# Stuttgart 2012 – wissenschaftliches Programm

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# SYQM: Symposium Quantum Limited Measurement: Applications in Metrology, Biology and Solid State Research

## SYQM 1: Quantum limited measurement applications 1

### SYQM 1.3: Vortrag

### Freitag, 16. März 2012, 11:30–11:45, V47.01

**Differential Magnetometry using Singlets** — •Iñigo Urizar-Lanz^{1}, Philipp Hyllus^{1}, Iñigo Egusquiza^{1}, and Géza Tóth^{1,2,3} — ^{1}Department of Theoretical Physics, The University of the Basque Country, P.O. Box 644, E-48080 Bilbao, Spain — ^{2}IKERBASQUE, Basque Foundation for Science, E-48011 Bilbao, Spain — ^{3}Research Institute for Solid State Physics and Optics, Hungarian Academy of Sciences, P.O. Box 49, H-1525 Budapest, Hungary

The gradient of a magnetic field can be measured using a single cloud of non-interacting
spins, prepared initially in a state with vanishing angular momentum.
The magnetic field gradient can be estimated from a measurement of the square of the angular momentum operator Ĵ_{x}.
The measurement uncertainty can then be estimated by the error propagation formula if ⟨ Ĵ_{x}^{2}⟩ and
⟨ Ĵ_{x}^{4}⟩ are known as a function of the gradient. We show how these quantities can be computed
for the ideal state. Finally, we discuss how the results can be applied to a state close to a singlet which can be realistically
prepared experimentally with a cloud of cold atoms.