Stuttgart 2012 – scientific programme
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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: Talk
Friday, March 16, 2012, 11:30–11:45, V47.01
Differential Magnetometry using Singlets — •Iñigo Urizar-Lanz1, Philipp Hyllus1, Iñigo Egusquiza1, and Géza Tóth1,2,3 — 1Department of Theoretical Physics, The University of the Basque Country, P.O. Box 644, E-48080 Bilbao, Spain — 2IKERBASQUE, Basque Foundation for Science, E-48011 Bilbao, Spain — 3Research 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 Ĵx. The measurement uncertainty can then be estimated by the error propagation formula if ⟨ Ĵx2⟩ and ⟨ Ĵx4⟩ 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.