Diffraction of fast atomic projectiles during grazing scattering from a LiF(001) surface

Light atoms and molecules with energies from 300 eV to 25 keV are scattered under a grazing angle of incidence from a LiF(001) surface. For impact of neutral projectiles along low index directions for strings of atoms in the surface plane we observe a defined pattern of intensity spots in the angular distribution of reflected particles which is consistently described using concepts of diffraction theory and specific features of grazing scattering of atoms from insulator surfaces. Experimental results for scattering of H, D, 3He, and 4He atoms as well as H2 and D2 molecules can be unequivocally referred to atom diffraction with de Broglie wavelengths as low as about 0.001 Angstroms.     

High-order Talbot fringes for atomic matter waves

We observe the interference of de Broglie waves in the diffraction near field of a microfabricated grating. The reduction of the grating period by self-imaging of second to seventh order is spatially resolved. We investigate the dependence of this effect on the de Broglie wavelength by a time-to-flight technique.     

Measurement of the photonic de broglie wavelength of entangled photon pairs generated by spontaneous parametric down-conversion

Using a basic Mach-Zehnder interferometer, we demonstrate experimentally the measurement of the photonic de Broglie wavelength of entangled photon pairs (biphotons) generated by spontaneous parametric down-conversion. The observed interference manifests the concept of the photonic de Broglie wavelength. We also discuss the phase uncertainty obtained from the experiment.     

Observation of atom wave phase shifts induced by van der Waals atom-surface interactions

The development of nanotechnology and atom optics relies on understanding how atoms behave and interact with their environment. Isolated atoms can exhibit wavelike (coherent) behavior with a corresponding de Broglie wavelength and phase which can be affected by nearby surfaces. Here an atom interferometer is used to measure the phase shift of Na atom waves induced by the walls of a 50 nm wide cavity. To our knowledge this is the first direct measurement of the de Broglie wave phase shift caused by atom-surface interactions. The magnitude of the phase shift is in agreement with that predicted by Lifshitz theory for a nonretarded van der Waals interaction. This experiment also demonstrates that atom waves can retain their coherence even when atom-surface distances are as small as 10 nm.     

Wave nature of biomolecules and fluorofullerenes

We demonstrate quantum interference for tetraphenylporphyrin, the first biomolecule exhibiting wave nature, and for the fluorofullerene C60F48 using a near-field Talbot-Lau interferometer. For the porphyrins, which are distinguished by their low symmetry and their abundant occurrence in organic systems, we find the theoretically expected maximal interference contrast and its expected dependence on the de Broglie wavelength. For C60F48, the observed fringe visibility is below the expected value, but the high contrast still provides good evidence for the quantum character of the observed fringe pattern. The fluorofullerenes therefore set the new mark in complexity and mass (1632 amu) for de Broglie wave experiments, exceeding the previous mass record by a factor of 2.     

De Broglie waves and the nature of mass

In this paper an attempt is made to interpret inertial mass as a consequence of the invariant periodicity associated with physical de Broglie waves. In the case of a free particle, such waves, observed from an arbitrary reference frame, would exhibit the velocity-dependent wavelength given by de Broglie's relation; and it is conjectured that the inertial and additive properties of mass (or, more precisely, the conservation of momentum and energy) can be related to nonlinear interference effects occurring between the de Broglie waves for different particles. This picture could throw light on the physical meaning of quantization and suggests the possibility of reformulating classical and quantum mechanics in terms of a quasi-classical nonlinear field theory in which both inertial and quantization effects result essentially from the periodicity of de Broglie waves.     

Interference effects on the photoionization cross sections between two neighbouring atoms: nitrogen as an example

Interference effects on the photoionization cross sections between two neighbouring atoms are considered based on the coherent scattering of the ionized electrons by the two nuclei when their separation is less than or comparable to the de Broglie wave length of the ionized electrons. As an example, the single atomic nitrogen ionization cross section and the total cross sections of two nitrogen atoms with coherently added photoionization amplitudes are calculated from the threshold to about 60~\AA (1~\AA=0.1~nm) of the photon energy. The photoionization cross sections of atomic nitrogen are obtained by using the close-coupling R-matrix method. In the calculation 19 states are included. The ionization energy of the atomic nitrogen and the photoionization cross sections agree well with the experimental results. Based on the R-matrix results of atomic nitrogen, the interference effects between two neighbouring nitrogen atoms are obtained. It is shown that the interference effects are considerable when electrons are ionized just above the threshold, even for the separations between the two atoms are larger than two times of the bond length of N₂ molecules. Therefore, in hot and dense samples, effects caused by the coherent interference between the neighbours are expected to be observable for the total photoionization cross sections.     

