Longitudinal coherence in two-beam interferometers means that the two partial wave packets arrive in the plane of interference simultaneously. In charged-particle interferometers, this simultaneity can be lost due to a difference in the geometrical path lengths, a difference in the optical path length, or a difference in the group velocities for the two wave packets on parts of or all of the beam paths. Several of those influences can combine to yield a net relative spatial delay between the wave packets in the interference plane, thus causing a reduction of the interference fringe contrast. A Wien filter can be used in charged-matter-wave interferometry to compensate for this relative delay and thus to reestablish longitudinal coherence. A Wien filter consists of an electric and a magnetic field perpendicular both to each other and the beam path. In its matched state, i.e., when the electrostatic and the magnetic forces on the electrons exactly cancel each other, the Wien filter neither deflects the beams nor exerts any phase shift on the wave packets. However, wave packets traveling through the Wien filter on laterally separated paths propagate in regions of different electric potentials and in turn with different group velocities, which leads to a longitudinal shift of the wave packets relative to each other. Maximum longitudinal coherence (and thereby fringe contrast) can be restored by choosing the compensating delay caused by the Wien filter exactly opposite to the net relative delay caused by the influences mentioned.

An experiment is presented that demonstrates this property of a Wien filter. The coherence-reviving action of a Wien filter is discussed in the context of the incoherent superposition in the registration plane of the plane waves corresponding to different wavelengths in the electron spectrum. It demonstrates that the quantum-mechanical coherence of the self-interacting plane-wave components of the wave packets describing the particle ensemble is more robust than the experimental loss of interference-fringe contrast often suggests. The availability of such a contrast-restoring device is especially important for very-low-energy (a few keV or less) electron interferometry. It is also likely to become important for future ion-beam interferometers.

• Received 17 November 1992

DOI:https://doi.org/10.1103/PhysRevA.48.152