Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

Physical Review A

Coupled-mode theory for general free-space resonant scattering of waves

Rafif E. Hamam, Aristeidis Karalis, John D. Joannopoulos, Marin Soljacic A

Published May 2, 2007• 150 citations
Publisher

Abstract

We present a universal coupled-mode-theory treatment of free-space scattering of waves from resonant objects. The range of applicability of the presented approach is fairly broad: it can be used for almost any linear wave system, as long as the resonant scatterer has either three-dimensional (3D) spherical or 2D cylindrical symmetry, or else is sufficiently smaller than the resonant wavelength of the incident wave. The presented framework, while being intuitive and analytically simple, can nevertheless provide quantitatively very accurate modeling of scattering cross sections, absorption cross sections, and many other quantities of interest. We illustrate this approach by showing how it applies to the particular examples of scattering of light from spherically symmetric resonant objects and atoms, and scattering of neutrons off nuclei.

DOI
10.1103/physreva.75.053801

Related papers

Scattering Theory

P. J. E. Peebles

This chapter studies applications drawn from scattering theory. A powerful and commonly used way to explore the interaction between particles is to study the way they scatter off each other. In the scattering problems considered here, motions are non-relativistic and particles are conserved: two particles move together, interact, and then move apart again. It is assumed that the range of the interaction is finite, so when the particles are well separated they move freely. In a scattering experiment, one imagines that the particles approach each other as wave packets with fairly definite momenta and positions. The motion is initially free, because the particles are separated by great distances compared to the range of their interaction. As the wave packets move together, the particles interact through a potential V that is some function of the particle separation. The wave packets then move apart in a scattering pattern that is determined by the interaction potential. The chapter simplifies the partial wave analysis by concentrating on s-wave scattering; this allows an easy treatment of interesting effects such as resonances and absorption.

Princeton University Press eBooks•May 14, 2019•0 citations

Photon Localization in Quantum Field Theory: From Point Detector to Finite-Size Detector

Jinhong Xu

Abstract: Starting from the physical intuition that light (massless fields) is delocalized while massive matter is localized, we develop a three-dimensional quantum field theory model to study photon absorption by a material detector. The detector is modeled as a two-level system coupled to a massless scalar field via a linear interaction. We consider three progressively realistic scenarios: (i) a point-like detector absorbing an s-wave spherical photon, (ii) a point-like detector absorbing a plane-wave photon, and (iii) a finite-size detector with a spatial distribution. Using Fermi's golden rule, we compute the transition rates and absorption cross sections. We show that for a point detector, the absorption cross section for s-wave photons is finite and frequency-independent, and for plane-wave photons it is independent of the incident direction. For a finite-size detector, the absorption efficiency is modulated by a form factor that suppresses absorption when the photon wavelength is shorter than the detector size. This provides a quantitative explanation for why microscopic objects (atoms) absorb light efficiently, while macroscopic objects are transparent or reflective. Our model offers an operational understanding of how a localized detector registers an event from a delocalized quantum field, linking quantum measurement theory with concrete detector models.

•Jan 1, 2025•0 citations

Scattering-matrix model of light scattering from atoms

Francesco Bariani, Davide Sarchi, Iacopo Carusotto

We develop a scattering-matrix formalism to numerically study the resonant scattering of light on generic assemblies of atoms. Protocols to eliminate the artifacts of the method and extract physical information from the numerical data are discussed. The efficiency of the approach is validated by comparing its predictions with analytical results in simple geometries.Paper withdrawn.

