Enhancing Phase Estimation in an SU(1,1) Interferometer via Kerr Nonlinearity and Photon Addition

Abstract

We enhance phase sensitivity in an SU(1,1) interferometer by combining a Kerr nonlinear phase shifter with multi-photon addition. Using coherent and vacuum states as inputs, we analyze phase sensitivity and the quantum Fisher information under ideal and lossy conditions. We show that both phase sensitivity and the quantum Cramér-Rao bound (QCRB) improve gradually as the total mean photon number increases. For the standard SU(1,1) interferometer, phase sensitivity does not saturate the QCRB, even with multi-photon addition. In contrast, for the Kerr-based SU(1,1) interferometer, phase sensitivity nearly saturates the QCRB under ideal conditions and remains optimal at high transmissivity under loss. The Kerr-based scheme surpasses the standard quantum limit, approaches the sub-Heisenberg limit, and exhibits enhanced robustness against moderate losses. Our scheme is feasible with current technology and provides a promising route for high-precision quantum metrology.