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:2007.10648 · Physical review. B./Physical review. B

Localization of light in a three-dimensional disordered crystal of atoms

S. E. Skipetrov

Published Oct 12, 2020• 15 citations
arXivHTMLPDF

Abstract

We demonstrate that a weak disorder in atomic positions introduces spatially localized optical modes in a dense three-dimensional ensemble of immobile two-level atoms arranged in a diamond lattice and coupled by the electromagnetic field. The frequencies of the localized modes concentrate near band edges of the unperturbed lattice. Finite-size scaling analysis of the percentiles of Thouless conductance reveals two mobility edges and yields an estimation $\ensuremath{\nu}=0.8--1.1$ for the critical exponent of the localization length. The localized modes disappear when the disorder becomes too strong and the system starts to resemble a fully disordered one where all modes are extended.

DOI
10.1103/physrevb.102.134206

Related papers

Anderson localization in optical lattices with correlated disorder

Elisa Fratini, Sebastiano Pilati

We study the Anderson localization of atomic gases exposed to simple-cubic optical lattices with a superimposed disordered speckle pattern. The two mobility edges in the first band and the corresponding critical filling factors are determined as a function of the disorder strength, ranging from vanishing disorder up to the critical disorder intensity where the two mobility edges merge and the whole band becomes localized. Our theoretical analysis is based both on continuous-space models that take into account the details of the spatial correlation of the speckle pattern, and also on a simplified tight-binding model with an uncorrelated distribution of the on-site energies. The mobility edges are computed via the analysis of the energy-level statistics, and we determine the universal value of the ratio between consecutive level spacings at the mobility edge. We analyze the role of the spatial correlation of the disorder, and we also discuss a qualitative comparison with available experimental data for interacting atomic Fermi gases obtained in the moderate interaction regime.

arXiv:1510.05121•Physical Review A•Dec 14, 2015•23 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

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

Quantitative study of two- and three-dimensional strong localization of matter waves by atomic scatterers

Mauro Antezza, Yvan Castin, David A. W. Hutchinson

We study the strong localization of atomic matter waves in a disordered potential created by atoms pinned at the nodes of a lattice, for both three-dimensional (3D) and two-dimensional (2D) systems. The localization length of the matter wave, the density of localized states, and the occurrence of energy mobility edges (for the 3D system), are numerically investigated as a function of the effective scattering length between the atomic matter wave and the pinned atoms. Both positive and negative matter wave energies are explored. Interesting features of the density of states are discovered at negative energies, where maxima in the density of bound states for the system can be interpreted in terms of bound states of a matter wave atom with a few pinned atomic scatterers. In 3D we found evidence of up to three mobility edges, one at positive energies, and two at negative energies, the latter corresponding to transitions between extended and localized bound states. In 2D, no mobility edge is found, and a rapid exponential-like increase of the localization length is observed at high energy.

arXiv:1006.4429•Physical Review A•Oct 7, 2010•19 citations

Two- and three-dimensional strong localization of matter waves by atomic scatterers

Mauro Antezza

We study the strong localization of atomic matter waves in a disordered potential created by atoms pinnedat the nodes of a lattice, for both three-dimensional (3D) and two-dimensional (2D) systems. The localizationlength of the matter wave, the density of localized states, and the occurrence of energy mobility edges (for the 3Dsystem), are numerically investigated as a function of the effective scattering length between the atomic matterwave and the pinned atoms. Both positive and negative matter wave energies are explored. Interesting featuresof the density of states are discovered at negative energies, where maxima in the density of bound states for thesystem can be interpreted in terms of bound states of a matter wave atom with a few pinned atomic scatterers.In 3D we found evidence of up to three mobility edges, one at positive energies, and two at negative energies,the latter corresponding to transitions between extended and localized bound states. In 2D, no mobility edge isfound, and a rapid exponential-like increase of the localization length is observed at high energy.

•Dec 15, 2010•0 citations
We demonstrate that a weak disorder in atomic positions introduces spatially localized optical modes in a dense three-dimensional ensemble of immobile two-level atoms arranged in a diamond lattice and coupled by the electromagnetic field. The frequencies of the localized modes concentrate near band edges of the unperturbed lattice. Finite-size scaling analysis of the percentiles of Thouless conductance reveals two mobility edges and yields an estimation \ensuremathν=0.8−−1.1\ensuremath{\nu}=0.8--1.1\ensuremathν=0.8−−1.1 for the critical exponent of the localization length. The localized modes disappear when the disorder becomes too strong and the system starts to resemble a fully disordered one where all modes are extended.
We study the Anderson localization of atomic gases exposed to simple-cubic optical lattices with a superimposed disordered speckle pattern. The two mobility edges in the first band and the corresponding critical filling factors are determined as a function of the disorder strength, ranging from vanishing disorder up to the critical disorder intensity where the two mobility edges merge and the whole band becomes localized. Our theoretical analysis is based both on continuous-space models that take into account the details of the spatial correlation of the speckle pattern, and also on a simplified tight-binding model with an uncorrelated distribution of the on-site energies. The mobility edges are computed via the analysis of the energy-level statistics, and we determine the universal value of the ratio between consecutive level spacings at the mobility edge. We analyze the role of the spatial correlation of the disorder, and we also discuss a qualitative comparison with available experimental data for interacting atomic Fermi gases obtained in the moderate interaction regime.
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 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 study the strong localization of atomic matter waves in a disordered potential created by atoms pinned at the nodes of a lattice, for both three-dimensional (3D) and two-dimensional (2D) systems. The localization length of the matter wave, the density of localized states, and the occurrence of energy mobility edges (for the 3D system), are numerically investigated as a function of the effective scattering length between the atomic matter wave and the pinned atoms. Both positive and negative matter wave energies are explored. Interesting features of the density of states are discovered at negative energies, where maxima in the density of bound states for the system can be interpreted in terms of bound states of a matter wave atom with a few pinned atomic scatterers. In 3D we found evidence of up to three mobility edges, one at positive energies, and two at negative energies, the latter corresponding to transitions between extended and localized bound states. In 2D, no mobility edge is found, and a rapid exponential-like increase of the localization length is observed at high energy.
We study the strong localization of atomic matter waves in a disordered potential created by atoms pinnedat the nodes of a lattice, for both three-dimensional (3D) and two-dimensional (2D) systems. The localizationlength of the matter wave, the density of localized states, and the occurrence of energy mobility edges (for the 3Dsystem), are numerically investigated as a function of the effective scattering length between the atomic matterwave and the pinned atoms. Both positive and negative matter wave energies are explored. Interesting featuresof the density of states are discovered at negative energies, where maxima in the density of bound states for thesystem can be interpreted in terms of bound states of a matter wave atom with a few pinned atomic scatterers.In 3D we found evidence of up to three mobility edges, one at positive energies, and two at negative energies,the latter corresponding to transitions between extended and localized bound states. In 2D, no mobility edge isfound, and a rapid exponential-like increase of the localization length is observed at high energy.