arXiv:1007.3521•Jul 20, 2010•0 citations

Pseudopotential treatment of two body interactions

Krittika Kanjilal

Ultracold atomic gases have been of great theoretical and experimental interest in the last two decades. In these systems, the de Broglie wavelength of the particles is much greater than the two body van der Waals length. As a result, the details of the two body interaction potential are irrelevant for a large number of applications and the realistic two body interaction potential can be replaced by a simple finite range or zero range model potential that reproduces the scattering quantities of the full interaction potential. This thesis develops zero range pseudopotentials and applies them to trapped two-particle systems. Ultracold gases loaded into optical lattices can be used to realize two particle systems under approximately harmonic confinement. We use pseudopotentials to obtain the eigenspectrum of two particles under external harmonic confinement semi-analytically. Advancements in trapping technology have resulted in the realization of low dimensional systems. We develop pseudopotentials to treat two body interactions in one and two dimensions. We also elaborate on the physics that is unique to one and two dimensional systems. Feshbach resonances allow for the tunability of the effective two body interaction strength in the presence of a magnetic field. To model Feshbach resonances in two and three dimensions we develop coupled two channel zero range potentials. Dipole-dipole interactions in Chromium and polar molecules have been the subject of a lot of recent research. Unlike the interactions between two alkali atoms, these interactions are long range and anisotropic. We explore the scattering properties of two aligned dipoles using a simple shape dependent model potential. To understand a system two aligned dipoles under confinement, we develop a pseudopotential treatment for cylindrically symmetric interaction potentials under cylindrically symmetric harmonic confinement. This pseudopotential can be used to model any cylindrically symmetric interaction potential. Our zero range treatment describes many features of two aligned dipoles under spherically symmetric harmonic confinement accurately but breaks down when applied to two aligned dipoles under cylindrically symmetric harmonic confinement. The breakdown is unique to the long range nature of the dipole-dipole interaction and expected to be absent for short range interactions.

•Jan 1, 2009•0 citations

Generalization of Resonant Scattering Calculations

David L. Huber

Previous calculations of the differential cross section for the resonant scattering of monochromatic light in gases are generalized. The connection between the integrated and coherent cross sections and the absorption line shape is displayed.

Physical Review•Nov 5, 1969•29 citations

Light Scattering in Terms of Oscillator Strengths and Refractive Indices

Carl M. Penney

Quantum-mechanical expressions for nonresonance-dipole light-scattering cross sections are related to corresponding expressions for oscillator strengths and refractive indices. In particular, Rayleigh and Raman cross sections for atoms are expressed in terms of oscillator strengths and vector-coupling coefficients. Several of our results, including the relationship between Rayleigh scattering and refractive index, differ in general from the corresponding results of classical dispersion theory. We show that these differences arise from antisymmetric components Ckja = (Ckj − Cjk)/2 of the polarizability tensor, which have been neglected in the classical analyses. Calculated Rayleigh cross sections for cesium and aluminum atoms, and Raman cross sections for aluminum atoms are presented to illustrate our results. The antisymmetric contribution is found to be substantial in all of these cross sections; its most obvious effect is to cause the depolarization (for linearly polarized incident light) to exceed 34 over extended wavelength ranges away from resonance. On the other hand, for atoms initially in states of zero angular momentum, and molecules under conditions which allow the use of Placzek’s polarizability approximation, our results agree with those of classical dispersion theory.

