Differential magnetometry with partially flipped Dicke states

TL;DR

This paper explores how partially flipped Dicke states can be used for quantum-enhanced multiparameter magnetometry, achieving higher precision in gradient estimation by exploiting entanglement and optimized measurement schemes.

Contribution

It introduces a method to transform Dicke states into gradient-sensitive states and demonstrates their optimality and enhanced precision in multiparameter magnetic field estimation.

Findings

Partially flipped Dicke states saturate precision bounds for gradient estimation.

Entanglement between ensembles roughly doubles the achievable precision.

Explicit measurement schemes are provided for small ensembles.

Abstract

We study magnetometry of gradients and homogeneous background fields along the three orthogonal directions using two spatially separated spin ensembles. We derive trade-off relations for the achievable estimation precision of these parameters. Dicke states, optimal for homogeneous field estimation, can be locally rotated into states sensitive to magnetic gradients by rotating the spins in one subensemble. We determine bounds for the precision for gradient metrology in the three orthogonal directions as a function of the sensitivities to the homogenous field in those directions. The resulting partially flipped Dicke state saturates the bounds above, showing similar sensitivity in two directions but significantly reduced sensitivity in the third. Exploiting entanglement between the two ensembles, this state achieves roughly twice the precision attainable by the best bipartite separable state, which is a product of local Dicke states. For small ensembles, we explicitly identify measurement operators saturating the quantum Cram\'er-Rao bound, while for larger ensembles, we propose simpler but suboptimal schemes. In both cases, the gradient is estimated from second moments and correlations of angular momentum operators. Our results demonstrate how the metrological properties of Dicke states can be exploited for quantum-enhanced multiparameter estimation.