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

arXiv:1410.3634 · Physical Review Letters

Magnetic-Field-Driven Localization of Light in a Cold-Atom Gas

S. E. Skipetrov, Igor M. Sokolov

Published Feb 5, 2015• 89 citations
arXivHTMLPDF

Abstract

We discover a transition from extended to localized quasimodes for light in a gas of immobile two-level atoms in a magnetic field. The transition takes place either upon increasing the number density of atoms in a strong field or upon increasing the field at a high enough density. It has many characteristic features of a disorder-driven (Anderson) transition but is strongly influenced by near-field interactions between atoms and the anisotropy of the atomic medium induced by the magnetic field.

DOI
10.1103/physrevlett.114.053902

Related papers

Localization Transition for Light Scattering by Cold Atoms in an External Magnetic Field

S. E. Skipetrov

We establish a localization phase diagram for light in a random three-dimensional (3D) ensemble of motionless two-level atoms with a threefold degenerate upper level, in a strong static magnetic field. Localized modes appear in a narrow spectral band when the number density of atoms $\ensuremath{\rho}$ exceeds a critical value ${\ensuremath{\rho}}_{c}\ensuremath{\simeq}0.1{k}_{0}^{3}$, where ${k}_{0}$ is the wave number of light in the free space. A critical exponent of the localization transition taking place upon varying the frequency of light at a constant $\ensuremath{\rho}>{\ensuremath{\rho}}_{c}$ is estimated to be $\ensuremath{\nu}=1.57\ifmmode\pm\else\textpm\fi{}0.07$. This classifies the transition as an Anderson localization transition of 3D orthogonal universality class.

arXiv:1805.04314•Physical Review Letters•Aug 29, 2018•33 citations

Search for Anderson localization of light by cold atoms in a static electric field

S. E. Skipetrov, Igor M. Sokolov

We explore the potential of a static electric field to induce Anderson localization of light in a large three-dimensional cloud of randomly distributed, immobile atoms with a nondegenerate ground state (total angular momentum ${J}_{g}=0$) and a threefold-degenerate excited state (${J}_{e}=1$). We study both the spatial structure of quasimodes of the atomic cloud and the scaling of the Thouless number with the size of the cloud. Our results indicate that unlike the static magnetic field, the electric field does not induce Anderson localization of light by atoms. We explain this conclusion by the incomplete removal of degeneracy of the excited atomic state by the field and the relatively strong residual dipole-dipole coupling between atoms which is weaker than in the absence of external fields but stronger than in the presence of a static magnetic field. A joint analysis of these results together with our previous results concerning Anderson localization of scalar waves and light suggests the existence of a critical strength of dipole-dipole interactions that should not be surpassed for Anderson localization to be possible in three dimensions.

arXiv:1901.04853•Physical review. B./Physical review. B•Apr 2, 2019•17 citations

Delocalization transition for light in two dimensions

S. Lucas, Christian Miniatura, S. E. Skipetrov

Common belief, confirmed by existing experiments, is that arbitrarily weak disorder should lead to spatial localization of eigenmodes of scalar wave equations when wave propagation is two-dimensional (2D). We predict that contrary to this belief, a localization-delocalization transition can take place for light scattered by two-level atoms placed at random positions in the middle plane of a parallel-plate 2D waveguide fed by its fundamental transverse-magnetic (TM) mode (electric field polarized perpendicular to the waveguide and atomic planes). This transition, driven by near-field dipole-dipole interactions between atoms, occurs upon increasing the areal number density of atoms beyond some critical value. A finite-size scaling analysis of the transition yields an estimate of its critical exponent $ν$ = 1.4 $\pm$ 0.2.

arXiv:2604.22919•Physical Review A•Aug 19, 2026•0 citations

Anderson localization of light by cold atoms

S. E. Skipetrov

Large ensembles of cold, immobile atoms might serve as ideal model systems to study Anderson localization of light. In contrast to dielectric systems, atomic clouds allow for a fine experimental control and admit a precise theoretical description. In this talk, we will review the recent theoretical developments aimed at paving a path towards an experimental realization of Anderson localization of light in three-dimensional (3D) atomic systems. Because atoms are the simplest point scatterers, considering light scattering on them is a good opportunity to illustrate several basic concepts and methods of the localization theory (Thouless conductance and Ioffe-Regel criterion, the mobility edge and the critical behavior, the scaling and self-consistent theories, the finite-size scaling procedure, etc.) on a concrete example. We will show that, surprisingly, Anderson localization of light by atoms is impossible in 3D if no special efforts are made to suppress near-field interactions between atoms. The necessary suppression may be achieved by subjecting the atoms to a constant external magnetic field or by arranging them in a crystalline structure in which a small amount of disorder is introduced. However, even when spatially localized states appear in a system of immobile atoms, their experimental observation remains challenging because of the residual thermal motion of atoms.

