OH molecule as a quantum probe to jointly estimate electric and magnetic fields

TL;DR

This paper explores using the OH molecule as a quantum sensor for simultaneously estimating electric and magnetic fields, analyzing stationary and dynamical strategies, and overcoming measurement incompatibility.

Contribution

It introduces a comprehensive multiparameter quantum estimation framework for the OH molecule, including optimal strategies and robustness analysis against measurement incompatibility.

Findings

Thermal states can reduce estimation error by weakening parameter correlations.

Optimal sequential control protocols can surpass limitations from measurement incompatibility.

Nontrivial effects of temperature and initial states on estimation accuracy are identified.

Abstract

The hydroxyl radical, hereafter referred to as the OH molecule (OHM), carries both electric and magnetic dipole moments and, as a diatomic molecule, admits a comparatively simple and accurate model. This makes it a natural quantum probe for the joint estimation of electric and magnetic fields. Here we study simultaneous estimation of both fields using the tools of multiparameter quantum estimation theory, explicitly accounting for the performance loss caused by measurement incompatibility. We analyze and optimize both stationary and dynamical estimation strategies. In the stationary regime we consider ground and thermal states of the Stark-Zeeman Hamiltonian and identify optimal operating points. For thermal probes we find a nontrivial multiparameter effect: increasing the temperature can reduce the overall estimation error by weakening parameter correlations. In the dynamical regime we study both pure and thermal initial states, illustrating nontrivial manifestations of incompatibility for mixed probes. Finally, we show that an optimal sequential control protocol can overcome limitations due to noncommutativity, and we assess its robustness in the multiparameter setting.