Matter-wave Diffraction Research Articles

Comprehensive peak-width analysis in matter-wave diffraction under grazing incidence conditions

Comprehensive peak-width analysis in matter-wave diffraction under grazing incidence conditions

Quantum description of atomic diffraction by material nanostructures

We present a theoretical model of matter-wave diffraction through a material nanostructure. This model is based on the numerical solution of the time-dependent Schrödinger equation, which goes beyond the standard semiclassical approach. In particular, we consider the dispersion force interaction between the atoms and the material, which is responsible for high energy variations. The effect of such forces on the quantum model is investigated, along with a comparison with the semiclassical model. In particular, for atoms at low velocity and close to the material surface, the semiclassical approach fails, while the quantum model accurately describes the expected diffraction pattern. This description is thus relevant for slow and cold atom experiments where increased precision is required, e.g., for metrological applications. Published by the American Physical Society 2024

Low-energy scattering of ultracold atoms by a dielectric nanosphere

We theoretically study the low-energy scattering of ultracold atoms by a dielectric nanosphere of silica glass levitated in a vacuum. The atom and dielectric surface interact via dispersion force of which strength sensitively depends on the polarizability, dielectric function, and geometry. For cesium and rubidium atoms, respectively, we compute the atom-surface interaction strength and characterize the stationary scattering states by taking adsorption of the atoms onto the surface into account. As the energy of the incoming atoms is lowered, we find that differences between quantum and classical scatterings emerge in two steps. First, the quantum-mechanical differential cross section of the elastic scattering starts to deviate from the classical one at an energy scale comparable to a few microkelvin in units of temperature due to the de Broglie matter-wave diffraction. Second, the differences are found in the cross sections in a regime lower than a few nanokelvin, where the classically forbidden reflection occurs associated with the $s$-wave scattering and the discrete nature of angular momentum. We also study the dependencies of quantum and classical scattering properties on the radius of the nanosphere. This paper paves the way to identify the quantum regime and to understand the physical origin of quantum effects in the collisions between a nanoparticle and environmental gas over various temperatures.

Magic Numbers in Boson 4He Clusters: The Auger Evaporation Mechanism.

The absence of magic numbers in bosonic 4He clusters predicted by all theories since 1984 has been challenged by high-resolution matter-wave diffraction experiments. The observed magic numbers were explained in terms of enhanced growth rates of specific cluster sizes for which an additional excitation level calculated by diffusion Monte Carlo is stabilized. The present theoretical study provides an alternative explanation based on a simple independent particle model of the He clusters. Collisions between cluster atoms in excited states within the cluster lead to selective evaporation via an Auger process. The calculated magic numbers as well as the shape of the number distributions are in quite reasonable agreement with the experiments.

Superpositions of Chiral Molecules

Matter-wave diffraction can put chiral molecules into superpositions of left- and right-handed forms, enabling new studies of how the two states interact with their environment.

Enantiomer Superpositions from Matter-Wave Interference of Chiral Molecules

Molecular matter-wave interferometry enables novel strategies for manipulating the internal mechanical motion of complex molecules. Here, we show how chiral molecules can be prepared in a quantum superposition of two enantiomers by far-field matter-wave diffraction and how the resulting tunneling dynamics can be observed. We determine the impact of rovibrational phase averaging and propose a setup for sensing enantiomer-dependent forces, parity-violating weak interactions, and environment-induced superselection of handedness, as suggested to resolve Hund’s paradox. Using ab initio tunneling calculations, we identify [4]-helicene derivatives as promising candidates to implement the proposal with state-of-the-art techniques. This work opens the door for quantum sensing with chiral molecules.Received 20 January 2021Revised 4 June 2021Accepted 14 July 2021DOI:https://doi.org/10.1103/PhysRevX.11.031056Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article’s title, journal citation, and DOI.Published by the American Physical SocietyPhysics Subject Headings (PhySH)Research AreasChiralityCold atoms & matter wavesQuantum opticsQuantum sensingPhysical SystemsAtomic & molecular beamsMoleculesTechniquesAb initio calculationsDensity functional theoryInterferometryQuantum chemistry methodsQuantum master equationAtomic, Molecular & OpticalQuantum InformationCondensed Matter, Materials & Applied Physics

Diffraction in time in the relativistic domain

The diffraction of matter waves in time is investigated by using the kinetic energy based relativistic wave equation for the quantum shutter problem. The differential equation is solved with the aid of the Fourier integral transform according to the spatial coordinate. A new Green’s function is obtained and a scattering integral is composed for the wave function. The boundary condition of the quantum shutter problem is expressed in the kernel of the integral. Two field components are derived by the asymptotic evaluation of the scattering integral. The behavior of the scattered matter waves is studied in the relativistic and non-relativistic domains numerically.

