Phase sensitivity of a modified Grover-Michelson interferometer

Power recycling techniques are usually used to improve the phase sensitivity of interferometers by reusing the input light energy, and can beat the shot noise level. Recent studies have demonstrated that the phase sensitivity of the interferometer is significantly improved via the addition of a recycling cavity, that is, coupling the interferometer with an external optical device. This study reviewed such types of interferometers named Grover-Michelson interferometers (GMI), and discusses their phase sensitivity with coherent states as inputs. Subsequently, a detailed comparison in terms of the scale of 1/ N and the standard quantum limit (SQL) is presented. The results demonstrate that the phase sensitivity of GMI improved owing to the power recycling and exceeded the value of 1/ N . Further, we proposed a modified Grover-Michelson interferometer (MGMI) with two input ports and examined its phase sensitivity with single photon or coherent states, respectively. Finally, in the presence of photon losses, we investigated the phase sensitivity of the four different interferometers, including MGMI, GMI, Mach-Zehnder interferometer (MZI), and SU(1,1) interferometer (SU(1,1)I), and conducted detailed comparisons. The results of this study indicated that the phase sensitivity of MGMI significantly improved owing to the increase in input energy, and MGMI exhibited the strongest robustness against photon number loss. These theoretical results are expected to facilitate improvements in interferometers and the detection of weak signals.