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Physical Review A

Interferometric measurement of an atomic wave function

Matthias Freyberger, Stefan H. Kienle, Valery P. Yakovlev

Published Jul 1, 1997• 31 citations
Publisher

Abstract

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 $\ensuremath{\psi}(x)$.

DOI
10.1103/physreva.56.195

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We discuss a simple method to probe the wave function \ensuremathψ(x)\ensuremath{\psi}(x)\ensuremathψ(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 \ensuremathψ∗(x)\ensuremathψ(x\ensuremath−\ensuremathΔx){\ensuremath{\psi}}^{*}(x)\ensuremath{\psi}(x\ensuremath{-}\ensuremath{\Delta}x)\ensuremathψ∗(x)\ensuremathψ(x\ensuremath−\ensuremathΔx), which finally allows us to reconstruct the phase of \ensuremathψ(x)\ensuremath{\psi}(x)\ensuremathψ(x).
The spatial coherence of an atomic wavepacket can be detected in scattered photons, even when the center-of-mass motion is in the quantum coherent superposition of two distant, nonoverlapping wavepackets. Spatial coherence manifests itself in the power spectrum of the emitted photons, whose spectral components can exhibit interference fringes as a function of the emission angle. The contrast and the phase of this interference pattern provide information about the quantum state of the center of mass of the scattering atom.
We present a simple spectroscopic method based on Autler-Townes spectroscopy to determine the center-of-mass atomic wave function. The detection of spontaneously emitted photons from a three-level atom, in which two upper levels are driven by a classical standing light, yields information about the position and momentum distribution of the atom [A. M. Herkommer, W. P. Schleich, and M. S. Zubairy, J. Mod. Opt. 44,44,44, 2507 (1997)]. In this paper, we show that both the amplitude and phase information of the center-of-mass atomic wave function can be obtained from these distributions after a series of conditional measurements on the atom and the emitted photon.