Four-photon interference with asymmetric beam splitters

Two experiments of four-photon interference are performed with two pairs of photons from parametric downconversion with the help of asymmetric beam splitters. The first experiment is a generalization of the Hong-Ou-Mandel interference effect to two pairs of photons while the second one utilizes this effect to demonstrate a four-photon de Broglie wavelength of lambda/4 by projection measurement.     

Propagation of cold atoms along a miniature magnetic guide

A cloud of laser-cooled 85Rb atoms is coupled through a magnetic funnel into a miniature waveguide formed by four current-carrying wires embedded in a silica fiber. The atom cloud has a approximately 100 &mgr;m radius within the fiber and propagates over cm distances. We study the coupling, propagation, and transverse distribution of atoms in the fiber, and find good agreement with theory. This prototype demonstrates the feasibility of miniature guides as a tool in the new field of integrated atom optics, leading to single-mode propagation of de Broglie waves and the possible preparation of 1D atom clouds.     

Resonant transmission of cold atoms through subwavelength apertures

Recently, it has been observed that transmission of light through subwavelength apertures, which is usually negligible, can be significantly enhanced when surface plasmons are resonantly excited. Here we introduce the idea that similar effects can be expected for cold atoms in structures supporting surface matter waves. We show that surface matter waves are possible in properly designed structures, and then we theoretically demonstrate 100% transmission of rubidium atoms through an array of slits much narrower than the de Broglie wavelength of the atoms. Our results open up the possibility of using surface matter waves to control the flow of neutral atoms.     

Electron transfer in proton-hydrogen collisions in dense semi-classical hydrogen plasma

Quantum mechanical calculations have been accomplished to study the dynamics of the reaction: p + H(1s) → H(nlm) + p in dense semi-classical hydrogen plasma. Interactions among the charged particles in plasma are represented by a pseudopotential which takes care of the collective effects at large distances and quantum effect of diffraction at small distances. Various capture cross sections are computed for the incident proton energy lying within 10 to 500 keV by applying a distorted wave method which uses a variationally determined closed-form wave function of hydrogen atom. Moreover, an inclusive study is made to explore the effects of screening of plasma and quantum diffraction on various capture cross sections for a wide range of thermal Debye length and de Broglie wave length. It has been found that various cross sections suffer considerable changes due to varying Debye length and de Broglie wave length.     

Controlling two-center interference in molecular high harmonic generation

We experimentally investigate the process of intramolecular quantum interference in high-order harmonic generation in impulsively aligned CO2 molecules. The recombination interference effect is clearly seen through the order dependence of the harmonic yield in an aligned sample. The experimental results can be well modeled assuming that the effective de Broglie wavelength of the returning electron wave is not significantly altered by the Coulomb field of the molecular ion. We demonstrate that such interference effects can be effectively controlled by changing the ellipticity of the driving laser field.     

A Case for Lorentzian Relativity

The Lorentz transformation (LT) is explained by changes occurring in the wave characteristics of matter as it changes inertial frame. This explanation is akin to that favoured by Lorentz, but informed by later insights, due primarily to de Broglie, regarding the underlying unity of matter and radiation. To show the nature of these changes, a massive particle is modelled as a standing wave in three dimensions. As the particle moves, the standing wave becomes a travelling wave having two factors. One is a carrier wave displaying the dilated frequency and contracted ellipsoidal form described by the LT, while the other (identified as the de Broglie wave) is a modulation defining the dephasing of the carrier wave (and thus the failure of simultaneity) in the direction of travel. The superluminality of the de Broglie wave is thus explained, as are several other mysterious features of the optical behaviour of matter, including the physical meaning of the Schrödinger equation and the relevance to scattering processes of the de Broglie wave vector. Consideration is given to what this Lorentzian approach to relativity might mean for the possible existence of a preferred frame and the origin of the observed Minkowski metric.     

