Atomic Scatterers Research Articles

Modeling Optical Materials at the Single Scatterer Level: The Transition from Homogeneous to Heterogeneous Materials

AbstractMaterials that contain distinct scatterers, for example, nanoparticles, with sizes exceeding 100 nm scatter light heavily and are heterogeneous. In contrast, the atomic or molecular scatterers in conventional optical materials form a homogeneous distribution on the scale of the wavelength. In this paper, the transition between homogeneous and heterogeneous materials is investigated. To this end, a procedure is introduced that allows for retrieving reliable refractive index values from full wave optical numerical simulations of the underlying multibody scattering problem. Using this procedure, it is shown that the concept of an effective refractive index breaks down on multiple levels as a material transitions out of the homogeneous regime. These findings allow for quantifying how novel dispersion‐engineered nanocomposites for bulk optical applications must be designed and show that Maxwell–Garnett‐type effective medium theories are accurate tools for the design of nanocomposites. The procedure can be readily generalized to other types of scatterers, including atoms and molecules and hence guide the design of different kinds of novel materials.

Nonlinear quantum transport of light in a cold atomic cloud

We outline the non-perturbative theory of multiple scattering of resonant, intense laser light off a dilute cloud of cold atoms. A combination of master equation and diagrammatic techniques allows, for the first time, a quantitative description of nonlinear diffusive transport as well as of coherent backscattering of the injected electromagnetic field, notwithstanding the exponential growth of Hilbert space with the number of atomic scatterers. As an exemplary application, we monitor the laser light's intensity profile within the medium, the spectrum of the backscattered light and the coherent backscattering peak's height with increasing pump intensity. Our theory establishes a general, microscopic, scalable approach to nonlinear transport phenomena in complex quantum materials.

Lasing and Amplification from Two-Dimensional Atom Arrays.

We explore the ability of two-dimensional periodic atom arrays to produce light amplification and generate laser emission when gain is introduced through external optical pumping. Specifically, we predict that lasing can take place for arbitrarily weak atomic scatterers assisted by cooperative interaction among atoms in a 2D lattice. We base this conclusion on analytical theory for three-level scatterers, which additionally reveals a rich interplay between lattice and atomic resonances. Our results provide a general background to understand light amplification and lasing in periodic atomic arrays, with promising applications in the generation, manipulation, and control of coherent photon states at the nanoscale.

Jacob's ladder of approximations to paraxial dynamic electron scattering

Dynamical scattering theory describes the dominant scattering process of beam electrons at targets in the transmission electron microscope (TEM). Hence, practically every quantitative TEM study has to consider its ramifications, typically by some approximate modeling. Here, we elaborate on a hierarchy within the various approximations focusing on the two principal approaches used in practice, Bloch wave and multislice. We reveal characteristic differences in the capability of these methods to reproduce the correct local propagation of the wave function, while convergent results are obtained over larger propagation distances. We investigate the dependency of local variations of the wave function on the atomic number of the atomic scatterers and discuss their significance for, e.g., inelastic scattering.

Insights into the Geometric and Electronic Structure of Transition Metal Centers from Valence-to-Core X-ray Emission Spectroscopy

