We predict a new quantum interference effect for phase coherent loops containing a superconducting arm, in which the energy gap (superconducting phase gradient) plays the role of a scalar (vector) potential. By solving the Bogoliubov–de Gennes equation for small loops in one and two dimensions, it is demonstrated that if either the magnitude or the phase gradient of the superconducting order parameter is increased monotonically, the differential conductance oscillates. The frequency of oscillation is a factor of two lower than that of Tomasch oscillations and therefore defines a first harmonic for quasi-particle interference phenomena in mesoscopic superconductors.