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Europhysics Letters (EPL)

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

Walid Chaibi, Christophe Blondel, Christian Delsart, Cyril Drag

Published Mar 28, 2008• 10 citations
Publisher

Abstract

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.

DOI
10.1209/0295-5075/82/20005

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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.
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Although interferometry's earliest and most familiar use is with photons, the discovery of matter-wave (deBroglie-wave) interference for electrons demanded the development of quantum mechanics. Since then, matter-wave interferometry has been performed with neutrons, Cooper electron-pairs, and most recently, with whole atoms and diatomic molecules. This talk describes our recent high-flux atom interferometry experiments using the generalized Talbot-vonLau effect. Our interferometer consists of a sequence of three planar vacuum-slit diffraction gratings, microfabricated from silicon nitride membranes. DeBroglie-wave interference fringes are sensed by measuring the transmission of potassium atoms on a hot- wire as a function of grating relative position. Different spatial Fourier components (up to sixth) in the diffraction pattern are resonant in the interferometer at different atomic velocities (i.e., at different wavelengths). When a laser cooled slow atomic beam is incident, various different diffraction patterns are observed as a function of atomic velocity. In an alternative `Heisenberg Microscope' configuration an incident thermal beam produces a velocity average over different fringe Fourier components. AC modulated weak laser light passing through the interferometer interacts selectively with atoms at a specific velocity. The associated fringe pattern is then ac modulated and revealed by its selective destruction.
We review different attempts to show the decoherence process in double-slit-like experiments both for charged particles (electrons) and for neutral particles with permanent dipole moments. Interference is studied when electrons or atomic systems are coupled to classical or quantum electromagnetic fields. The interaction between the particles and time-dependent fields induces a time-varying Aharonov phase. Averaging over the phase generates a suppression of fringe visibility in the interference pattern. We show that, for suitable experimental conditions, the loss of contrast for dipoles can be almost as large as the corresponding one for coherent electrons and therefore can be observed. We analyse different trajectories in order to show the dependence of the decoherence factor on the velocity of the particles.
Many different formalisms exist for computing the phase of a matter-wave interferometer. However, it can be challenging to develop physical intuition about what a particular interferometer is actually measuring or about whether a given classical measurement provides equivalent information. Here, we investigate the physical content of the interferometer phase through a series of thought experiments. In low-order potentials, a matter-wave interferometer with a single internal state provides the same information as a sum of position measurements of a classical test object. In high-order potentials, the interferometer phase becomes decoupled from the motion of the interferometer arms, and the phase contains information that cannot be obtained by any set of position measurements on the interferometer trajectory. This phase shift in a high-order potential fundamentally distinguishes matter-wave interferometers from classical measuring devices.
We review the concept of matter-wave assisted molecule metrology and present the most recent experiments which exploit the capability of universal matter-wave interferometers to measure forces as small as 10-26 N via shifts of the interference fringes in the presence of well-controlled fields. This technique allows us to compare, in the same instrument, a variety of electronic and magnetic properties for a large range of atoms and molecules. We exemplify this here with precision measurements of the static polarizability of cesium atoms and the fullerenes C60 and C70 as well as dynamically-induced susceptibilities of tailored tripeptides. We also present measurements of magnetic properties such as the diamagnetic susceptibility of ground-state atoms and aromatic and non-aromatic hydrocarbons.
We study the quantal motion of electrons emitted by a pointlike monochromatic isotropic source into parallel uniform electric and magnetic fields. The two-path interference pattern in the emerging electron wave due to the electric force is modified by the magnetic lens effect which periodically focuses the beam into narrow filaments along the symmetry axis. There, four classical paths interfere. With increasing electron energy, the current distribution changes from a quantum regime governed by the uncertainty principle, to an intricate spatial pattern that yields to a semiclassical analysis.