A long-standing goal of inorganic chemists is the ability to decipher the geometric and electronic structures of chemical species. This is particularly true for the study of small molecule and biological catalysts, where this knowledge is critical for understanding how these molecules effect chemical transformations. Numerous techniques are available for this task, and collectively they have enabled detailed understanding of many complex chemical systems. Despite this battery of probes, however, challenges still remain, particularly when the structural question involves subtle perturbations of the ligands bound to a metal center, as is often the case during chemical reactions. It is here that, as an emerging probe of chemical structure, valence-to-core (VtC) X-ray emission spectroscopy (XES) holds promise. VtC XES begins with ionization of a 1s electron from a metal ion by high energy X-ray photons. Electrons residing in ligand-localized valence orbitals decay to fill the 1s hole, emitting fluorescent photons in the process; in this manner, VtC XES primarily probes the filled, ligand-based orbitals of a metal complex. This is in contrast to other X-ray based techniques, such as K-edge X-ray absorption and EXAFS, which probe the unoccupied d-manifold orbitals and atomic scatterers surrounding the metal, respectively. As a hard X-ray technique, VtC XES experiments can be performed on a variety of sample states and environments, enabling application to demanding systems, such as high pressure cells and dilute biological samples. VtC XES thus can offer unique insights into the geometric and electronic structures of inorganic complexes. In recent years, we have sought to use VtC XES in the study of inorganic and bioinorganic complexes; doing so, however, first required a thorough and detailed understanding of the information content of these spectra. Extensive experimental surveys of model compounds coupled to the insights provided by DFT calculated spectra of real and hypothetical compounds allowed the development of a framework whereby VtC XES spectra may be understood in terms of a molecular orbital picture. Specifically, VtC spectra may be interpreted as a probe of electronic structure for the ligands bound to a metal center, enabling access to chemical information that can be difficult to obtain with other methods. Examples of this include the ability to (1) assess the identity and number of atomic/small molecule ligands bound to a metal center, (2) quantify the degree of bond activation of a small molecule substrate, and (3) establish the protonation state of donor atoms. With this foundation established, VtC has been meaningfully applied to long-standing questions in bioinorganic chemistry, with the potential for numerous future applications in all areas of metal-mediated catalysis.

Light transmission of the dense and cold atomic ensembles

On the basis of the general theoretical results developed previously (Sokolov et al 2011 J. Exp. Theor. Phys. 112 246) we calculate the light transmission coefficient of a disordered dense ensemble of motionless atomic scatterers. We analyze dependence of this coefficient on thickness of the ensemble as well as on frequency of the light. This analysis shows no manifestation of light localization effects, even in those parameter regimes where the Ioffe–Regel criterion of strong localization is satisfied. An analogous calculation made in the framework of scalar approximation when the vector character of light is neglected demonstrates strong localization under some conditions.

Multiple scattering of light in cold atomic clouds in a magnetic field

Starting from a microscopic theory for atomic scatterers, we describe the scattering of light by a single atom and study the coherent propagation of light in a cold atomic cloud in the presence of a magnetic field B in the mesoscopic regime. Non-pertubative expressions in B are given for the magneto-optical effects and optical anisotropy. We then consider the multiple scattering regime and address the fate of the coherent backscattering (CBS) effect. We show that, for atoms with nonzero spin in their ground state, the CBS interference contrast can be increased compared to its value when B=0, a result at variance with classical samples. We validate our theoretical results by a quantitative comparison with experimental data.

Coherent flash of light emitted by a cold atomic cloud

When a resonant laser sent on an optically thick cold atomic cloud is abruptly switched off, a coherent flash of light is emitted in the forward direction. This transient phenomenon is observed due to the highly resonant character of the atomic scatterers. We analyze quantitatively its temporal properties and show very good agreement with theoretical predictions. Based on complementary experiments, the phase of the coherent field is reconstructed without interferometric tools.

Quantitative study of two- and three-dimensional strong localization of matter waves by atomic scatterers

We study the strong localization of atomic matter waves in a disordered potential created by atoms pinned at the nodes of a lattice, for both three-dimensional (3D) and two-dimensional (2D) systems. The localization length of the matter wave, the density of localized states, and the occurrence of energy mobility edges (for the 3D system), are numerically investigated as a function of the effective scattering length between the atomic matter wave and the pinned atoms. Both positive and negative matter wave energies are explored. Interesting features of the density of states are discovered at negative energies, where maxima in the density of bound states for the system can be interpreted in terms of bound states of a matter wave atom with a few pinned atomic scatterers. In 3D we found evidence of up to three mobility edges, one at positive energies, and two at negative energies, the latter corresponding to transitions between extended and localized bound states. In 2D, no mobility edge is found, and a rapid exponential-like increase of the localization length is observed at high energy.

