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arXiv:1511.08697 · Physical Review Letters

Visibility of Young’s Interference Fringes: Scattered Light from Small Ion Crystals

Sebastian Wolf, Julian Wechs, Joachim von Zanthier, Ferdinand Schmidt‐Kaler

Published May 2, 2016• 19 citations
arXivHTMLPDF

Abstract

We observe interference in the light scattered from trapped ^{40}Ca^{+} ion crystals. By varying the intensity of the excitation laser, we study the influence of elastic and inelastic scattering on the visibility of the fringe pattern and discriminate its effect from that of the ion temperature and wave-packet localization. In this way we determine the complex degree of coherence and the mutual coherence of light fields produced by individual atoms. We obtain interference fringes from crystals consisting of two, three, and four ions in a harmonic trap. Control of the trapping potential allows for the adjustment of the interatomic distances and thus the formation of linear arrays of atoms serving as a regular grating of microscopic scatterers.

DOI
10.1103/physrevlett.116.183002

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We observe interference in the light scattered from trapped ^{40}Ca^{+} ion crystals. By varying the intensity of the excitation laser, we study the influence of elastic and inelastic scattering on the visibility of the fringe pattern and discriminate its effect from that of the ion temperature and wave-packet localization. In this way we determine the complex degree of coherence and the mutual coherence of light fields produced by individual atoms. We obtain interference fringes from crystals consisting of two, three, and four ions in a harmonic trap. Control of the trapping potential allows for the adjustment of the interatomic distances and thus the formation of linear arrays of atoms serving as a regular grating of microscopic scatterers.
We report the first observation of interference in the light scattered from two trapped atoms ({sup 198}Hg{sup +} ions localized in a linear Paul trap). The visibility of the interference fringes can be explained in the frame-work of Bragg scattering by a harmonic crystal, but with important differences compared to the case of a large crystal. Comparison of the experimental data with theory shows that the interference pattern offers another method to determine ion temperatures and separations. Furthermore, by exploiting the atom`s internal structure we have found a way to obtain {open_quotes}which path{close_quotes} information without invoking the position-momentum uncertainty relation. If the light scattered by the atoms is detected in a polarization-sensitive way, then it is possible to selectively demonstrate either the particle-nature or the wave-nature of the scattered photons.
The demonstration of coherence between a large number of quantum emitters is essential for the realization of many paradigmatic experiments in quantum optics. Here we present the observation of controlled interference of light scattered from crystal strings of up to 53\,trapped ions. The scattered light is collected along the crystal symmetry axis, which guarantees spatial indistinguishability of photons scattered by different ions and allows for convenient scaling of the number of contributing particles. The interference phase is tuned by changing the mutual distance between the ions and the observed pattern corresponds qualitatively to a simple theoretical model considering point-like emitters. The observed interference visibility remains in the 0.34 to 0.53 range for all the measured string sizes, limited mostly by the spatially inhomogeneous laser intensity seen by the long ion strings. The presented results open the possibility for experimental investigation of a whole range of fundamental physical phenomena, including engineered directional photon emission, direct detection of quadrature squeezing of atomic resonance fluorescence, and optical generation of genuine multi-partite entanglement between a large number of trapped ions.
We have observed interference fringes, like those in Young’s classic experiment, in the laser light scattered by two trapped atoms. The interference fringes are present only in one polarization of the scattered light. The polarization dependence is related to the complementarity principle, which forbids the simultaneous observation of wave-like and particle-like aspects of light. The interference fringes are due to processes in which a single photon scatters from two atoms. We describe methods which might be used to observe other interference eects due to two photons scattering from two atoms.
The efficient detection of light from trapped ions in free space is paramount for most of their applications. We propose a scheme to enhance the photon collection from linear ion strings. It employs the constructive interference of light scattered from ions along the axial direction in linear Paul traps. The coherent enhancement of photon collection is numerically optimized for a range of feasible spatial angles and realistic ion positions in a single harmonic Coulomb potential. Despite the large mutual distance of scatterers on the order of many wavelengths of scattered light, presented experimental tests confirm the feasibility of enhancements by a factor of 3.05±0.093.05 \pm 0.093.05±0.09 with a crystal of nine 40^{40}40Ca+^++ ions. Further significant improvements using different ion species, which allow for suppression of the sensitivity to the residual thermal motion, are predicted. The proposed collection geometry is intrinsic to diverse linear ion trap designs and the methodology can be directly applied to an observation of scattering from ion crystals prepared in collective electronic excitations.
The study of collective atomic behavior is an important problem which has attracted much interest in recent years. Motivated by recent advances in ion trapping technology,1 and by a calculation of interference in the fluorescence from two atoms,2 we have investigated the effects of collective behavior on the interference fringe visibility. Interference in the fluorescence from two atoms separated by a fixed distance is examined as a function of driving laser and cavity parameters. The fringe visibility, a measure of the coherence of the atomic radiation, is calculated for the system of two driven atoms and the cavity mode. In free space, as the atoms are driven towards saturation, the visibility drops due to loss of coherence. The visibility goes from unity, at weak field, to 10% at saturation and falls off to zero asymptotically at higher fields. Dramatic improvement in visibility is found in the presence of the atom-cavity coupling, with the largest enhancement at intermediate driving field. This result indicates that induced coherence is a sensitive measure of collective behavior. Our progress in the experimental realization of this system with laser cooled beryllium ions confined in a linear trap is described, and directions for future work are indicated.