•Oct 7, 2020•0 citations

Transport of light through a dense ensemble of cold atoms in a static electric field

S. E. Skipetrov, Igor M. Sokolov

We demonstrate that the transport of coherent quasiresonant light through a dense cloud of immobile two-level atoms subjected to a static external electric field can be described by a simple diffusion process up to atomic number densities of the order of at least ${10}^{2}$ atoms per wavelength cubed. Transport mean-free paths well below the wavelength of light in the free space can be reached without inducing any sign of Anderson localization of light or of any other mechanism of breakdown of diffusion.

arXiv:1904.06408•Physical Review A•Jul 12, 2019•5 citations

Anderson localization of light by impurities in a solid transparent matrix

S. E. Skipetrov, Igor M. Sokolov

A solid transparent medium with randomly positioned, immobile impurity atoms is a promising candidate for observation of Anderson localization of light in three dimensions. It can have low losses and allows for mitigation of the detrimental effect of longitudinal optical fields by an external magnetic field, but it has its own issues: thermal oscillations of atoms around their equilibrium positions and inhomogeneous broadening of atomic spectral lines due to random local electric fields. Our calculations suggest that these complications should not impede observation of Anderson localization of light in such materials provided that a sufficiently high number densities of impurities can be reached. The thermal oscillations hardly affect light propagation whereas the inhomogeneous broadening can be compensated for by increasing the number density of impurities.

arXiv:2408.01381•Physical review. B./Physical review. B•Jul 28, 2025•1 citation
We discover a transition from extended to localized quasimodes for light in a gas of immobile two-level atoms in a magnetic field. The transition takes place either upon increasing the number density of atoms in a strong field or upon increasing the field at a high enough density. It has many characteristic features of a disorder-driven (Anderson) transition but is strongly influenced by near-field interactions between atoms and the anisotropy of the atomic medium induced by the magnetic field.
We establish a localization phase diagram for light in a random three-dimensional (3D) ensemble of motionless two-level atoms with a threefold degenerate upper level, in a strong static magnetic field. Localized modes appear in a narrow spectral band when the number density of atoms $\ensuremath{\rho}$ exceeds a critical value ${\ensuremath{\rho}}_{c}\ensuremath{\simeq}0.1{k}_{0}^{3}$, where k0{k}_{0}k0​ is the wave number of light in the free space. A critical exponent of the localization transition taking place upon varying the frequency of light at a constant $\ensuremath{\rho}>{\ensuremath{\rho}}_{c}$ is estimated to be $\ensuremath{\nu}=1.57\ifmmode\pm\else\textpm\fi{}0.07$. This classifies the transition as an Anderson localization transition of 3D orthogonal universality class.
We explore the potential of a static electric field to induce Anderson localization of light in a large three-dimensional cloud of randomly distributed, immobile atoms with a nondegenerate ground state (total angular momentum Jg=0{J}_{g}=0Jg​=0) and a threefold-degenerate excited state (Je=1{J}_{e}=1Je​=1). We study both the spatial structure of quasimodes of the atomic cloud and the scaling of the Thouless number with the size of the cloud. Our results indicate that unlike the static magnetic field, the electric field does not induce Anderson localization of light by atoms. We explain this conclusion by the incomplete removal of degeneracy of the excited atomic state by the field and the relatively strong residual dipole-dipole coupling between atoms which is weaker than in the absence of external fields but stronger than in the presence of a static magnetic field. A joint analysis of these results together with our previous results concerning Anderson localization of scalar waves and light suggests the existence of a critical strength of dipole-dipole interactions that should not be surpassed for Anderson localization to be possible in three dimensions.
Common belief, confirmed by existing experiments, is that arbitrarily weak disorder should lead to spatial localization of eigenmodes of scalar wave equations when wave propagation is two-dimensional (2D). We predict that contrary to this belief, a localization-delocalization transition can take place for light scattered by two-level atoms placed at random positions in the middle plane of a parallel-plate 2D waveguide fed by its fundamental transverse-magnetic (TM) mode (electric field polarized perpendicular to the waveguide and atomic planes). This transition, driven by near-field dipole-dipole interactions between atoms, occurs upon increasing the areal number density of atoms beyond some critical value. A finite-size scaling analysis of the transition yields an estimate of its critical exponent ννν = 1.4 ±\pm± 0.2.
Large ensembles of cold, immobile atoms might serve as ideal model systems to study Anderson localization of light. In contrast to dielectric systems, atomic clouds allow for a fine experimental control and admit a precise theoretical description. In this talk, we will review the recent theoretical developments aimed at paving a path towards an experimental realization of Anderson localization of light in three-dimensional (3D) atomic systems. Because atoms are the simplest point scatterers, considering light scattering on them is a good opportunity to illustrate several basic concepts and methods of the localization theory (Thouless conductance and Ioffe-Regel criterion, the mobility edge and the critical behavior, the scaling and self-consistent theories, the finite-size scaling procedure, etc.) on a concrete example. We will show that, surprisingly, Anderson localization of light by atoms is impossible in 3D if no special efforts are made to suppress near-field interactions between atoms. The necessary suppression may be achieved by subjecting the atoms to a constant external magnetic field or by arranging them in a crystalline structure in which a small amount of disorder is introduced. However, even when spatially localized states appear in a system of immobile atoms, their experimental observation remains challenging because of the residual thermal motion of atoms.
We demonstrate that the transport of coherent quasiresonant light through a dense cloud of immobile two-level atoms subjected to a static external electric field can be described by a simple diffusion process up to atomic number densities of the order of at least 102{10}^{2}102 atoms per wavelength cubed. Transport mean-free paths well below the wavelength of light in the free space can be reached without inducing any sign of Anderson localization of light or of any other mechanism of breakdown of diffusion.
A solid transparent medium with randomly positioned, immobile impurity atoms is a promising candidate for observation of Anderson localization of light in three dimensions. It can have low losses and allows for mitigation of the detrimental effect of longitudinal optical fields by an external magnetic field, but it has its own issues: thermal oscillations of atoms around their equilibrium positions and inhomogeneous broadening of atomic spectral lines due to random local electric fields. Our calculations suggest that these complications should not impede observation of Anderson localization of light in such materials provided that a sufficiently high number densities of impurities can be reached. The thermal oscillations hardly affect light propagation whereas the inhomogeneous broadening can be compensated for by increasing the number density of impurities.