Scattering laser light on cold atoms: Toward multiple scattering signals from single-atom responses

We deduce the coherent backscattering signal from two distant laser-driven atoms using single-atom equations. In contrast to the standard master equation treatment, this new approach is suitable for the generalization to a large number of atomic scatterers.

Light Transport in Cold Atoms and Thermal Decoherence

We use the coherent backscattering interference effect to investigate experimentally and theoretically how coherent transport of light inside a cold atomic vapor is affected by the residual motion of atomic scatterers. As the temperature of the atomic cloud increases, the interference contrast decreases dramatically. This emphasizes the role of motion-induced decoherence for resonant scatterers even in the sub-Doppler regime of temperature. We derive analytical expressions for the corresponding coherence time.

Coherent backscattering of light with nonlinear atomic scatterers

We study coherent backscattering of a monochromatic laser by a dilute gas of cold two-level atoms in the weakly nonlinear regime. The nonlinear response of the atoms results in a modification of both the average field propagation (nonlinear refractive index) and the scattering events. Using a perturbative approach, the nonlinear effects arise from inelastic two-photon scattering processes. We present a detailed diagrammatic derivation of the elastic and inelastic components of the backscattering signal for both scalar and vectorial photons. In particular, we show that the coherent backscattering phenomenon originates in some cases from the interference between three different scattering amplitudes. This is in marked contrast with the linear regime where it is due to the interference between two different scattering amplitudes. In particular we show that, if elastically scattered photons are filtered out from the photodetection signal, the nonlinear backscattering enhancement factor exceeds the linear barrier of 2, consistently with a three-amplitude interference effect.

TheComputational Crystallography Toolbox: crystallographic algorithms in a reusable software framework

The advent of structural genomics initiatives has led to a pressing need for high-throughput macromolecular structure determination. To accomplish this, new methods and inevitably new software must be developed to accelerate the process of structure solution. To minimize duplication of effort and to generate maintainable code efficiently, a toolbox of basic crystallographic software components is required. The development of theComputational Crystallography Toolbox(cctbx) has been undertaken for this purpose. In this paper, the fundamental requirements for thecctbxare outlined and the decisions that have lead to its implementation are explained. Thecctbxcurrently contains algorithms for the handling of unit cells, space groups and atomic scatterers, and is released under an Open Source license to allow unrestricted use and continued development. It will be developed further to become a comprehensive library of crystallographic tools useful to the entire community of software developers.

Multiple scattering of light by atoms in the weak localization regime

Coherent backscattering is a multiple scattering interference effect which enhances the diffuse reflection off a disordered sample in the backward direction. Classically, the enhanced intensity is twice the average background under well chosen experimental conditions. We show how the quantum internal structure of atomic scatterers leads to a significantly smaller enhancement. Theoretical results for double scattering in the weak localization regime are presented which confirm recent experimental observations.

Kramers–Heisenberg and Weisskopf–Wigner descriptions of resonant X-ray Raman scattering

Abstract An overview is presented of the theory of X-ray Raman scattering as originally formulated by Kramers and Heisenberg and by Weisskopf and Wigner. Two particular aspects of the theory are described in some detail; the formation of band profiles and the role of symmetry. These aspects are discussed in connection with recent results for atomic and molecular scatterers obtained in radiative and nonradiative scattering experiments conducted with 2nd and 3rd generation synchrotron radiation sources.

Erratum: Relation between the electron scattering length and the van der Waals approximation to the equation of state

A theoretical relation between the electron scattering length and the van der Waals approximation to the equation of state is described. The theory provides a simple calculation for the scattering length of neutral atomic scatterers such as rare gases, using two experimental parameters: the hard-core radius (calculated from the van der Waals equation of state, using critical data) and the atomic polarizability. The results for the calculated electron scattering length agree with measured values derived either from the energy shifts of highly excited molecular Rydberg states, perturbed by He, Ne, Ar, Kr, and Xe, or from swarm electron cross-section data for the same gases.

