Probing the superconducting condensate on a nanometer scale

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-T$_c$ 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 MgB$_2$ film, subject to a normal magnetic field, is considered.