Sagnac experiment with electrons: Reanalysis of a rotationally induced phase shift for charged particles

Using a path-integral formalism, we present a reanalysis of the Sagnac experiment with electrons of Hasselbach and Nicklaus [Phys. Rev. A 48, 143 (1993)]. Our analysis, from an inertial frame of reference, makes explicit the central role of the electrostatic biprism in generating interference fringes and recovers the Sagnac formula for the phase shift induced when rotating the interferometer. This phase shift, however, is shown to differ significantly in physical origin from the similar experiment with neutrons. In the electron Sagnac experiment, rotation displaces all classical electron paths closer to (or further from, depending upon direction) the electrostatic biprisms, thereby perturbing the electrostatic potential along these paths, and a phase shift of an electrostatic nature arises. Our analysis yields a corrected expression for the projected area of the interferometer and small numerical corrections to previous work are consequently given.