Scattering of quantum wave packets by shallow potential islands: A quantum lens

Goussev, Arseni; Richter, Klaus

doi:10.1103/physreve.87.052918

Cited by 4 publications

(5 citation statements)

References 12 publications

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“…Such a 3D packet hits a protein of typical diameter 5 nm. The resulting interaction is complex (44,45). For the interpretation of the scattering data, the values of τ n and δ n are crucial.…”

Section: Qens Explainedmentioning

confidence: 99%

A wave-mechanical model of incoherent quasielastic scattering in complex systems

Frauenfelder

Fenimore

Young

2014

Proc. Natl. Acad. Sci. U.S.A.

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Quasielastic incoherent neutron scattering (QENS) is an important tool for the exploration of the dynamics of complex systems such as biomolecules, liquids, and glasses. The dynamics is reflected in the energy spectra of the scattered neutrons. Conventionally these spectra are decomposed into a narrow elastic line and a broad quasielastic band. The band is interpreted as being caused by Doppler broadening due to spatial motion of the target molecules. We propose a quantum-mechanical model in which there is no separate elastic line. The quasielastic band is composed of sharp lines with twice the natural line width, shifted from the center by a random walk of the protein in the free-energy landscape of the target molecule. The walk is driven by vibrations and by external fluctuations. We first explore the model with the Mössbauer effect. In the subsequent application to QENS we treat the incoming neutron as a de Broglie wave packet. While the wave packet passes the protons in the protein and the hydration shell it exchanges energy with the protein during the passage time of about 100 ns. The energy exchange broadens the ensemble spectrum. Because the exchange involves the free-energy landscape of the protein, the QENS not only provides insight into the protein dynamics, but it may also illuminate the free-energy landscape of the protein-solvent system. quasielastic neutron scattering | neutron wave packet | protein free-energy landscape Q uasielastic effects are a key to understanding the dynamics of complex systems, from water to proteins (1, 2). A novice trying to understand quasielastic incoherent neutron scattering (QENS) is easily mystified. "Quasielastic" is usually taken to mean broadening of the elastic line due to spatial diffusion of the scattering particle. This definition is vague. We introduce a model that permits an unambiguous definition. It describes the QENS of proteins as involving a random walk in the free-energy landscape (FEL), driven by external fluctuations and by thermal vibrations. During the walk, the neutrons exchange energy with the protein, thus broadening the energy spectrum.In QENS the energy spectrum I(ΔE) of the scattered neutrons is measured as a function of the energy transfer ΔE relative to the energy of the elastic line at ΔE = 0. At present the QENS spectra are separated into a narrow elastic peak and a broad quasielastic band shown schematically in Fig. 1A. The band is taken to consist of broad Lorentzians with width Γ h centered at ΔE = 0 as sketched in Fig. 1B. The broadening is attributed to spatial motion of the target atoms, for instance by continuous diffusion, by jumps from one lattice site to another, or by conformational changes in proteins. The motions lead to different width Γ h for different proteins. We call this model SMM, for "spatial motion model," and discuss it in more detail later. We have introduced a radically different model, ELM, for "energy landscape model" (3). In the ELM, there is no separate elastic line pinned to the center. The entire spectrum is ...

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Section: Qens Explainedmentioning

confidence: 99%

A wave-mechanical model of incoherent quasielastic scattering in complex systems

Frauenfelder

Fenimore

Young

2014

Proc. Natl. Acad. Sci. U.S.A.

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“…The results presented here are based on classical trajectories, providing a concrete demonstration of the principles behind classical catastrophe theory 9 , 10 in a context beyond the usual setting in optics. Extending these to include quantum effects can proceed through a semi-classical expansion, with leading order corrections given by the WKB approximation 52 , 58 – 60 , and full quantum effects included numerically (see, e.g., refs. 13 , 61 – 63 ).…”

Section: Discussionmentioning

confidence: 99%

Gravitational caustics in an atom laser

et al. 2021

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Typically discussed in the context of optics, caustics are envelopes of classical trajectories (rays) where the density of states diverges, resulting in pronounced observable features such as bright points, curves, and extended networks of patterns. Here, we generate caustics in the matter waves of an atom laser, providing a striking experimental example of catastrophe theory applied to atom optics in an accelerated (gravitational) reference frame. We showcase caustics formed by individual attractive and repulsive potentials, and present an example of a network generated by multiple potentials. Exploiting internal atomic states, we demonstrate fluid-flow tracing as another tool of this flexible experimental platform. The effective gravity experienced by the atoms can be tuned with magnetic gradients, forming caustics analogous to those produced by gravitational lensing. From a more applied point of view, atom optics affords perspectives for metrology, atom interferometry, and nanofabrication. Caustics in this context may lead to quantum innovations as they are an inherently robust way of manipulating matter waves.

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“…The results presented here are based on classical trajectories, providing a concrete demonstration of the principles behind classical catastrophe theory [9,10] in a context beyond the usual setting in optics. Extending these to include quantum effects can proceed through a semi-classical expansion, with leading order corrections given by the wkb [44,[49][50][51], and full quantum effects included numerically (see e.g. [13,[52][53][54]).…”

Section: Discussionmentioning

confidence: 99%

Catastrophe Atom Optics: Fold and Cusp Caustics in an Atom Laser

Mossman,

Bersano,

Forbes

et al. 2021

Preprint

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Typically discussed in the context of optics, caustics are envelopes of classical trajectories (rays) where the density of states diverges, resulting in pronounced observable features such as bright points, curves, and extended networks of patterns. Despite the apparent complexity of such patterns, they are based on just a small number of fundamental forms described by the theory of catastrophe optics. Here, we demonstrate caustics in the matter waves of an atom laser, extending catastrophe optics to catastrophe atom optics. We showcase the generic forms of fold and cusp caustics, and exploit internal state manipulation to trace the flow of atoms. Atom optics affords new perspectives for fundamental science, metrology, atom interferometry and nano-fabrication techniques. Exploring the role of caustics in this context may lead to innovation as the generation of caustics is inherently robust, and leads to a variety of pronounced and sharply delineated features.

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Scattering of quantum wave packets by shallow potential islands: A quantum lens

Cited by 4 publications

References 12 publications

A wave-mechanical model of incoherent quasielastic scattering in complex systems

A wave-mechanical model of incoherent quasielastic scattering in complex systems

Gravitational caustics in an atom laser

Catastrophe Atom Optics: Fold and Cusp Caustics in an Atom Laser

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