Do fringes and trajectories shift equally in matter-wave interferometers? the example of photodetachment microscopy in a magnetic field

Matter-wave interferometers, either with electrons, atoms or molecules, owe their sensitivity to the accuracy of phase-shift measurements. One may, however, raise the question whether the shift undergone by interference fringes, when external forces are applied, actually differs from the shift of classical trajectories. For the case of a magnetic perturbation, we provide experimental evidence and a vector demonstration that interference patterns only undergo a global shift. The experiment is performed with the photodetachment microscope, with a uniform magnetic field superimposed over the whole volume accessible to the interfering electron. Identity of the fringe and trajectory shifts is established for any two-wave interferometer using charged particles, submitted to a magnetic field.