# Erlangen 2018 – wissenschaftliches Programm

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# Q: Fachverband Quantenoptik und Photonik

## Q 15: Quantum Information (Concepts and Methods) II

### Q 15.2: Vortrag

### Montag, 5. März 2018, 14:30–14:45, K 1.019

**Precision bounds for gradient magnetometry with atomic ensembles** — •Iagoba Apellaniz^{1}, Iñigo Urizar-Lanz^{1}, Zoltán Zimborás^{1,2,3}, Philipp Hyllus^{1}, and Géza Tóth^{1,3,4} — ^{1}Theoretical Physics, University of the Basque Country UPV/EHU, E-48080 Bilbao, Spain — ^{2}Dahlem Center for Complex Quantum Systems, Freie Universität Berlin, 14195 Berlin, Germany — ^{3}Wigner Research Centre for Physics, H-1525 Budapest, Hungary — ^{4}IKERBASQUE, Basque Foundation for Science, E-48011 Bilbao, Spain

We study gradient magnetometry with an ensemble of atoms with arbitrary spin. We consider the case of a very general spatial probability distribution function. We calculate precision bounds for estimating the gradient of the magnetic field based on the quantum Fisher information. For quantum states that are invariant under homogeneous magnetic fields, we need to measure a single observable to estimate the gradient. On the other hand, for states that are sensitive to homogeneous fields, the measurement of two observables are needed, as the homogeneous field must also be estimated. This leads to a two-parameter estimation problem. We present a method to calculate precision bounds for gradient estimation with a chain of atoms or with two spatially separated atomic ensembles feeling different magnetic fields. We also consider a single atomic ensemble with an arbitrary density profile, in which the atoms cannot be addressed individually, and which is a very relevant case for experiments. Our model can take into account even correlations between particle positions.