Relation between the electron scattering length and the van der Waals approximation to the equation of state.

A theoretical relation between the electron scattering length and the van der Waals approximation to the equation of state is described. The theory provides a simple calculation for the scattering length of neutral atomic scatterers such as rare gases, using two experimental parameters: the hard-core radius (calculated from the van der Waals equation of state, using critical data) and the atomic polarizability. The results for the calculated electron scattering length agree with measured values derived either from the energy shifts of highly excited molecular Rydberg states, perturbed by He, Ne, Ar, Kr, and Xe, or from swarm electron cross-section data for the same gases.

Assessment of phase accuracy by cross validation: the free R value. Methods and applications.

Analogies between the free R statistic [Brünger (1992). Nature (London), 355, 472-474] and the statistical methods of cross validation and bootstrap are discussed. Several new applications which make use of the previously observed correlation between the free R value and the phase accuracy of crystal structures are presented. One application concerns the relative weighting of individual restraint classes in macromolecular refinement. The free R value provides an objective statistical basis for the optimal choice of the weights. The results for the refinement of a penicillopepsin crystal structure at 1.8 A resolution indicate that overall bond length and bond angle weights, derived from uncertainties observed in small-molecule crystal structures, appear to be transferable to macromolecules. In another application, the landscape of the R value around the crystal structure was investigated for unrestrained modeling of diffraction data with equal atomic scatterers. Others have suggested applications to ab initio phasing because of the simplicity of the liquid-like system of equal atomic scatterers. However, there are a large number of incorrect configurations of the scatterers whose R values at 1.8 A resolution are close to that of the correct configuration given by the positions of the non-hydrogen atoms in the penicillopepsin crystal structure. A substantial number of the incorrect configurations have higher free R values than the correct one. It is therefore conceivable that the free R value could be used as a selection criterion to distinguish between certain incorrect configurations and configurations close to the correct one.

Imaging Surface Atomic Structure by Means of Auger Electrons

Measurements of the complete angular distribution of Auger electrons emitted from well-defined platinum[111] single-crystal surfaces have led to the discovery that the distributions are composed of "silhouettes" of surface atoms "back lit" by emission from atoms deeper in the solid. Theoretical simulations of Auger electron angular distributions based upon atomic point emitters and spherical atomic scatterers of uniform cross section are in close agreement with these experimental results, but opposite to previous theoretical predictions. In view of the definitive results obtained and the straightforward agreement between theory and experiment, angular distribution Auger microscopy (ADAM) is useful for direct imaging of interfacial structure and investigation of electron-solid interactions in the physical and biological sciences and engineering. Applicability of ADAM is illustrated by images obtained for monolayers of silver and iodine on platinum[111].

Density effects on high-n molecular Rydberg states: CH3I and C6H6 in H2 and Ar

The absorption spectra of high-n Rydberg states of methyl iodide and benzene perturbed by varying number densities of hydrogen or argon, range 0.9×1020–10.5×1020 cm−3 for H2 and 0.6×1020–7.5×1020 cm−3 for Ar, have been investigated. The high-n molecular states of both absorbers were found to shift linearly with the number density of atomic Ar and molecular H2 scatterers. The Fermi formula modified by the Alekseev–Sobel’man polarization term provides an excellent fit of the shift data. The electron scattering lengths obtained are: 0.93 a0 for H2 and −1.63 a0 for Ar using the CH3I absorber; and 0.99 a0 for H2 and −1.57 a0 for Ar using the C6H6 absorber. The electron scattering lengths for H2 and Ar agree with the results of an empirical model that correlates scattering lengths and the polarizabilities α(spherical) for inert atoms and α2(nonspherical) for H2 molecule.