Anomalous diffraction of matter waves with minimal quantum metasurfaces

In the last few years, there is a huge upsurge in the number of closed deals regarding quantum technologies for materials, computing, communication and instrumentation. Such a trend has inevitably affected the research funding market; thus, large state initiatives are taken that are directly expected to drive the formulation of novel research concepts and the development of quantum device prototypes from sensors and circuitry to quantum memory and repeaters. A fundamental operation behind all these applications is the effective steering of electrons, constituting matter waves, along specific directions and with certain magnitudes, due to development of various reflective and refractive orders. The objective of this study is to optimize the simplest structure that supports such anomalous diffraction, namely a quantum metasurface comprising cylindrical rods embedded in suitable crystalline matter. Several highly-performing designs from these minimal setups are proven to work exceptionally as multiport components, employable to a variety of quantum engineering implementations.

Role of wavefront and velocity distribution with magnetic lens on matter-wave diffraction in near-field regime

Near-field diffraction has been widely studied and applied in many research fields including optics, quantum mechanics and sensor technology. High accuracy sensors, for instance, have been developed based on the Talbot effect, i.e., the self-imaging effect, due to the high sensitivity of the near-field diffraction pattern. Since the visibility of the diffraction pattern depends intensively on velocity distribution and wavefront of the incoming wave, the Talbot-Lau effect is generally used to improve the spatial coherence of the incident wave and hence a better fringe contrast. This research aims to investigate the influences of the wavefront spreading out radially involving the Gaussian velocity distribution on the diffraction pattern of a matter-wave which are key points in design optimization and development of tools for improving fringe quality. The probability density to find the particles in the Talbot-Lau interference pattern can be obtained by employing Feynman path integrals. The theoretical simulation results show that the alteration of wavefront leads to changes in fringe contrast and the width of fringe peaks, whereas the velocity distribution affects only the fringe visibility.

Experimental test of Babinet's principle in matter-wave diffraction.

We report on an experimental test of Babinet's principle in quantum reflection of an atom beam from diffraction gratings. The He beam is reflected and diffracted from a square-wave grating at near grazing-incidence conditions. According to Babinet's principle the diffraction peak intensities (except for the specular-reflected beam) are expected to be identical for any pair of gratings of complementary geometry. We observe conditions where Babinet's principle holds and also where it fails. Our data indicate breakdown conditions when either the incident or a diffracted beam propagates close to the grating surface. At these conditions, the incident or the diffracted He beam is strongly affected by the dispersive interaction between the atoms and the grating surface. Babinet's principle is also found to break down, when the complementary grating pair shows a large asymmetry in the strip widths. For very small strip widths, edge diffraction from half planes becomes dominant, whereas for the complementary wide strips the atom-surface interactions leads to a strong reduction of all non-specular diffraction peak intensities.

Position measurement-induced collapse states and boundary bound diffraction: an idealised experiment

In an earlier work, it was shown that single-slit diffraction of matter waves can be considered as position measurement of particles and that the Fresnel and Fraunhofer diffraction patterns result from the time evolution of the same collapsed quantum wave function. This quantum mechanical treatment of diffraction of particles, based on the standard postulates of quantum mechanics and the postulate of existence of quantum trajectories, leads to the ‘position measurement-induced collapse’ (PMIC) states. In the present work, an idealised experimental set-up to test these PMIC states is proposed. The apparatus consists of a modified Lloyd’s mirror in optics, with two reflectors instead of one. The diffraction patterns for this case predicted by the PMIC formalism are presented. They exhibit quantum fractal structures in space-time called ‘quantum carpets’, first discovered by Berry. The PMIC formalism in this case closely follows the ‘boundary bound diffraction’ analysed in a previous work by Tounli, Alverado and Sanz. In addition to having obtained their results, we have identified that the Fresnel and Fraunhofer patterns are indeed present here. It is anticipated that the verification of fractal and nonfractal features of the wave function at various times and also the predicted revival distances to the screen by this experiment will help to better understand ‘quantum collapse’.

Observing Localization in a 2D Quasicrystalline Optical Lattice.

Quasicrystals are long-range ordered but not periodic, representing an interesting middle ground between order and disorder. We experimentally and numerically study the localization transition in the ground state of noninteracting and weakly interacting bosons in an eightfold symmetric quasicrystalline optical lattice. In contrast to typically used real space insitu techniques, we probe the system in momentum space by recording matter wave diffraction patterns. Shallow lattices lead to extended states whereas we observe a localization transition at a critical lattice depth of V_{0}≈1.78(2)E_{rec} for the noninteracting system. Our measurements and Gross-Pitaevskii simulations demonstrate that in interacting systems the transition is shifted to deeper lattices, as expected from superfluid order counteracting localization. Quasiperiodic potentials, lacking conventional rare regions, provide the ideal testing ground to realize many-body localization in 2D.

Signature of Short-Range van der Waals Forces Observed in Poisson Spot Diffraction with Indium Atoms.

The phase of de Broglie matter waves is a sensitive probe for small forces. In particular, the attractive van der Waals force experienced by polarizable atoms in the close vicinity of neutral surfaces is of importance in nanoscale systems. It results in a phase shift that can be observed in matter-wave diffraction experiments. Here, we observe Poisson spot diffraction of indium atoms at submillimeter distances behind spherical submicron silicon dioxide particles to probe the dispersion forces between atoms and the particle surfaces. We compare the measured relative intensity of Poisson's spot to theoretical results derived from first principles in an earlier communication and find a clear signature of the atom-surface interaction.