Journal of the Optical Society of America•Jan 1, 1969•107 citations
We present a universal coupled-mode-theory treatment of free-space scattering of waves from resonant objects. The range of applicability of the presented approach is fairly broad: it can be used for almost any linear wave system, as long as the resonant scatterer has either three-dimensional (3D) spherical or 2D cylindrical symmetry, or else is sufficiently smaller than the resonant wavelength of the incident wave. The presented framework, while being intuitive and analytically simple, can nevertheless provide quantitatively very accurate modeling of scattering cross sections, absorption cross sections, and many other quantities of interest. We illustrate this approach by showing how it applies to the particular examples of scattering of light from spherically symmetric resonant objects and atoms, and scattering of neutrons off nuclei.
This chapter studies applications drawn from scattering theory. A powerful and commonly used way to explore the interaction between particles is to study the way they scatter off each other. In the scattering problems considered here, motions are non-relativistic and particles are conserved: two particles move together, interact, and then move apart again. It is assumed that the range of the interaction is finite, so when the particles are well separated they move freely. In a scattering experiment, one imagines that the particles approach each other as wave packets with fairly definite momenta and positions. The motion is initially free, because the particles are separated by great distances compared to the range of their interaction. As the wave packets move together, the particles interact through a potential V that is some function of the particle separation. The wave packets then move apart in a scattering pattern that is determined by the interaction potential. The chapter simplifies the partial wave analysis by concentrating on s-wave scattering; this allows an easy treatment of interesting effects such as resonances and absorption.
Abstract: Starting from the physical intuition that light (massless fields) is delocalized while massive matter is localized, we develop a three-dimensional quantum field theory model to study photon absorption by a material detector. The detector is modeled as a two-level system coupled to a massless scalar field via a linear interaction. We consider three progressively realistic scenarios: (i) a point-like detector absorbing an s-wave spherical photon, (ii) a point-like detector absorbing a plane-wave photon, and (iii) a finite-size detector with a spatial distribution. Using Fermi's golden rule, we compute the transition rates and absorption cross sections. We show that for a point detector, the absorption cross section for s-wave photons is finite and frequency-independent, and for plane-wave photons it is independent of the incident direction. For a finite-size detector, the absorption efficiency is modulated by a form factor that suppresses absorption when the photon wavelength is shorter than the detector size. This provides a quantitative explanation for why microscopic objects (atoms) absorb light efficiently, while macroscopic objects are transparent or reflective. Our model offers an operational understanding of how a localized detector registers an event from a delocalized quantum field, linking quantum measurement theory with concrete detector models.
Ultracold atomic gases have been of great theoretical and experimental interest in the last two decades. In these systems, the de Broglie wavelength of the particles is much greater than the two body van der Waals length. As a result, the details of the two body interaction potential are irrelevant for a large number of applications and the realistic two body interaction potential can be replaced by a simple finite range or zero range model potential that reproduces the scattering quantities of the full interaction potential. This thesis develops zero range pseudopotentials and applies them to trapped two-particle systems. Ultracold gases loaded into optical lattices can be used to realize two particle systems under approximately harmonic confinement. We use pseudopotentials to obtain the eigenspectrum of two particles under external harmonic confinement semi-analytically. Advancements in trapping technology have resulted in the realization of low dimensional systems. We develop pseudopotentials to treat two body interactions in one and two dimensions. We also elaborate on the physics that is unique to one and two dimensional systems. Feshbach resonances allow for the tunability of the effective two body interaction strength in the presence of a magnetic field. To model Feshbach resonances in two and three dimensions we develop coupled two channel zero range potentials. Dipole-dipole interactions in Chromium and polar molecules have been the subject of a lot of recent research. Unlike the interactions between two alkali atoms, these interactions are long range and anisotropic. We explore the scattering properties of two aligned dipoles using a simple shape dependent model potential. To understand a system two aligned dipoles under confinement, we develop a pseudopotential treatment for cylindrically symmetric interaction potentials under cylindrically symmetric harmonic confinement. This pseudopotential can be used to model any cylindrically symmetric interaction potential. Our zero range treatment describes many features of two aligned dipoles under spherically symmetric harmonic confinement accurately but breaks down when applied to two aligned dipoles under cylindrically symmetric harmonic confinement. The breakdown is unique to the long range nature of the dipole-dipole interaction and expected to be absent for short range interactions.
Quantum-mechanical expressions for nonresonance-dipole light-scattering cross sections are related to corresponding expressions for oscillator strengths and refractive indices. In particular, Rayleigh and Raman cross sections for atoms are expressed in terms of oscillator strengths and vector-coupling coefficients. Several of our results, including the relationship between Rayleigh scattering and refractive index, differ in general from the corresponding results of classical dispersion theory. We show that these differences arise from antisymmetric components Ckja = (Ckj − Cjk)/2 of the polarizability tensor, which have been neglected in the classical analyses. Calculated Rayleigh cross sections for cesium and aluminum atoms, and Raman cross sections for aluminum atoms are presented to illustrate our results. The antisymmetric contribution is found to be substantial in all of these cross sections; its most obvious effect is to cause the depolarization (for linearly polarized incident light) to exceed 34 over extended wavelength ranges away from resonance. On the other hand, for atoms initially in states of zero angular momentum, and molecules under conditions which allow the use of Placzek’s polarizability approximation, our results agree with those of classical dispersion theory.