Using trapped ions in an entangled state we propose detecting a magnetic
dipole of a single atom at distance of a few μm. This requires a
measurement of the magnetic field gradient at a level of about 10−13
Tesla/μm. We discuss applications e.g. in determining a wide variation of
ionic magnetic moments, for investigating the magnetic substructure of ions
with a level structure not accessible for optical cooling and detection,and for
studying exotic or rare ions, and molecular ions. The scheme may also be used
for measureing spin imbalances of neutral atoms or atomic ensembles trapped by
optical dipole forces. As the proposed method relies on techniques well
established in ion trap quantum information processing it is within reach of
current technology.Comment: 4 pages, 2 fi