Quantum Estimation in Strong Fields: in situ ponderomotive sensing

TL;DR

This paper introduces a quantum estimation framework for in situ strong field measurements, demonstrating how high-resolution momentum spectroscopy can significantly reduce uncertainty in laser intensity measurements.

Contribution

It derives quantum and classical Fisher information for strong-field ionization, linking measurement scaling to interference effects and proposing methods to enhance measurement precision.

Findings

Fisher information scales quadratically with time in momentum basis

High-resolution momentum spectroscopy can reduce measurement uncertainty by over 25 times

Theoretical minimum uncertainty of 0.28% for in situ laser intensity measurement

Abstract

We develop a new framework to optimize and understand uncertainty from in situ strong field measurements of laser field parameters. We present the first derivation of quantum and classical Fisher information for an electron undergoing strong-field ionization. This is used for parameter estimation and to characterize the uncertainty of the ponderomotive energy, directly proportional to laser intensity. In particular, the quantum and classical Fisher information for the momentum basis displays quadratic scaling over time. This can be linked to above-threshold ionization interference rings for measurements in the momentum basis and to the `ponderomotive phase' for the `ideal' quantum measurements. Preferential scaling is found for increasing laser pulse length and intensity. We use this to demonstrate for in situ measurements of laser intensity, that high resolution momentum spectroscopy has the capacity to reduce the uncertainty by over $25$ times compared to measurements employing the ionization rate, while using the `ideal' quantum measurement would reduce it by a further factor of $2.6$. A minimum uncertainty of the order $2.8 \times 10^{-3}~\%$ is theorized for this framework. Finally, we examine previous in situ measurements formulating a measurement that matches the experimental procedure and suggest how to improve this.