We propose a scheme to improve the phase sensitivity of a Mach–Zehnder interferometer. In this scheme, a Kerr nonlinear phase shifter is used to replace the traditional linear phase shifter. We consider two detection approaches: the direct homodyne detection (DHD) and the indirect homodyne detection (IHD). We find that the Kerr nonlinear phase shifter can improve the phase sensitivity of the interferometer, and the DHD is better than the IHD. In addition, we also find that the phase sensitivity of the Kerr nonlinear interferometer is robust against photon losses.
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.
We propose a high-precision phase estimation scheme in a hybrid interferometer by synergistically combining a Kerr nonlinear phase shifter and multi-photon subtraction operations. Using a coherent state and a vacuum state as input resources, we systematically evaluate the phase sensitivity via homodyne detection and analyze the quantum Fisher information as well as the quantum Cramér-Rao bound under both ideal and lossy conditions. Our results show that the joint integration of Kerr nonlinearity and multi-photon subtraction yields remarkable advantages over either technique used alone. The proposed scheme enables the phase sensitivity to surpass the standard quantum limit, exceed the conventional Heisenberg scaling (
1/N), and approach the super-Heisenberg scaling (
1/N2)-a direct consequence of Kerr nonlinearity. More precisely, the super-Heisenberg scaling $\propto $
1/N2 is the ultimate precision limit permitted by the
k=2 Kerr nonlinearity and does not violate the fundamental Heisenberg limit for linear phase accumulation. Even under moderate internal photon loss, the system maintains high precision and exhibits enhanced robustness to decoherence. The Kerr nonlinearity introduces an intensity-dependent phase shift proportional to the squared photon number, while multi-photon subtraction tailors non-Gaussian states to strengthen phase information extraction. Compared with existing schemes based on hybrid interferometers or SU(1,1) interferometers, our architecture achieves superior precision and stronger loss resilience. All components are experimentally accessible with current quantum optical technologies. This work provides a promising route for practical high-precision quantum metrology and quantum sensing.