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Europhysics Letters (EPL)

Atomic-Position Measurement via Internal-State Encoding

S Kunze, Gerhard Rempe, Martin Wilkens

Published Jul 10, 1994• 105 citations
Publisher

Abstract

The position of a polarized atom passing through a standing light wave can be localized by observing the phase of the atomic-dipole moment in a Ramsey-type experiment. Depending on the outcome of the measurement, the diffraction pattern in the far field corresponds to atoms with their momentum changed by integer multiples of 4 ℏk . Position measurements with standard deviation of ≈ λ/40 seem to be possible with optical techniques.

DOI
10.1209/0295-5075/27/2/007

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The position of a polarized atom passing through a standing light wave can be localized by observing the phase of the atomic-dipole moment in a Ramsey-type experiment. Depending on the outcome of the measurement, the diffraction pattern in the far field corresponds to atoms with their momentum changed by integer multiples of 4 ℏk . Position measurements with standard deviation of ≈ λ/40 seem to be possible with optical techniques.
We consider atoms traversing a cavity filled with an optical field. When the atoms are well detuned from the optical resonance the output momentum distribution of the atoms is found to be a sensitive probe of the photon statistics of the light field. Near resonance spontaneous emission smears the diffractive peaks. We obtain a good fit to the experimental data of Gould et at. (1991). As the atoms pass through the optical field they impart a position-dependent phase shift to the field. By making a quadrature phase measurement on the optical field a position measurement of the atom is achieved. We show that it is possible to prepare the atom in a 'contractive state' which beats the standard quantum limit for position measurements.
We study localization of atomic position when a three-level atom interacts with a quantized standing-wave field in the Ramsey interferometer setup. Both the field quadrature amplitude and the atomic internal state are measured to obtain the atomic-position information. It is found that this dual-measurement scheme produces an interference pattern superimposed on a diffractionlike pattern in the atomic-position distribution, where the former pattern originates from the state-selective measurement and the latter from the field measurement. The present scheme results in a better resolution in the position localization than the field-alone measurement schemes. We also discuss the measurement-correlated mechanical action of the standing-wave field on the atom in the light of Popper's test.
We report on an experiment with polarized atoms passing a standing light wave, where the atom's position is encoded (entangled) with the excitation amplitude of two long lived electronic states. Position information can be obtained a posteriori by measuring the electronic state. If this measurement is performed, the atom is localized in an array of virtual slits. This gives rise to diffraction of the atomic de Broglie waves from a measurement induced amplitude grating, thus showing the back action onto the momentum due to the localization. We further demonstrate experimentally that the encoding can be totally erased.