Probing the Boundary between Classical and Quantum Mechanics by Analyzing the Energy Dependence of Single-Electron Scattering Events at the Nanoscale
The relation between the energy-dependent particle and wave descriptions of electron–matter interactions on the nanoscale was analyzed by measuring the delocalization of an evanescent field from energy-filtered amplitude images of sample/vacuum interfaces with a special aberration-corrected electron...
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| Format: | Article |
| Language: | English |
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MDPI AG
2023-03-01
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| Series: | Nanomaterials |
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| Online Access: | https://www.mdpi.com/2079-4991/13/6/971 |
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| author | Christian Kisielowski Petra Specht Stig Helveg Fu-Rong Chen Bert Freitag Joerg Jinschek Dirk Van Dyck |
| author_facet | Christian Kisielowski Petra Specht Stig Helveg Fu-Rong Chen Bert Freitag Joerg Jinschek Dirk Van Dyck |
| author_sort | Christian Kisielowski |
| collection | DOAJ |
| description | The relation between the energy-dependent particle and wave descriptions of electron–matter interactions on the nanoscale was analyzed by measuring the delocalization of an evanescent field from energy-filtered amplitude images of sample/vacuum interfaces with a special aberration-corrected electron microscope. The spatial field extension coincided with the energy-dependent self-coherence length of propagating wave packets that obeyed the time-dependent Schrödinger equation, and underwent a Goos–Hänchen shift. The findings support the view that wave packets are created by self-interferences during coherent–inelastic Coulomb interactions with a decoherence phase close to Δ<i>φ</i> = 0.5 rad. Due to a strictly reciprocal dependence on energy, the wave packets shrink below atomic dimensions for electron energy losses beyond 1000 eV, and thus appear particle-like. Consequently, our observations inevitably include pulse-like wave propagations that stimulate structural dynamics in nanomaterials at any electron energy loss, which can be exploited to unravel time-dependent structure–function relationships on the nanoscale. |
| first_indexed | 2024-03-11T06:06:12Z |
| format | Article |
| id | doaj.art-6bb424ef6c164b53b87a8fe6e6ad77e6 |
| institution | Directory Open Access Journal |
| issn | 2079-4991 |
| language | English |
| last_indexed | 2024-03-11T06:06:12Z |
| publishDate | 2023-03-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Nanomaterials |
| spelling | doaj.art-6bb424ef6c164b53b87a8fe6e6ad77e62023-11-17T12:59:42ZengMDPI AGNanomaterials2079-49912023-03-0113697110.3390/nano13060971Probing the Boundary between Classical and Quantum Mechanics by Analyzing the Energy Dependence of Single-Electron Scattering Events at the NanoscaleChristian Kisielowski0Petra Specht1Stig Helveg2Fu-Rong Chen3Bert Freitag4Joerg Jinschek5Dirk Van Dyck6The Molecular Foundry, Lawrence Berkeley National Laboratory, One Cyclotron Rd., Berkeley, CA 94720, USADepartment of Materials Science and Engineering, University of California Berkeley, Berkeley, CA 94720, USACenter for Visualizing Catalytic Processes (VISION), Department of Physics, Technical University of Denmark, 2800 Kongens Lyngby, DenmarkDepartment of Materials Science and Engineering, City University of Hong Kong, Kowloon Tong, Hong Kong SAR, ChinaThermo Fisher Scientific, Achtseweg Noord 5, 5651 GG Eindhoven, The NetherlandsNational Centre for Nano Fabrication and Characterization (DTU Nanolab), Technical University of Denmark, 2800 Kongens Lyngby, DenmarkEMAT, University of Antwerp, 2020 Antwerp, BelgiumThe relation between the energy-dependent particle and wave descriptions of electron–matter interactions on the nanoscale was analyzed by measuring the delocalization of an evanescent field from energy-filtered amplitude images of sample/vacuum interfaces with a special aberration-corrected electron microscope. The spatial field extension coincided with the energy-dependent self-coherence length of propagating wave packets that obeyed the time-dependent Schrödinger equation, and underwent a Goos–Hänchen shift. The findings support the view that wave packets are created by self-interferences during coherent–inelastic Coulomb interactions with a decoherence phase close to Δ<i>φ</i> = 0.5 rad. Due to a strictly reciprocal dependence on energy, the wave packets shrink below atomic dimensions for electron energy losses beyond 1000 eV, and thus appear particle-like. Consequently, our observations inevitably include pulse-like wave propagations that stimulate structural dynamics in nanomaterials at any electron energy loss, which can be exploited to unravel time-dependent structure–function relationships on the nanoscale.https://www.mdpi.com/2079-4991/13/6/971electron beam–sample interactionsfunctional behaviorinelastic scatteringtime-dependent Schrödinger equationself-interferencecoherence |
| spellingShingle | Christian Kisielowski Petra Specht Stig Helveg Fu-Rong Chen Bert Freitag Joerg Jinschek Dirk Van Dyck Probing the Boundary between Classical and Quantum Mechanics by Analyzing the Energy Dependence of Single-Electron Scattering Events at the Nanoscale Nanomaterials electron beam–sample interactions functional behavior inelastic scattering time-dependent Schrödinger equation self-interference coherence |
| title | Probing the Boundary between Classical and Quantum Mechanics by Analyzing the Energy Dependence of Single-Electron Scattering Events at the Nanoscale |
| title_full | Probing the Boundary between Classical and Quantum Mechanics by Analyzing the Energy Dependence of Single-Electron Scattering Events at the Nanoscale |
| title_fullStr | Probing the Boundary between Classical and Quantum Mechanics by Analyzing the Energy Dependence of Single-Electron Scattering Events at the Nanoscale |
| title_full_unstemmed | Probing the Boundary between Classical and Quantum Mechanics by Analyzing the Energy Dependence of Single-Electron Scattering Events at the Nanoscale |
| title_short | Probing the Boundary between Classical and Quantum Mechanics by Analyzing the Energy Dependence of Single-Electron Scattering Events at the Nanoscale |
| title_sort | probing the boundary between classical and quantum mechanics by analyzing the energy dependence of single electron scattering events at the nanoscale |
| topic | electron beam–sample interactions functional behavior inelastic scattering time-dependent Schrödinger equation self-interference coherence |
| url | https://www.mdpi.com/2079-4991/13/6/971 |
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