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Physical Review A

Probing of atomic beams by using a self-referencing principle

Stefan H. Kienle, Dietmar Fischer, Matthias Freyberger

Published Aug 1, 1999• 3 citations
Publisher

Abstract

We discuss a method for reconstructing the wave function of an atomic beam with the help of a self-referencing principle. At the heart of the method lies the controlled superposition of the original atomic matter wave with a single reference wave. For this purpose, Bragg scattering of atomic beams at standing light fields turns out to be perfectly suited.

DOI
10.1103/physreva.60.1471

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•Sep 15, 2004•0 citations
We discuss a method for reconstructing the wave function of an atomic beam with the help of a self-referencing principle. At the heart of the method lies the controlled superposition of the original atomic matter wave with a single reference wave. For this purpose, Bragg scattering of atomic beams at standing light fields turns out to be perfectly suited.
We discuss a simple method to probe the wave function $\ensuremath{\psi}(x)$ describing the transverse center-of-mass motion of an atomic beam. We detect position distributions of the atoms after they have interacted with two counterpropagating laser beams. The resulting interference pattern depends crucially on the cross term ${\ensuremath{\psi}}^{*}(x)\ensuremath{\psi}(x\ensuremath{-}\ensuremath{\Delta}x)$, which finally allows us to reconstruct the phase of $\ensuremath{\psi}(x)$.
Atoms undergo two types of momentum changes as they pass across a near-resonant standing wave. First, their transverse momentum spreads. Second, if the atoms cross the field at an angle, they undergo Bragg scattering from the periodic structure provided by the wave. Classically, this behavior can be understood in terms of traveling waves: the atom catalyzes the transfer of momentum from one traveling wave to the other, thereby changing its own transverse momentum. In the quantum regime, however, there is an essential difference between scattering by two running waves and by a standing wave. With running waves, we can in principle know which of the two waves has exchanged a unit of momentum with the atom. In contrast, a standing wave is an inseparable quantum unit whose average momentum remains zero at all times. This unity is imposed by the fixed mirrors that establish the standing wave. These act as infinite sinks of momentum. Quantum mechanics forbids one even in principle to determine, via a field measurement from which traveling wave the atom picked up its momentum. To demonstrate this point, we discuss the diffraction and deflection of an atom in both a standing wave and a superposition of two counter-propagating running waves.
The long range goal of this project was the creation of nanostructures using light fields to manipulate atoms. By passing an atomic beam through one or more standing wave light fields, it is possible to create modulations in the atomic density having periods which are a fraction of the period of the standing wave light fields. Patterns having periods as small as lambda/10 were observed using optical masks and clear evidence for matter-wave effects were established. Several theoretical methods for achieving sub-lambda matter wave patterns were developed, Moreover it was shown that it is possible to create optical lattices having reduced periodicity using Raman transitions in a novel atom-field geometry Experiments were carried out in both magneto-optical traps and atomic beams. In both experimental set-ups, pulsed standing wave optical fields were used to excite the atoms. At some later time the atoms were probed by a traveling wave field, revealing the spatial patterns that had evolved as a result of the atom-field interaction.