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Cooperative Effects in the Optical Response of Dense Atomic Gases

Yi Li

Published Jan 1, 2016• 0 citations
OpenAlex

Abstract

At high density, dipole-dipole interactions between the atoms may have a major impact on light propagation in a dense gas. We have developed a classical-electrodynamics simulation to study the cooperative response of a near-resonant gas to light. We take into account the motion of the radiators using classical trajectories, including collisions with the walls of the container and atom-atom collisions, and describe the transition from homogeneously broadened to inhomogeneously broadened phenomenology.

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•Dec 14, 2023•0 citations
At high density, dipole-dipole interactions between the atoms may have a major impact on light propagation in a dense gas. We have developed a classical-electrodynamics simulation to study the cooperative response of a near-resonant gas to light. We take into account the motion of the radiators using classical trajectories, including collisions with the walls of the container and atom-atom collisions, and describe the transition from homogeneously broadened to inhomogeneously broadened phenomenology.
We study light propagation through a slab of cold gas using both the standard electrodynamics of polarizable media and massive atom-by-atom simulations of the electrodynamics. The main finding is that the predictions from the two methods may differ qualitatively when the density of the atomic sample $\ensuremath{\rho}$ and the wave number of resonant light kkk satisfy $\ensuremath{\rho}{k}^{\ensuremath{-}3}\ensuremath{\gtrsim}1$. The reason is that the standard electrodynamics is a mean-field theory, whereas for sufficiently strong light-mediated dipole-dipole interactions the atomic sample becomes strongly correlated. The deviations from mean-field theory appear to scale with the parameter $\ensuremath{\rho}{k}^{\ensuremath{-}3}$, and we demonstrate noticeable effects already at $\ensuremath{\rho}{k}^{\ensuremath{-}3}\ensuremath{\simeq}{10}^{\ensuremath{-}2}$. In dilute gases and in gases with an added inhomogeneous broadening the simulations show shifts of the resonance lines in qualitative agreement with the predicted Lorentz-Lorenz shift and ``cooperative Lamb shift,'' but the quantitative agreement is unsatisfactory. Our interpretation is that the microscopic basis for the local-field corrections in electrodynamics is not fully understood.
We study the emergence of a collective optical response of a cold and dense 87Rb^{87}\mathrm{Rb}87Rb atomic cloud to a near-resonant low-intensity light when the atom number is gradually increased. Experimental observations are compared with microscopic stochastic simulations of recurrent scattering processes between the atoms that incorporate the atomic multilevel structure and the optical measurement setup. We analyze the optical response of an inhomogeneously broadened gas and find that the experimental observations of the resonance line shifts and the total collected scattered light intensity in cold atom clouds substantially deviate from those of thermal atomic ensembles, indicating strong light-induced resonant dipole-dipole interactions between the atoms. At high densities, the simulations also predict a significantly slower decay of light-induced excitations in cold than in thermal atom clouds. The role of dipole-dipole interactions is discussed in terms of resonant coupling examples and the collective radiative excitation eigenmodes of the system.
When atoms are coupled to a common electromagnetic environment, the exchange of photons through dipole-dipole interactions leads to the emergence of cooperative effects. As a particular example, superradiance arises from spontaneous emission when this exchange leads to constructive interference of the emitted photons. Here, we introduce an integrated method for studying cooperative radiation in many-body systems. This method, which allows to study extended systems with arbitrarily large number of particles, can be formulated by an effective, nonlinear, two-atom master equation that describes the dynamics using a closed form which treats single- and many-body terms on an equal footing. We apply this method to a homogeneous gas of initially inverted two-level atoms, and demonstrate the appearance of both superradiance and subradiance, identifying a many-body coherence term as the source of these cooperative effects. We describe the many-body induced broadening -- which is analytically found to scale with the optical depth of the system -- and light shifts, and distinguish spontaneous effects from induced ones. In addition, we theoretically predict the time-dependence of subradiance, and the phase change of the radiated field during the cooperative decay.
In this paper, our experimental studies of dipole-dipole interactions in excited resonance gases are discussed. In weakly excited gas the dipole broadening of optical transitions is proportional to its density N. A gas medium can be identified by its density N as rarefied gas, where dipole broadening of atomic transitions is much less than Doppler width, or as dense gas, where dipole broadening is much more than Doppler width. According to our experiments the dipole broadening in rarefied gas does not depend on the optical excitation. This behavior is in a good agreement with predictions of standard theory for impact atomic collisions. In excited dense gas we observed the strong reduction of the dipole broadening. These experimental results are not described by standard theory for impact collisions. We suggested a simple description of the optical properties for excited dense gas.
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.