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arXiv:1304.0545 · Modern Physics Letters B

QUANTUM PARTICLES PASSING THROUGH A MATTER-WAVE APERTURE

Jianping Peng

Published Sep 16, 2013• 0 citations
arXivHTMLPDF

Abstract

In this paper, we investigate theoretically a dilute stream of free quantum particles passing through a macroscopic circular aperture of matter-waves and then moving in a space at a finite temperature, taking into account the dissipative coupling with the environment. The portion of particles captured by the detection screen is studied by varying the distance between the aperture and the screen. Depending on the wavelength, the temperature, and the dimension of the aperture, an unusual local valley-peak structure is found in increasing the distance, in contrast to traditional thinking that it decreases monotonically. The underlying mechanism is the nonlocality in the process of decoherence for an individual particle.

DOI
10.1142/s0217984913501881

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In this paper, we investigate theoretically a dilute stream of free quantum particles passing through a macroscopic circular aperture of matter-waves and then moving in a space at a finite temperature, taking into account the dissipative coupling with the environment. The portion of particles captured by the detection screen is studied by varying the distance between the aperture and the screen. Depending on the wavelength, the temperature, and the dimension of the aperture, an unusual local valley-peak structure is found in increasing the distance, in contrast to traditional thinking that it decreases monotonically. The underlying mechanism is the nonlocality in the process of decoherence for an individual particle.
Quantum physics rules the dynamics of small objects as they interact over microscopic length scales. Nevertheless, quantum correlations involving macroscopic distances can be observed between entangled photons as well as in atomic gases and matter waves at low temperatures. The long-range nature of the electromagnetic coupling between charged particles and extended objects could also trigger quantum phenomena over large distances. Here, we reveal a manifestation of quantum mechanics that involves macroscopic distances and results in a nearly complete depletion of coherence associated with which-way free-electron interference produced by electron-radiation coupling in the presence of distant extended objects. This is a ubiquitous effect that we illustrate through a rigorous theoretical analysis of a two-path electron beam interacting with a semi-infinite metallic plate and find the inter-path coherence to vanish proportionally to the path separation at zero temperature and exponentially at finite temperature. The investigated regime of large distances originates in the coupling of the electron to radiative modes assisted by diffraction at material structures but without any involvement of material excitations. Besides the fundamental interest of this macroscopic quantum phenomenon, our results suggest an approach to measuring the vacuum temperature and nondestructively sensing the presence of distant objects.
The coherence of free electrons sets fundamental limits on the resolution and contrast of phase-sensitive electron microscopy because coherence is lost whenever the electron leaves a distinguishing excitation in its environment. We develop a quantitative theory of fast-electron decoherence in two canonical geometries: a cylindrical hole drilled through a realistic metal and a circular aperture in a thin perfectly conducting film. By combining an electromagnetic Green-tensor formulation with the fluctuation--dissipation theorem while fully retaining retardation, we obtain the decoherence probability and elastic phase as functions of the electron trajectory, temperature, and material response. For the cylindrical hole, we obtain a closed-form, azimuthally resolved expression that separates the dependences on path position, temperature, and conductivity. In the high-conductivity and high-temperature limits, this result reduces to a universal expression that is linear in temperature and independent of both conductivity and electron velocity. For the circular aperture, which we solve using a cylindrical-wave modal expansion, the energy-loss probability diverges as 1/ω1/ω1/ω at low frequency, whereas the decoherence probability remains finite and reaches a maximum when the aperture radius is comparable to the relevant electromagnetic wavelength. Because the interaction is spatially localized, aperture-induced decoherence is generally weaker than that produced by a cylindrical hole, except for sufficiently large apertures at high temperature. Finally, we show that, for sufficiently large holes, decoherence can dominate the spatial broadening of a focused electron probe and must therefore be incorporated into the design of coherent electron-beam instruments.
Starting from the circular aperture diffraction experiment, this paper decomposes the intrinsic interactions underlying wave–particle duality and proposes a specific interaction force: the velocity-perpendicular interaction force. We derive the characterization formula of this force and show that it can induce the phenomenon of circular aperture diffraction of light, with the theoretical results being highly consistent with those calculated by the Huygens–Fresnel principle. The direction of this force is perpendicular to the relative velocity, originating from the coupling effect between the wave nature of light and the particle nature of the circular aperture structure, and it satisfies a modified inverse square law of distance related to the relative velocity. When photons pass through different positions of the circular aperture, the symmetry effect generates a net interaction time. The product of the main component of this force, the net interaction time, and the radius of the circular aperture constitutes a modulation quantity (a ratio of the Planck’s constant), which exerts an on–off modulation effect on the interaction force, thereby inducing the emergence of annular diffraction fringes. This study provides a novel physical interpretation for the circular aperture diffraction of light from the perspective of interaction forces and clarifies the possible existence form of wave–matter interaction forces. This force formula is expected to effectively describe the behavior of microscopic particles, just like the Schrödinger equation, while providing a brand-new perspective on interactions. It holds great application prospects in fields such as single-photon manipulation and quantum precision measurement.