We study theoretically the scattering of light by an ensemble of N resonant atoms in a subwavelength volume. We consider the low intensity regime so that each atom responds linearly to the field. While N noninteracting atoms would scatter N^{2} more than a single atom, we find that N interacting atoms scatter less than a single atom near resonance. In addition, the scattered power presents strong fluctuations, either from one realization to another or when varying the excitation frequency. We analyze this counterintuitive behavior in terms of collective modes resulting from the light-induced dipole-dipole interactions. We find that for small samples and sufficiently large atom number, their properties are governed only by their volume.
We study theoretically the scattering of light by an ensemble of N resonant atoms in a subwavelength volume. We consider the low intensity regime so that each atom responds linearly to the field. While N noninteracting atoms would scatter N^{2} more than a single atom, we find that N interacting atoms scatter less than a single atom near resonance. In addition, the scattered power presents strong fluctuations, either from one realization to another or when varying the excitation frequency. We analyze this counterintuitive behavior in terms of collective modes resulting from the light-induced dipole-dipole interactions. We find that for small samples and sufficiently large atom number, their properties are governed only by their volume.
We study theoretically the concept of homogenization in optics using an ensemble of randomly distributed resonant stationary atoms with density $\ensuremath{\rho}$. The ensemble is dense enough for the usual condition for homogenization, viz. $\ensuremath{\rho}{\ensuremath{\lambda}}^{3}\ensuremath{\gg}1$, to be reached. Introducing the coherent and incoherent scattered powers, we define two criteria to define the homogenization regime. We find that when the excitation field is tuned in a broad frequency range around the resonance, neither of the criteria for homogenization is fulfilled, meaning that the condition $\ensuremath{\rho}{\ensuremath{\lambda}}^{3}\ensuremath{\gg}1$ is not sufficient to characterize the homogenized regime around the atomic resonance. We interpret these results as a consequence of the light-induced dipole-dipole interactions between the atoms, which implies a description of scattering in terms of collective modes rather than as a sequence of individual scattering events. Finally, we show that, although homogenization can never be reached for a dense ensemble of randomly positioned laser-cooled atoms around resonance, it becomes possible if one introduces spatial correlations in the positions of the atoms or nonradiative losses, such as would be the case for organic molecules or quantum dots coupled to a phonon bath.
We study the emergence of collective scattering in the presence of dipole-dipole interactions when we illuminate a cold cloud of rubidium atoms with a near-resonant and weak intensity laser. The size of the atomic sample is comparable to the wavelength of light. When we gradually increase the number of atoms from 1 to ~450, we observe a broadening of the line, a small redshift and, consistently with these, a strong suppression of the scattered light with respect to the noninteracting atom case. We compare our data to numerical simulations of the optical response, which include the internal level structure of the atoms.
The interaction of light with an atomic sample containing a large number of particles gives rise to many collective (or cooperative) effects, such as multiple scattering, superradiance, and subradiance, even if the atomic density is low and the incident optical intensity weak (linear optics regime). Tracing over the degrees of freedom of the light field, the system can be well described by an effective atomic Hamiltonian, which contains the light-mediated dipole-dipole interaction between atoms. This long-range interaction is at the origin of the various collective effects, or of collective excitation modes of the system. Even though an analysis of the eigenvalues and eigenfunctions of these collective modes does allow distinguishing superradiant modes, for instance, from other collective modes, this is not sufficient to understand the dynamics of a driven system, as not all collective modes are significantly populated. Here, we study how the excitation parameters, i.e., the driving field, determines the population of the collective modes. We investigate in particular the role of the laser detuning from the atomic transition, and demonstrate a simple relation between the detuning and the steady-state population of the modes. This relation allows understanding several properties of cooperative scattering, such as why superradiance and subradiance become independent of the detuning at large enough detuning without vanishing, and why superradiance, but not subradiance, is suppressed near resonance. We also show that the spatial properties of the collective modes allow distinguishing diffusive modes, responsible for radiation trapping, from subradiant modes.
We experimentally study resonant light scattering by a one-dimensional randomly filled chain of cold two-level atoms. By a local measurement of the light scattered along the chain, we observe constructive interferences in light-induced dipole-dipole interactions between the atoms. They lead to a shift of the collective resonance despite the average interatomic distance being larger than the wavelength of the light. This result demonstrates that strong collective effects can be enhanced by structuring the geometrical arrangement of the ensemble. We also explore the high intensity regime where atoms cannot be described classically. We compare our measurement to a mean-field, nonlinear coupled-dipole model accounting for the saturation of the response of a single atom.
We study the emergence of a collective optical response of a cold and dense 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.
Over the past half century, atomic ensembles have been used to create sensors, clocks, and quantum information systems. As these devices become more compact, and as the number of atoms increases to improve the sensitivity for detection, the atomic samples are increasing in density and optical depth. As such, the spectroscopic properties of the atomic media are modified due to interactions among the particles in the ensemble. We report investigation of near-resonance light scattering from a cold atomic sample of 87Rb. Initially prepared in a magneto-optical trap, the atoms are loaded into a far-off-resonance optical dipole trap (FORT) in which the ensemble has a temperature near 100 mK and initial Gaussian radii of approximately 3 mm and 280 mm in the transverse and longitudinal directions, respectively. With atomic densities in the range of 1010 - 1013 atoms/cm3, measurements are made on the F=2 -> F'=3 nearly closed hyperfine transition. The experimental geometry consists of projecting a near-resonance collimated laser beam onto the entire volume of the FORT and detecting the diffusely scattered light. The measured scattered light intensity as a function of detuning, atomic number, and sample size suggests that collective light scattering depends on the optical depth of the system.