Dimensional reduction of cavities with axial symmetry: A complete analysis of when an optical fiber is approximately one dimensional

Grimmer, Daniel; Lopp, Richard; Martín-Martínez, Eduardo

doi:10.1103/physreva.104.013723

Phys. Rev. A

2021

DOI: 10.1103/physreva.104.013723

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Dimensional reduction of cavities with axial symmetry: A complete analysis of when an optical fiber is approximately one dimensional

Daniel Grimmer

Richard Lopp

Eduardo Martín-Martínez

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2024

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Dimensional reduction in quantum optics

Ströhle,

Lopp

2024

Phys. Rev. Research

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One-dimensional quantum optical models usually rest on the intuition of large-scale separation or frozen dynamics associated with the different spatial dimensions, for example when studying quasi one-dimensional atomic dynamics, potentially resulting in the violation of (3+1)-dimensional Maxwell's theory. Here, we provide a rigorous foundation for this approximation by means of the light-matter interaction. We show how the quantized electromagnetic field can be decomposed—exactly—into an infinite number of living on a lower-dimensional subspace and containing the entirety of the spectrum when studying axially symmetric setups, such as with an optical fiber, a laser beam, or a waveguide. The approximation then corresponds to a truncation in the number of such subfields that in turn, when considering the interaction with for instance an atom, corresponds to a modification to the atomic spatial profile. We explore under what conditions the standard approach is justified and when corrections are necessary in order to account for the dynamics due to the neglected spatial dimensions. In particular we examine what role vacuum fluctuations and structured laser modes play in the validity of the approximation. Published by the American Physical Society 2024

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Dimensional reduction in quantum optics

Ströhle,

Lopp

2024

Phys. Rev. Research

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show abstract

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Dimensional reduction of cavities with axial symmetry: A complete analysis of when an optical fiber is approximately one dimensional

Cited by 1 publication

References 30 publications

Dimensional reduction in quantum optics

Dimensional reduction in quantum optics

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