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arXiv:2601.14715

Light propagation in atomic stratified media: breakdown of the transfer-matrix method at high density

Sokolov, Igor M., William Guerin

Published Jan 21, 2026• 0 citations
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Abstract

The transfer-matrix method is a standard approach to wave propagation in stratified media. With the advent of cold-atom-based quantum and photonic technologies, several experiments and many proposals consider light propagation in one-dimensional optical lattices, using the transfer matrices as the main tool for the simulation. Here, we study the validity of this method by comparing its results to the microscopic coupled-dipole model, which is exact in the linear-optics regime. We show that the transfer-matrix method works very well at low density, even for thin disordered slices, and breaks down at high density because the dipole-dipole interaction induces a collective response from the atoms such that the properties of one layer are influenced by the others. We determine the boundary values of atomic densities for which this method is still applicable for describing experiments. Our findings are relevant for experimental realizations using ultra-cold atoms.

DOI
10.48550/arxiv.2601.14715

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The transfer-matrix method is a standard approach to wave propagation in stratified media. With the advent of cold-atom-based quantum and photonic technologies, several experiments and many proposals consider light propagation in one-dimensional optical lattices, using the transfer matrices as the main tool for the simulation. Here, we study the validity of this method by comparing its results to the microscopic coupled-dipole model, which is exact in the linear-optics regime. We show that the transfer-matrix method works very well at low density, even for thin disordered slices, and breaks down at high density because the dipole-dipole interaction induces a collective response from the atoms such that the properties of one layer are influenced by the others. We determine the boundary values of atomic densities for which this method is still applicable for describing experiments. Our findings are relevant for experimental realizations using ultra-cold atoms.
The transfer-matrix method is a standard approach to wave propagation in stratified media. With the advent of cold-atom-based quantum and photonic technologies, several experiments and many proposals consider light propagation in one-dimensional optical lattices, using the transfer matrices as the main tool for the simulation. Here, we study the validity of this method by comparing its results to the microscopic coupled-dipole model, which is exact in the linear-optics regime. We show that the transfer-matrix method works very well at low density, even for thin disordered slices, and breaks down at high density because the dipole–dipole interaction induces a collective response from the atoms such that the properties of one layer are influenced by the others. We determine the boundary values of atomic densities for which this method is still applicable for describing experiments. Our findings are relevant for experimental realizations using ultra-cold atoms.
Light propagation in disordered media is a fundamental and important problem in optics and photonics. In particular, engineering light-matter interaction in disordered cold atomic ensembles is one of the central topics in modern quantum and atomic optics. The collective response of dense atomic gases under light excitation, which crucially depends on the spatial distribution of atoms and the geometry of the ensemble, has important impacts on quantum technologies like quantum sensors, atomic clocks and quantum information storage. Here we analyze near-resonant light transmission in two-dimensional dense ultracold atomic ensembles with short-range positional correlations. Based on the coupled-dipole simulations under different atom number densities and correlation lengths, we show that the collective effects are strongly influenced by those positional correlations, manifested as significant shifts and broadening or narrowing of transmission resonance lines. We also analyze the eigenstate distribution of different atomic ensembles. This work may provide profound implications on collective and cooperative effects in cold atomic ensembles as well as the study of mesoscopic physics concerning light transport in strongly scattering disorder media.
The main objective of this research is to study a particular case of light-matter interaction: the scattering of light in dense atomic samples.The regime of high atomic densities is represented by samples where the distance between neighboring atoms is on the order of the wavelength associated with the atomic transition.In this regime, short-range atomic interactions cannot be neglected, and in these systems, we expect to observe significant modifications in collective effects such as subradiance or superradiance.Overall, the propagation of light through this type of system is not well-known to the scientific community, and the existing models work to describe very specific situations.To pave the way for achieving our overall goal, this work proposes an experimental setup to obtain a dense cloud of 88 Sr, which is the chemical species we work with in our laboratory.For this purpose, atoms previously trapped using a Magneto-Optical Trap are transferred to a Crossed Optical Dipole Trap.During the optimization and characterization of the optical trap, problems were encountered in producing an image with quantitative information of the atomic ensemble and in transferring a large number of atoms in a very small trapping volume.These problems were resolved with the implementation of a Phase Contrast Imaging system and the implementation of an Optical Molasses as an additional cooling step.Under these conditions, we obtained a cloud that can be suitable for conducting studies on collective effects, transitioning from the dilute to the dense regime.The initial experiments, once our atomic ensemble was prepared, involve measuring the coherent transmission of a low-intensity beam through the cloud.For this purpose, incident light near the resonance of a dipolar transition of the type J = 0 ↔ J = 1 of 88 Sr is used, interacting with a homogeneous region of the sample.Simulations of this type of process can be performed using the Coupled Dipole Model, which describes the overall response of light scattering by the sample considering dipole-dipole interactions mediated by light.With this work, we aim to advance the understanding of density effects by comparing the coherent optical response of the dense cloud with the theory based on the Coupled Dipole Model.
Manipulation of light using atoms plays a fundamental and important role in emerging technologies such as integrated photonics, information storage, and quantum sensors. Specifically, there have been intense theoretical efforts involving large samples of cold neutral atoms for coherent control of light. Here we present a theoretical scheme that enables efficient computation of collective optical responses of mono- and bi-layer planar square lattices of dense, cold two-level atoms using classical electrodynamics of coupled dipoles in the limit of low laser intensity. The steady-state transmissivity and reflectivity are obtained at a field point far away from the atomic lattices in the regime with no Bragg reflection. While our earlier method was based on exact solution of the electrodynamics for a small-scale lattice, here we calculate the dipole moments assuming that they are the same at all lattice sites, as for an infinite lattice. Atomic lattices with effectively over one hundred times more sites than in our earlier exact computations can then be simulated numerically with fewer computational resources. We have implemented an automatic selection of the number of sites under the given convergence criteria. We compare the numerical results from both computational schemes. We also find similarities and differences of a stack of two atomic lattices from a two-atom sample. Such aspects may be exploited to engineer a stack for potential applications.
With ready access to massive computer clusters we may now study light propagation in a dense cold atomic gas by means of basically exact numerical simulations. We report on a direct comparison between traditional optics, that is, electrodynamics of a polarizable medium, and numerical simulations in an elementary problem of light propagating through a slab of matter. The standard optics fails already at quite low atom densities, and the failure becomes dramatic when the average interatomic separation is reduced to around k(-1), where k is the wave number of resonant light. The difference between the two solutions originates from correlations between the atoms induced by light-mediated dipole-dipole interactions.
Collective effects in the atom–light interaction are of great importance for cold-atom-based quantum devices or fundamental studies on light transport in complex media. Here we discuss and compare three different approaches to light scattering by dilute cold atomic ensembles. The first approach is a coupled-dipole model, valid at low intensity, which includes cooperative effects, such as superradiance, and other coherent properties. The second one is a random-walk model, which includes classical multiple scattering and neglects coherence effects. The third approach is a crude approximation based only on the attenuation of the excitation beam inside the medium, the so-called shadow effect. We show that in the case of a low-density sample, the random-walk approach is an excellent approximation for steady-state light scattering and that the shadow effect surprisingly gives rather accurate results at least up to optical depths on the order of 15.