A nondispersive de Broglie wave packet

It is assumed that the motion of a particle in spacetime does not depend on the motion relative to it of any observer or of any frame of reference. Thus if the particle has an internal vibration of the type hypothesized by de Broglie, the phase of that vibration at any point in spacetime must appear to be the same to all observers, i.e., the same in all frames of reference. Each observer or reference frame will have its own de Broglie wave for the particle. The phase of the particle's vibration must, by definition, be the same as that of all possible de Broglie waves at the point where the particle is. By superimposing all these possible de Broglie waves, a wave packet is formed centered in space on the particle. The formation of such a packet is discussed with the help of spacetime diagrams; the packet does not spread with time. The relevance of this packet to the wave mechanics of Schrödinger is discussed; it is also pointed out that any vibration can lead to such a packet.     

Quantum Carpets: a Probe to Identify Wave-Packet Fractional Revivals

We explain quantum carpets in the position and momentum spaces woven by the self-interference of the de Broglie wave of an atom or an electron trapped in an infinitely deep potential well. The recurrence of self-similar structures in designs of these carpets mimics the phenomena of quantum revivals and fractional revivals. We identify fractional revivals of various order by means of these space–time and momentum–time interference patterns.     

Decoherence in a Talbot–Lau interferometer: the influence of molecular scattering

This work describes the interference of C₇₀ fullerenes in a Talbot–Lau interferometer with a large separation between the diffraction gratings. This permits the observation of recurrences of the interference contrast both as a function of the de Broglie wavelength and in dependence of the interaction of background gases. An exponential decrease of the fringe visibility with increasing background pressure was observed and good quantitative agreement with the predictions of decoherence theory was found. From extrapolation of the limits of matter wave interferometry it can be concluded that the influence of collisional decoherence may be well under control in future experiments with proteins and even larger objects. PACS 03.75.-b; 03.65.Yz; 39.20.+q     

Quantum scattering of fast atoms and molecules on surfaces

We present evidence for the diffraction of light keV atoms and molecules grazingly scattered on LiF(001) and NaCl(001) surfaces. At such energies, the de Broglie wavelength is 2 orders of magnitude smaller that the mean thermal atomic displacement in the crystal. Thus, no coherent scattering was expected and interaction of keV atoms with surfaces is routinely treated with classical mechanics. We show here that well-defined diffraction patterns can be observed indicating that, for grazing scattering, the pertinent wavelength is that associated with the slow motion perpendicular to the surface. The experimental data are well reproduced by an ab initio calculation.     

Quantum-optical predictions for an experiment on the de Broglie waves detection

An experimental apparatus to detect de Broglie waves is discussed. The wave packets of two photons generated in the parametric-down conversion are overlapped in a modified Mach-Zehnder interferometer. The coincidence photodetection rate of photon pairs is evaluated, as a function of path-length of two interferometer arms, both by using the de Broglie concept of a real quantum wave and by the quantum optical approach. The different results of these two theories are compared, and it is shown that the proposed experiment can disprove either the theories.     

Theory of cooling by flow through narrow pores

We consider the possibility of adding a stage to a dilution refrigerator to provide additional cooling by "filtering out" hot atoms. Three methods are considered: (1) effusion, where holes having diameters larger than a mean-free path allow atoms to pass through easily; (2) particle waveguidelike motion using very narrow channels that greatly restrict the quantum states of the atoms in a channel; (3) wall-limited diffusion through channels, in which the wall scattering is disordered so that local density equilibrium is established in a channel. We assume that channel dimensions are smaller than the mean-free path for atom-atom interactions. The particle waveguide and the wall-limited diffusion methods using channels on order of the de Broglie wavelength give cooling. Recent advances in nanofilters give this method some hope of being practical.     

Observation of atom pairs in spontaneous four-wave mixing of two colliding Bose-Einstein condensates

We study atom scattering from two colliding Bose-Einstein condensates using a position sensitive, time resolved, single atom detector. In analogy to quantum optics, the process can also be thought of as spontaneous, degenerate four-wave mixing of de Broglie waves. We find a clear correlation between atoms with opposite momenta, demonstrating pair production in the scattering process. We also observe a Hanbury Brown-Twiss correlation for collinear momenta, which permits an independent measurement of the size of the pair production source and thus the size of the spatial mode. The back-to-back pairs occupy very nearly two oppositely directed spatial modes, a promising feature for future quantum optics experiments.