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Physical review. B./Physical review. B

Maximal quantum scattering by homogeneous spherical inclusions

Constantinos A. Valagiannopoulos

Published Jul 18, 2019• 13 citations
Publisher

Abstract

Scattering of matter waves, present at multiple quantum setups, is required to be maximized in several applications from sensing and imaging to quantum switching and memory. The simplest case of a homogeneous spherical scatterer is rigorously solved and optimized with respect to its size, texture, and background by considering the effective quantum properties from a long directory of materials. In this context, several alternative layouts with maximal scattering efficiency are proposed, offering additional degrees of freedom in design without requirements for careful engineering of quantum texture. Many of the reported inclusions exhibit substantial selectivity in their scattering response, admitting them to operate as sharp filters for particle energies or sensitive detectors of electron beams.

DOI
10.1103/physrevb.100.035308

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Scattering of matter waves, present at multiple quantum setups, is required to be maximized in several applications from sensing and imaging to quantum switching and memory. The simplest case of a homogeneous spherical scatterer is rigorously solved and optimized with respect to its size, texture, and background by considering the effective quantum properties from a long directory of materials. In this context, several alternative layouts with maximal scattering efficiency are proposed, offering additional degrees of freedom in design without requirements for careful engineering of quantum texture. Many of the reported inclusions exhibit substantial selectivity in their scattering response, admitting them to operate as sharp filters for particle energies or sensitive detectors of electron beams.
Selecting the quantum signals with respect to features like direction of propagation or impinging energy makes a ubiquitous operation that is employed in a variety of quantum engineering applications. The conditions for optimally selective angular and energy filtering via homogeneous planar inclusions are determined and the derived designs exhibit substantial robustness with respect to fabrication defects. The reported findings may open new uncharted directions towards the efficient design of integrated devices exploiting quantum filtering from sharp sensors and tuners to multiport networks and quantum circuits.
A cornerstone in the operation of numerous detecting and sensing quantum setups is the sharp change in the response once a condition ceases to be effective; this regime is typically realized by perfectly cloaking a nanoinclusion from the propagating matter waves. Such a purpose is found well-served by optimally sized nanocylinders, embedded into a suitable quantum texture, that efficiently hide themselves from obliquely impinging electron beams. The optimal designs exhibit high selectivity for particle energies while being wideband with respect to incidence angles; these features render them deployable in various quantum devices from furtive sensors and detectors to quantum switches and matter-wave filters.
Abstract 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.
Synopsis: Students are introduced to the ideas of particle scattering in quantum mechanics in a one-dimensional context. ƒe integral Schrödinger equation is deduced using a Wronskian technique, and reflection and transmission amplitudes are defined. Several simple scattering problems are solved, and the Born series for the energy-wave function is explained. A three-dimensional spherical basis is introduced, which allows the integral Schrödinger equation in this context to be formulated. ƒe relation between plane waves and spherical waves is found from a solution to the unit-source Helmholtz equation, again using the Wronskian technique. Partial waves, phase shifts, and cross sections are defined, and finite range scattering is considered. ƒe chapter concludes with a consideration of identical particle scattering and an application to the protonproton case, where a dramatic manifestation of the underlying substructure emerges at high energies.
Exploiting quantum mechanics for sensing offers unprecedented possibilities. State-of-the-art proposals for novel quantum sensors often rely on the creation of large superpositions and generally detect a field. However, what is the optimal superposition size for detecting an incident particle from a specific direction? This question is nontrivial as, in general, this incident particle will scatter off with varied momenta, imparting varied recoils to the sensor, resulting in decoherence rather than a well-defined measurable phase. By considering scattering interactions of directional particulate environments with a system in a quantum superposition, we find that there is an optimal superposition size for measuring particles via a relative phase. As a consequence of the anisotropy of the environment, we observe a feature in the limiting behavior of the real and imaginary parts of the system's density matrix, linking the optimality of the superposition size to the wavelength of the scatterer. Published by the American Physical Society 2024