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arXiv:2604.22919 · Physical Review A

Delocalization transition for light in two dimensions

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

Published Aug 19, 2026• 0 citations
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Abstract

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.

DOI
10.1103/nzbs-456y

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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 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.
We numerically study the expansion dynamics of ultracold atoms in a one-dimensional disordered potential in the presence of a weak position measurement of the atoms. We specifically consider this position measurement to be realized by a combination of an external laser and a periodic array of optical microcavities along a waveguide. The position information is acquired through the scattering of a near-resonant laser photon into a specific eigenmode of one of the cavities. The time evolution of the atomic density in the presence of this light-scattering mechanism is described within a Lindblad master equation approach, which is numerically implemented using the Monte Carlo wave function technique. We find that an arbitrarily weak rate of photon emission leads to a breakdown of Anderson localization of the atoms.
In this thesis, we investigate the coherent scattering of light propagating in a random medium.We are interested in phenomena like the super-and subradiance and Anderson localization that are related to waves interferences and spatial disorder.However, the fundamental difference between subradiance and Anderson localization still needs to be clarified.This thesis gives new elements for the understanding of these phenomena and we present a new method to observe Anderson localization.A mean-field model that does not contain disorder is developed, and we show that super-and subradiance do not require disorder whereas Anderson localization does.In this theoretical work, the coupling between the light and many atoms is reduced to a coupling matrix between the atoms by tracing over the degrees of freedom of the light, which results in a linear problem for the atomic dipoles.The study of the eigenvalues and eigenmodes of this matrix then allows to determine the super-and subradiant modes, and to probe the Anderson localization phase transition with a scaling analysis.Furthermore, the link to the experiment is realized by showing that the intensity fluctuations present an increase at the localization transition.The system is studied in the steady-state regime when the medium is continuously charged by a laser until reaches a stationary regime, and the decay dynamics, when the laser is switched off, so the cloud releases the energy stored.Finally, we present a preliminary work that shows that the diagonal disorder might be a good strategy to reach Anderson localization.
Light transport in a disordered ensemble of resonant atoms placed in a waveguide is found to be very sensitive to the sizes of the cross section of a waveguide. Based on a self-consistent quantum microscopic model treating atoms as coherent radiating dipoles, we have shown that the nature of radiation transfer changes from Anderson localization regime in a single-mode waveguide to a traditional diffuse transfer in a multimode one. Moreover, the transmittance magnitude undergoes complicated steplike nonmonotonic dependence on the transverse sizes of a waveguide.