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arXiv:1902.04289 · Journal of the Optical Society of America B

Comparison of three approaches to light scattering by dilute cold atomic ensembles

Igor M. Sokolov, William Guerin

Published Jul 10, 2019• 13 citations
arXivHTMLPDF

Abstract

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.

DOI
10.1364/josab.36.002030

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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.
Cooperative scattering has been the subject of intense research in the last years. In this article, we discuss the concept of cooperative scattering from a broad perspective. We briefly review the various collective effects that occur when light interacts with an ensemble of atoms. We show that some effects that have been recently discussed in the context of ‘single-photon superradiance’, or cooperative scattering in the linear-optics regime, can also be explained by ‘standard optics’, i.e. using macroscopic quantities such as the susceptibility or the diffusion coefficient. We explain why some collective effects depend on the atomic density, and others on the optical depth. In particular, we show that, for a large and dilute atomic sample driven by a far-detuned laser, the decay of the fluorescence, which exhibits superradiant and subradiant dynamics, depends only on the on-resonance optical depth. We also discuss the link between concepts that are independently studied in the quantum-optics community and in the mesoscopic-physics community. We show that the coupled-dipole model predicts a departure from Ohm’s law for the diffuse light, that incoherent multiple scattering can induce a saturation of fluorescence and we also show the similarity between the weak-localization correction to the diffusion coefficient and the inaccuracy of Lorentz local field correction to the susceptibility.
We compare two different models of transport of light in a disordered system with a spherical Gaussian distribution of scatterers. A coupled dipole model, taking into account all interference effects, is compared to an incoherent model, using a random walk of particles. Besides the well-known coherent backscattering effect and a well pronounced forward lobe, the incoherent model reproduces extremely well all scattering features. In an experiment with cold atoms, we use the momentum recoil imparted on the center of mass of the sample as a partial probe of the light-scattering properties. We find that the force acting on the center of mass of the atoms is not well suited to exhibit the coherence effects in light propagation under multiple-scattering conditions.
In this thesis we investigate theoretically two distinct systems of dipole-coupled atoms. In Part I we investigate light scattering from a system of N ultracold atoms, with laser induced electric dipole interactions. We derive the equations of motion in the Heisenberg picture for the atomic operators, for an arbitrary dipole transition. Then we take the specific case of a jl = 0 → ju = 1 transition and derive the second and third-order inter-atomic correlations. We solve the resulting set of linear equations for two and three atoms exactly, with particular focus on the exact two-atom system. We find a steady-state analytic solution for the two atoms in a specific geometric configuration, and use this to derive explicit expressions for the spatial and coherence properties of the far-field scattered light intensity, valid for the full range of system parameters. A comprehensive survey of the scattering behaviour is given, with key features precisely characterised, including subradiant scattering. We examine in detail a decorrelation approximation that has potential applications for larger systems of atoms that are intractable in a full quantum treatment. We introduce the concept of an effective driving field and show that it can provide a direct and intuitive physical interpretation of key aspects of the system behaviour, including subradiant scattering. Finally, we show that this effective field interpretation, and the decorrelation approximation, is readily extended to a three atom system. In Part II of this thesis we present our investigation of the quantum many-body dynamics of a large ensemble of bosonic S = 3 chromium atoms in a three-dimensional lattice. We implement an extended Bose-Hubbard model which includes the tunnelling, onsite spinor in- teractions and dipole-dipole interactions (giving interactions between atoms on neighbouring sites). We study the dynamics of the population of the different Zeeman levels as a function of lattice depth following a sudden spin rotation, and provide comparison to experimental res- ults. We are able to identify two distinct regimes: At low lattice depths, where atoms are in the superfluid regime, we observe the spin dynamics are strongly determined by the competi- tion between particle transport, onsite interactions and external magnetic field gradients. On the contrary, at high lattice depths, transport is largely frozen out and the spin populations are mainly driven by the long range dipolar interactions and quantum fluctuations.
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.
Cooperative scattering in cold atoms has gained renewed interest, in particular in the context of single-photon superradiance, with the recent experimental observation of super- and subradiance in dilute atomic clouds. Numerical simulations to support experimental signatures of cooperative scattering are often limited by the number of dipoles which can be treated, well below the number of atoms in the experiments. In this paper, we provide systematic numerical studies aimed at matching the regime of dilute atomic clouds. We use a scalar coupled-dipole model in the low excitation limit and an exclusion volume to avoid density-related effects. Scaling laws for super- and subradiance are obtained and the limits of numerical studies are pointed out. We also illustrate the cooperative nature of light scattering by considering an incident laser field, where half of the beam has a π phase shift. The enhanced subradiance obtained under such condition provides an additional signature of the role of coherence in the detected signal.
We derive equations for the strongly coupled system of light and dense atomic ensembles. The formalism includes an arbitrary internal-level structure for the atoms and is not restricted to weak excitation of atoms by light. In the low-light-intensity limit for atoms with a single electronic ground state, the full quantum field-theoretical representation of the model can be solved exactly by means of classical stochastic electrodynamics simulations for stationary atoms that represent cold atomic ensembles. Simulations for the optical response of atoms in a quantum degenerate regime require one to synthesize a stochastic ensemble of atomic positions that generates the corresponding quantum statistical position correlations between the atoms. In the case of multiple ground levels or at light intensities where saturation becomes important, the classical simulations require approximations that neglect quantum fluctuations between the levels. We show how the model is extended to incorporate corrections due to quantum fluctuations that result from virtual scattering processes. In the low-light-intensity limit, we illustrate the simulations in a system of atoms in a Mott-insulator state in a two-dimensional optical lattice, where recurrent scattering of light induces strong interatomic correlations. These correlations result in collective many-atom subradiant and superradiant states and a strong dependence of the response on the spatial confinement within the lattice sites.