We discuss the application of Bose-Einstein condensates (BECs) as sensors for
magnetic and electric fields. In an experimental demonstration we have brought
one-dimensional BECs close to micro-fabricated wires on an atom chip and
thereby reached a sensitivity to potential variations of ~10e-14eV at 3 micron
spatial resolution. We demonstrate the versatility of this sensor by measuring
a two-dimensional magnetic field map 10 micron above a 100-micron-wide wire. We
show how the transverse current-density component inside the wire can be
reconstructed from such maps. The field sensitivity in dependence on the
spatial resolution is discussed and further improvements utilizing Feshbach
resonances are outlined.Comment: 4 pages, 3 figure