Enhanced Phase Estimation via Photon-Added Two-Mode Squeezed States and Kerr Nonlinearity

TL;DR

This work addresses surpassing the SQL in quantum phase estimation by integrating photon-added two-mode squeezed coherent states with a Kerr nonlinear phase shifter inside a Mach-Zehnder interferometer. By deriving both phase-sensitivity expressions for intensity-difference detection and quantum Fisher information, and by analyzing ideal and lossy scenarios, the authors show that increasing photon-addition order and input strength boosts both Δφ and Fk, with Kerr nonlinearity enhancing these gains further. The results indicate that the scheme can exceed the SQL and approach sub-Heisenberg and super-Heisenberg limits, even in the presence of photon losses, highlighting improved robustness and practical viability for high-precision quantum metrology. The combination of PA-TMSCS inputs, Kerr nonlinearity, and loss-tolerant analysis provides a promising route for implementing ultra-precise measurements in realistic quantum sensing platforms.

Abstract

Quantum metrology harnesses quantum resources to achieve measurement precision beyond classical limits. This work investigates a Mach-Zehnder interferometer incorporating a Kerr nonlinear phase shifter, using photon-added two-mode squeezed coherent states generated via four-wave mixing as input. This study demonstrates that increasing both the photon-addition order and input resource strength systematically enhances phase sensitivity, quantum Fisher information, and the quantum Cramér-Rao bound. The system not only surpasses the standard quantum limit but also approaches or exceeds the Heisenberg limit with linear phase shifts, while Kerr nonlinearity enables overcoming the super-Heisenberg limit. The proposed scheme exhibits enhanced robustness against photon loss, providing a promising approach for high-precision quantum metrology applications.

Figures (9)

• Figure 1: Schematic diagram of phase estimation using PA-TMSCS inputs in a KMZI, where photon addition operations on TMSCS in both $a$-mode and $b$-mode are considered. Photon loss within the KMZI is simulated by a virtual beam splitter, and intensity difference detection is implemented at the output port.
• Figure 2: Phase sensitivity $\Delta\phi$ versus phase shift $\phi$ for squeezing parameter $r=0.9$ and coherent amplitude $\alpha=1$.
• Figure 3: For fixed phase shift $\phi=3.12$: (a) phase sensitivity $\Delta\phi$ versus squeezing parameter $r$ with coherent amplitude $\alpha=1$; (b) $\Delta\phi$ versus $\alpha$ with $r=0.9$.
• Figure 4: Linear phase shift case: phase sensitivity $\Delta\phi$ versus loss rate $l$ for (a) $m=n=0$, (b) $m=n=1$, (c) $m=n=2$, with fixed phase shift $\phi=3.12$, squeezing parameter $r=0.9$, and coherent amplitude $\alpha=1$. SQL and HL are shown for comparison.
• Figure 5: Kerr nonlinear phase shift case: phase sensitivity $\Delta\phi$ versus loss rate $l$ for (a) $m=n=0$, (b) $m=n=1$, (c) $m=n=2$, with fixed phase shift $\phi=3.12$, squeezing parameter $r=0.9$, and coherent amplitude $\alpha=1$. SQL, HL, sub-HL, and SHL are shown for comparison.