Enhancement in phase sensitivity in displacement-assisted SU(1,1) interferometer via photon recycling

We propose a novel method for enhancing phase estimation in the displacement-assisted SU(1,1) (DSU(1,1)) interferometer by incorporating the photon recycling technique, evaluated under single-intensity detection (SID) and homodyne detection (HD) schemes. Our analysis showed that utilizing the photon recycling technique, the photon-recycled DSU(1,1) interferometer performs better than the conventional DSU(1,1) interferometer for some conditions. We also showed that this improvement is possible in both SID and HD schemes. In addition, to discuss the maximum sensitivity achieved by our proposed model, we have calculated the quantum Cramér-Rao bound (QCRB) within the framework and found that our proposed model approaches the QCRB. Therefore, we believe that our findings offer a promising new approach to improve phase sensitivity through photon recycling.