Spatial coherence of a strongly interacting Bose gas in the trimerized kagome lattice

We produce a trimerized kagome lattice for ultracold atoms using an optical superlattice formed by overlaying triangular lattices generated with two colors of light at a 2:1 wavelength ratio. Adjusting the depth of each lattice tunes the strong intra-trimer (J) and weak inter-trimer (J') tunneling energies, and also the on-site interaction energy U. Two different trimerization patterns are distinguished using matter-wave diffraction. We characterize the coherence of a strongly interacting Bose gas in this lattice, observing persistent nearest-neighbor spatial coherence in the large U/J' limit, and that such coherence displays asymmetry between the strongly and the weakly coupled bonds.

Matter-wave interferometry from near-field to far-field diffraction

A simplified explanation of near-field and far-field diffraction with matter-wave is described using the path integral formulation. Our approach is demonstrated with cold Rb atoms in single-, double-, and multiple-slit configurations. With the use of an initial wave for the particle beam that corresponds to the slit opening and the number of slits, the transition from near-field to far-field diffraction can also be explored. Identifying the boundary between near-field and far-field diffraction is the first priority for implementing matter-wave diffraction experiments.

Matter-Wave Diffraction from a Quasicrystalline Optical Lattice.

Quasicrystals are long-range ordered and yet nonperiodic. This interplay results in a wealth of intriguing physical phenomena, such as the inheritance of topological properties from higher dimensions, and the presence of nontrivial structure on all scales. Here, we report on the first experimental demonstration of an eightfold rotationally symmetric optical lattice, realizing a two-dimensional quasicrystalline potential for ultracold atoms. Using matter-wave diffraction we observe the self-similarity of this quasicrystalline structure, in close analogy to the very first discovery of quasicrystals using electron diffraction. The diffraction dynamics on short timescales constitutes a continuous-time quantum walk on a homogeneous four-dimensional tight-binding lattice. These measurements pave the way for quantum simulations in fractal structures and higher dimensions.

Mechanical diffraction reveals the role of passive dynamics in a slithering snake

Limbless animals like snakes inhabit most terrestrial environments, generating thrust to overcome drag on the elongate body via contacts with heterogeneities. The complex body postures of some snakes and the unknown physics of most terrestrial materials frustrates understanding of strategies for effective locomotion. As a result, little is known about how limbless animals contend with unplanned obstacle contacts. We studied a desert snake, Chionactis occipitalis, which uses a stereotyped head-to-tail traveling wave to move quickly on homogeneous sand. In laboratory experiments, we challenged snakes to move across a uniform substrate and through a regular array of force-sensitive posts. The snakes were reoriented by the array in a manner reminiscent of the matter-wave diffraction of subatomic particles. Force patterns indicated the animals did not change their self-deformation pattern to avoid or grab the posts. A model using open-loop control incorporating previously described snake muscle activation patterns and body-buckling dynamics reproduced the observed patterns, suggesting a similar control strategy may be used by the animals. Our results reveal how passive dynamics can benefit limbless locomotors by allowing robust transit in heterogeneous environments with minimal sensing.

Matter-Wave Diffraction from a Periodic Array of Half Planes.

We report on reflection and diffraction of beams of He and D_{2} from square-wave gratings of a 400-μm period and strip widths ranging from 10 to 200 μm at grazing-incidence conditions. In each case we observe fully resolved matter-wave diffraction patterns including the specular reflection and diffracted beams up to the second diffraction order. With decreasing strip width, the observed diffraction efficiencies exhibit a transformation from the known regime of quantum reflection from the grating strips to the regime of edge diffraction from a half-plane array. The latter is described by a single-parameter model developed previously to describe phenomena as diverse as quantum billiards, scattering of radio waves in urban areas, and reflection of matter waves from microstructures. Our data provide experimental confirmation of the widespread model. Moreover, our results demonstrate that neither classical reflection nor quantum reflection are essential for reflective diffraction of matter waves from a structured solid, but it can result exclusively from half-plane edge diffraction.

A study of matter-wave diffraction for particle in the near field regime under the influence of a uniform electric field

For various experiments to investigate quantum effects, matter-wave diffraction is an apparent example. Particle diffractions have been measured even at the large molecular level, such as the C60 molecules. In order to describe the matter-wave diffraction of C60 beam, we assume the initial wave functions behind a grating in form of the Fourier series with a Gaussian distribution function. By applying the Feynman path integral, the exact wave functions of the molecule diffraction in the near-field regime can be derived analytically. The obtained probability density distributions are corresponding to interference fringes as found in the Fresnel diffraction. The probability of finding C60 molecules, behind the grating at the Talbot length, consistency with the mentioned experimental data of C60 diffractions.

Matter-wave diffraction approaching limits predicted by Feynman path integrals for multipath interference

Matter-wave diffraction approaching limits predicted by Feynman path integrals for multipath interference