High Precision Multi-parameter Weak Measurement with Hermite-Gaussian Pointer

TL;DR

This paper proposes a high-precision multi-parameter weak measurement scheme using Hermite-Gaussian pointers, demonstrating theoretical improvements and experimental validation for enhanced quantum metrology.

Contribution

It introduces a novel weak measurement formalism with Hermite-Gaussian pointers, showing improved precision bounds and practical experimental setup for multi-parameter estimation.

Findings

Precision improves by a factor of √(2n+1) with Hermite-Gaussian modes

Estimation approaches the quantum Fisher information limit

Experimental setup validates theoretical predictions

Abstract

The weak value amplification technique has been proved useful for precision metrology in both theory and experiment. To explore the ultimate performance of weak value amplification for multi-parameter estimation, we investigate a general weak measurement formalism with assistance of high-order Hermite-Gaussian pointer and quantum Fisher information matrix. Theoretical analysis shows that the ultimate precision of our scheme is improved by a factor of square root of 2n+1, where n is the order of Hermite-Gaussian mode. Moreover, the parameters' estimation precision can approach the precision limit with maximum likelihood estimation method and homodyne method. We have also given a proof-of-principle experimental setup to validate the H-G pointer theory and explore its potential applications in precision metrology.