometer (MZI), is to use high-intensity lasers. In this paper we study the phase sensitivity of a MZI in two detection setups (difference intensity detection and single-mode intensity detection) and for three input scenarios (coherent, double coherent, and coherent plus squeezed vacuum). For the coherent and double coherent input, both detection setups can reach the quantum Cramer-Rao bound, although at different values of the optimal phase shift. The double coherent input scenario has the unique advantage of changing the optimal phase shift by varying the input power ratio.