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arXiv:1006.0450 · Journal of Physics A Mathematical and Theoretical

Coherence loss and revivals in atomic interferometry: a quantum-recoil analysis

M Davidović, Ángel S. Sanz, M Božić, D. Arsenović

Published Apr 4, 2012• 3 citations
arXivHTMLPDF

Abstract

The coherence effects induced by external photons coupled to matter waves inside a Mach–Zehnder three-grating interferometer are analyzed. Alternatively to atom–photon entanglement scenarios, the model considered here only relies on the atomic wavefunction and the momentum shift induced in it by the photon scattering events. A functional dependence is thus found between the observables, namely the fringe visibility and the phase shift, and the transversal momentum transfer distribution. Good quantitative agreement is found when comparing the results obtained from our model with the experimental data.

DOI
10.1088/1751-8113/45/16/165303

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The coherence effects induced by external photons coupled to matter waves inside a Mach–Zehnder three-grating interferometer are analyzed. Alternatively to atom–photon entanglement scenarios, the model considered here only relies on the atomic wavefunction and the momentum shift induced in it by the photon scattering events. A functional dependence is thus found between the observables, namely the fringe visibility and the phase shift, and the transversal momentum transfer distribution. Good quantitative agreement is found when comparing the results obtained from our model with the experimental data.
Here, interference visibility in a three-grating atom interferometer with presence of photon-atom scattering events is analyzed. The model considered is entirely based on the atom wave function and the effects caused on it by both scattering events and subsequent diffractions through the interferometer gratings. A functional dependence of the interference visibility on the probability distribution of transferred momentum (by the photons) to the atoms is thus found, which is used to interpret the available experimental data. Within this model there is no need, therefore, to appeal for concepts such as “which-way” information or entanglement to explain the losses, revivals and regains of quantum coherence in this type of experiments. Rather, visibility losses and revivals are explained in terms of the sudden change induced in the atomic wave function by the momentum transfer, while regains are directly related to the visibility functional dependence on the statistical distribution of transferred momentum of the sample of atoms selected after passing through the interferometer (before they are detected).
Here, the influence of resonance photon-atom scattering on the atom interference pattern at the exit of a three-grating Mach-Zehnder interferometer is studied.It is assumed that the scattering process does not destroy the atomic wave function describing the state of the atom before the scattering process takes place, but only induces a certain shift and change of its phase.We find that the visibility of the interference strongly depends on the statistical distribution of transferred momenta to the atom during the photon-atom scattering event.This also explains the experimentally observed (Chapman et al 1995 Phys.Rev. Lett.75 2783) dependence of the visibility on the ratio d p /λ i = y 12 (2π/kdλ i ), where y 12 is the distance between the place where the scattering event occurs and the first grating, k is the wave number of the atomic centre-of-mass motion, d is the grating constant and λ i is the photon wavelength.Furthermore, it is remarkable that photon-atom scattering events happen experimentally within the Fresnel region, i.e. the near-field region, associated with the first grating, which should be taken into account when drawing conclusions about the relevance of 'which-way' information for the interference visibility.
In 1995, Chapman et al (1995 Phys. Rev. Lett. 75 2783) showed experimentally that the interference contrast in a three-grating atom interferometer does not vanish in the presence of scattering events with photons, as required by the complementarity principle. In this work, we present an analytical study of this experiment by determining the evolution of an atom's wave function along the three-grating Mach–Zehnder interferometer under the assumption that the atom is hit by a photon after passing through the first grating. The consideration of a transverse wave function in momentum representation is essential in this study. As is shown, the number of atoms transmitted through the third grating is given by a simple periodic function of the lateral shift along this grating, both in the absence and in the presence of photon scattering. Moreover, the relative contrast (laser on/laser off) is shown to be a simple analytical function of the ratio d p /λ i , where d p is the distance between atomic paths at the scattering locus and λ i the scattered photon wavelength. We argue that this dependence, being in agreement with experimental results, can be considered as showing compatibility between the wave and corpuscle properties of atoms.
We have developed a technique for measuring the atomic recoil frequency using a single-state echo-type atom interferometer that manipulates laser-cooled atoms in the ground state. The interferometer relies on momentum-state interference due to two standing-wave pulses that produce density gratings. The interference is modified by applying a third standing-wave pulse during the interferometer pulse sequence. As a result, the grating contrast exhibits periodic revivals at the atomic recoil frequency ${\ensuremath{\omega}}_{r}$ as a function of the time at which the third pulse is applied, allowing ${\ensuremath{\omega}}_{r}$ to be measured easily and precisely. The contrast is accurately described by a coherence function, which is the Fourier transform of the momentum distribution, produced by the third pulse and by the theory of echo formation. If the third pulse is a traveling wave, loss of grating contrast is observed, an effect also described by a coherence function. The decay of the grating contrast as a function of continuous-wave light intensity is used to infer the cross section for photon absorption.
We have developed a technique for measuring the atomic recoil frequency using a single-state echo-type atom interferometer that manipulates laser-cooled atoms in the ground state. The interferometer relies on momentum-state interference due to two standing-wave pulses that produce density gratings. The interference is modified by applying a third standing-wave pulse during the interferometer pulse sequence. As a result, the grating contrast exhibits periodic revivals at the atomic recoil frequency r as a function of the time at which the third pulse is applied, allowing r to be measured easily and precisely. The contrast is accurately described by a coherence function, which is the Fourier transform of the momentum distribution, produced by the third pulse and by the theory of echo formation. If the third pulse is a traveling wave, loss of grating contrast is observed, an effect also described by a coherence function. The decay of the grating contrast as a function of continuous-wave light intensity is used to infer the cross section for photon absorption.
In an atom interferometry experiment, the output phase shift depends on the wave vector of photons and the recoil momentum in optical transitions. This Letter puts forward a hypothesis that in light-atom interaction, the atom wave function could provide a transverse confinement to photons and thus could affect the mean recoil momentum. We propose a model to analyze the photon effective wave vector in a monochromatic optical field and calculate the relative shift of |k[over →]_{eff}| to k when an atom with a 3D Gaussian wave function absorbs one photon in a Gaussian beam. This shift could lead to a systematic effect related to the spatial distribution of atoms and the transverse beam profile in high-precision experiments based on atom interferometry.