  Superconductivity can be understood in terms of a phase transition from an
uncorrelated electron gas to a condensate of Cooper pairs in which the relative
phases of the constituent electrons are coherent over macroscopic length
scales. The degree of correlation is quantified by a complex-valued order
parameter, whose amplitude is proportional to the strength of the pairing
potential in the condensate. Supercurrent-carrying states are associated with
non-zero values of the spatial gradient of the phase. The pairing potential and
several physical observables of the Cooper condensate can be manipulated by
means of temperature, current bias, dishomogeneities in the chemical
composition or application of a magnetic field. Here we show evidence of
complete suppression of the energy gap in the local density of quasiparticle
states (DOS) of a superconducting nanowire upon establishing a phase difference
equal to pi over a length scale comparable to the superconducting coherence
length. These observations are consistent with a complete collapse of the
pairing potential in the center of the wire, in accordance with theoretical
modeling based on the quasiclassical theory of superconductivity in diffusive
systems. Our spectroscopic data, fully exploring the phase-biased states of the
condensate, highlight the profound effect that extreme phase gradients exert on
the amplitude of the pairing potential. Moreover, the sharp magnetic response
observed near the onset of the superconducting gap collapse regime can be
exploited to realize ultra-low noise magnetic flux detectors.
