Atomic focusing and near field imaging: A combination for producing small-period nanostructures

We present a scheme which combines focusing of atomic de Broglie waves by standing light waves and fractional Talbot imaging to produce nanostructures. Masking of the incoming atomic wave by an absorptive grating is used to eliminate atom-optical aberrations that would otherwise wash out the fractional Talbot images. The scheme allows the creation of structures of very small feature size as well as small period. Received: 1 October 1999 / Revised version: 25 November 1999 / Published online: 21 January 2000     

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.     

On the Interference of Fullerenes and Other Massive Particles

We report the results of an optical analogue of the fullerene molecule diffraction experiment. Our results, and an analysis of the fullerene experiment, suggest that the patterns observed in the latter can be explained using a localized particle model. There is no evidence that the grating period contributed to the published fullerene diffraction pattern. De Broglie waves, if they exist, are unlikely to have played a significant part in the fullerene diffraction experiment. The observed patterns are not consistent with those expected according to wave theory for the experimental geometry corresponding to the slit-detector system and the de Broglie wavelength. The measurements were performed in the near field, making the demonstration of wave properties difficult. We outline a new classical approach to the electron and neutron interference experiments. The magnetic moment is crucial to this model, which emphasizes a mechanism for generating narrow-band continuum X-radiation. Some experiments are proposed which can decide between the suggested model and quantum mechanics, and which can also rule out an alternative stochastic model.     

Modelling the diffraction of laser-cooled atoms from magnetic gratings

The diffraction of laser-cooled atoms from a spatially-periodic potential is modelled using rigorous coupled-wave analysis. This numerical technique, normally applied to light-diffraction, is adapted for use with atomic de Broglie waves incident on a reflecting diffraction grating. The technique approximates the potential by a large number of constant layers and successively solves the complex eigenvalue problem in each layer, propagating the solution up to the surface of the grating. The method enables the diffraction efficiencies to be calculated for any periodic potential. The results from the numerical model are compared with the thin phase-grating approximation formulae for evanescent light-wave diffraction gratings and idealised magnetic diffraction gratings. The model is applied to the problem of diffracting Rb atoms from a grating made from an array of permanent magnets. Received 13 June 2000 and Received in final form 15 December 2000     

Causal interpretation and quantum phase space

We show that the de Broglie–Bohm interpretation can be easily implemented in quantum phase space through the method of quasi-distributions. This method establishes a connection with the formalism of the Wigner function. As a by-product, we obtain the rules for evaluating the expectation values and probabilities associated with a general observable in the de Broglie–Bohm formulation. Finally, we discuss some aspects of the dynamics.     

Evidence of wave-particle duality for single fast hydrogen atoms

We report the direct observation of interference effects in a Young's double-slit experiment where the interfering waves are two spatially separated components of the de Broglie wave of single 1.3 MeV hydrogen atoms formed close to either target nucleus in H++H2 electron-transfer collisions. Quantum interference strongly influences the results even though the hydrogen atoms have a de Broglie wavelength, lambda_{dB}, as small as 25 fm.     

Diffraction of metastable helium atoms by a transmission grating

We report on the diffraction of metastable helium atoms (de Broglie wavelength _dB 1Å) passing a free-standing gold grating with a periodicity of 0.5 m. The observed positions and intensities of the different diffraction peaks are in good agreement with a theoretical model for the grating shape. The overall transmission of the grating for the excited state atoms is about 30%, mainly determined by the grating geometry. Our result indicates that microfabricated transmission gratings can be used as efficient and coherent beam splitters for rare gas atoms in long-lived excited states. This fact offers interesting possibilities in view of atom interferometry with metastable noble gas atoms.     

Equivalent Forms of Dirac Equations in Curved Space-times and Generalized de Broglie Relations

One may ask whether the relations between energy and frequency and between momentum and wave vector, introduced for matter waves by de Broglie, are rigorously valid in the presence of gravity. In this paper, we show this to be true for Dirac equations in a background of gravitational and electromagnetic fields. We first transform any Dirac equation into an equivalent canonical form, sometimes used in particular cases to solve Dirac equations in a curved space-time. This canonical form is needed to apply Whitham’s Lagrangian method. The latter method, unlike the Wentzel–Kramers–Brillouin method, places no restriction on the magnitude of Planck’s constant to obtain wave packets and furthermore preserves the symmetries of the Dirac Lagrangian. We show by using canonical Dirac fields in a curved space-time that the probability current has a Gordon decomposition into a convection current and a spin current and that the spin current vanishes in the Whitham approximation, which explains the negligible effect of spin on wave packet solutions, independent of the size of Planck’s constant. We further discuss the classical-quantum correspondence in a curved space-time based on both Lagrangian and Hamiltonian formulations of the Whitham equations. We show that the generalized de Broglie relations in a curved space-time are a direct consequence of Whitham’s Lagrangian method and not just a physical hypothesis as introduced by Einstein and de Broglie and by many quantum mechanics textbooks.     

REPLY TO “COMMENT ON QUANTUM PHASE SHIFT CAUSED BY SPATIAL CONFINEMENT” BY M. PESHKIN

We describe a force-free phase shift due only to temporal geometric boundary conditions placed on a neutron de Broglie wave packet.     

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.     

De Broglie Matter Waves from the Linearized Einstein Field Equations

We suggest a connection between matter waves and gravitational waves. We find solutions of the linearized Einstein field equations in the form of de Broglie waves. These therefore acquire a new geometrical meaning.     

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.     

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.     

德布罗意物质波公式的建立

本文根据德布罗意在诺贝尔奖获奖典礼上的演讲稿“电子的波动性”的内容,系统介绍了德布罗意通过综合运用波动学、狭义相对论等的基本原理,一步步建立起了关于物质波理论的基本公式的过程,同时自然地引出了物质波的相速度和群速度,并清晰地阐明了它们对应的物理意义．     

Wave-particle dualism and the interpretation of quantum mechanics

The realist interpretations of quantum theory, proposed by de Broglie and by Bohm, are re-examined and their differences, especially concerning many-particle systems and the relativistic regime, are explored. The impact of the recently proposed experiments of Vigier et al. and of Ghose et al. on the debate about the interpretation of quantum mechanics is discussed. An indication of how de Broglie and Bohm would account for these experimental results is given.     

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.     

A particle-wave steering mechanism

A freely-moving electron cannot emit a photon, but it can emit a tachyon. If the momentum transfer in this process is small, then the tachyon travels forward at the de Broglie phase velocity. This suggests a particle-wave steering mechanism, with an exchange of momentum between the electron and its de Broglie phase wave. Using this steering mechanism, we calculate the electron trajectories in a virtual-double-slit experiment. These calculations demonstrate the distinction between channel trapping and channel focusing. The trajectories obtained here are different from the double-slit deterministic trajectories calculated using the de Broglie-Bohm quantum potential.