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Journal of Modern Optics

Tomography of Atom Beams

U. Janicke, Martin Wilkens

Published Nov 1, 1995• 75 citations
Publisher

Abstract

We investigate the accuracy of an experimental reconstruction of the Wigner function of the transverse motion in an atom beam using numerical wave packet simulations. For the example of a superposition of two Gaussians (the outcome of a double slit, for example) we study in detail the influence of experimental restraints on the quality of the reconstruction. For the potential candidate, metastable helium, we demonstrate that an accurate reconstruction of the Wigner function, especially of its negative parts, is well within experimental reach.

DOI
10.1080/09500349514551901

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We investigate the accuracy of an experimental reconstruction of the Wigner function of the transverse motion in an atom beam using numerical wave packet simulations. For the example of a superposition of two Gaussians (the outcome of a double slit, for example) we study in detail the influence of experimental restraints on the quality of the reconstruction. For the potential candidate, metastable helium, we demonstrate that an accurate reconstruction of the Wigner function, especially of its negative parts, is well within experimental reach.
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To quantify the effect of decoherence in quantum measurements, it is desirable to measure not merely the square modulus of the spatial wave function, but the entire density matrix, whose phases carry information about momentum and how pure the state is. An experimental setup is presented that can measure the density matrix (or equivalently, the Wigner function) of a beam of identically prepared charged particles to an arbitrary accuracy, limited only by count statistics and detector resolution. The particles enter into an electric field, causing simple harmonic oscillation in the transverse direction. This corresponds to rotating the Wigner function in phase space. With a slidable detector, the marginal distribution of the Wigner function can be measured from all angles. Thus the phase-space tomography formalism can be used to recover the Wigner function by the standard inversion of the radon transform. By applying this technique to, for instance, double-slit experiments with various degrees of environment-induced decoherence, it should be possible to make our understanding of decoherence and apparent wave-function collapse less qualitative and more quantitative. \textcopyright{} 1996 The American Physical Society.
Using the unique detection properties offered by metastable helium atoms we have produced high resolution images of the transverse spatial profiles of an atom laser beam. We observe fringes on the beam, resulting from quantum mechanical interference between atoms that start from rest at different transverse locations within the outcoupling surface and end up at a later time with different velocities at the same transverse position. Numerical simulations in the low output-coupling limit give good quantitative agreement with our experimental data.
Summary form only given.We show experimentally the reconstructions of Wigner functions for the output states of a laser. These states have classical Wigner functions with Gaussian cross-sections. In order to investigate the spectral properties of the output states, we normalize the Wigner functions in the inverse Radon transform algorithm to a coherent state. In this way, we are able to compare the full spectrum of Wigner functions obtained with different detection frequencies, paying particular attention to Wigner functions near the laser relaxation oscillation. The same normalized Wigner function is also used to measure squeezed optical states from an optical parametric oscillator. When large modulation is introduced to the laser beam, a dc component is introduced in the Wigner function. We show that Wigner functions of incoherent superposition states can be reconstructed using this modulation technique. In some cases, fluctuations can be large enough to produce highly non-Gaussian Wigner functions. We provide examples of such cases and show that optical homodyne tomography can provide essentially new information not detectable with standard quadrature variance measurements. Furthermore, we demonstrate that single sideband analysis used to date will sometimes no longer suffice in the analysis of such optical states. We include the higher order sideband correlations experimentally and discuss the necessity of these higher order sidebands for measuring non-Gaussian quantum states, e.g. Schrodinger's cat and Fock states.