Superconductivity is a rare example of a quantum system in which the
wavefunction has a macroscopic quantum effect, due to the unique condensate of
electron pairs. The amplitude of the wavefunction is directly related to the
pair density, but both amplitude and phase enter the Josephson current : the
coherent tunneling of pairs between superconductors. Very sensitive devices
exploit the superconducting state, however properties of the {\it condensate}
on the {\it local scale} are largely unknown, for instance, in unconventional
high-Tc​ cuprate, multiple gap, and gapless superconductors.
The technique of choice would be Josephson STS, based on Scanning Tunneling
Spectroscopy (STS), where the condensate is {\it directly} probed by measuring
the local Josephson current (JC) between a superconducting tip and sample.
However, Josephson STS is an experimental challenge since it requires stable
superconducting tips, and tunneling conditions close to atomic contact. We
demonstrate how these difficulties can be overcome and present the first
spatial mapping of the JC on the nanometer scale. The case of an MgB2​ film,
subject to a normal magnetic field, is considered.Comment: 7 pages, 6 figure