Enhanced phase sensitivity in a Mach-Zehnder interferometer via photon recycling

We propose an alternative scheme for phase estimation in a Mach-Zehnder interferometer (MZI) with photon recycling. It is demonstrated that with the same coherent-state input and homodyne detection, our proposal possesses a phase sensitivity beyond the traditional MZI. For instance, it can achieve an enhancement factor of ∼9.32 in the phase sensitivity compared with the conventional scheme even with a photon loss of 10% on the photon-recycled arm. From another point of view, the quantum Cramér-Rao bound (QCRB) is also investigated. It is found that our scheme is able to achieve a lower QCRB than the traditional one. Intriguingly, the QCRB of our scheme is dependent of the phase shift ϕ while the traditional scheme has a constant QCRB regardless of the phase shift. Finally, we present the underlying mechanisms behind the enhanced phase sensitivity. We believe that our results provide another angle from which to enhance the phase sensitivity in a MZI via photon recycling.