Factorization of Numbers with the Temporal Talbot Effect: Optical Implementation by a Sequence of Shaped Ultrashort Pulses
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We report on the successful operation of an analogue computer designed to factor numbers. Our device relies solely on the interference of classical light and brings together the field of ultrashort laser pulses with number theory. Indeed, the frequency component of the electric field corresponding to a sequence of appropriately shaped femtosecond pulses is determined by a Gauss sum which allows us to find the factors of a number.
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The analogy of Hamiltonian (2) with the Jaynes-Cummings model allows relating zitterbewegung and Rabi oscillations.
“Interestingly, the analogy of Hamiltonian (2) with the JaynesCummings model allows us to relate ZB and Rabi oscillations, as other authors have pointed out 7,29,30 .”
From Revivals, classical periodicity, and zitterbewegung of electron currents in monolayer graphene (2009) · cites this paper as [29]
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- Authors
- Bigourd, D., Chatel, B., Schleich, W. P., & Girard, B.
- Affiliations
- Centre National de la Recherche Scientifique (FR)
- Universität Ulm (DE)
- Venue
- Physical Review Letters
- Publisher
- American Physical Society (APS)
- Published
- 2008-01-24
- Volume
- 100
- Issue
- 3
- Pages
- 030202-030202
- ISSN
- 0031-9007 (ISSN-L)
- 1079-7114
- OpenAlex
- W2056298292
- Cited by
- 84
- References
- 46
- Citations by year
- 2026: 1 · 2025: 2 · 2024: 5 · 2023: 2 · 2022: 3 · 2021: 1 · 2020: 6 · 2019: 1 · 2018: 4 · 2017: 2 · 2016: 3 · 2015: 3 · 2013: 3 · 2012: 7
- FWCI
- 7.93
- Type
- journal article
- Language
- en
- Open access
- green
- arxiv.org
- Locations
- Physical Review Letters (publishedVersion)
- PubMed (publishedVersion)
- arXiv (Cornell University) (submittedVersion)
- HAL (submittedVersion, other-oa)
- arXiv (Cornell University)
- Topics
- Physical Sciences › Physics and Astronomy › Atomic and Molecular Physics, and Optics › Laser-Matter Interactions and Applications
- Physical Sciences › Computer Science › Artificial Intelligence › Quantum Information and Cryptography
- Physical Sciences › Computer Science › Artificial Intelligence › Quantum Computing Algorithms and Architecture
- Keywords
- temporal Talbot effect, femtosecond pulses, Gauss sums, number theory, optical interference, quantum computing
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