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.
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.
We study the collective optical response of an atomic ensemble confined within a single-mode optical cavity by stochastic electrodynamics simulations that include the effects of atomic position correlations, internal level structure, and spatial variations in cavity coupling strength and atom density. In the limit of low light intensity, the simulations exactly reproduce the full quantum field-theoretical description for cold stationary atoms and at higher light intensities we introduce semiclassical approximations to atomic saturation that we compare with the exact solution in the case of two atoms. We find that collective subradiant modes of the atoms, with very narrow linewidths, can be coupled to the cavity field by spatial variation of the atomic transition frequency and resolved at low intensities, and show that they can be specifically driven by tailored transverse pumping beams. We show that the cavity optical response, in particular both the subradiant mode profile and the resonance shift of the cavity mode, can be used as a diagnostic tool for the position correlations of the atoms and hence the atomic quantum many-body phase. The quantum effects are found to be most prominent close to the narrow subradiant mode resonances at high light intensities. Although an optical cavity can generally strongly enhance quantum fluctuations via light confinement, we show that the semiclassical approximation to the stochastic electrodynamics model provides at least a qualitative agreement with the exact optical response outside the subradiant mode resonances even in the presence of significant saturation of the atoms.
We study propagation of low-intensity light in a medium within a one-dimensional (1D) model electrodynamics. It is shown that the coupled theory for light and matter fields may be solved, in principle exactly, by means of stochastic simulations that account for both collective linewidths and line shifts, and for quantum statistical position correlations of the atoms. Such simulations require that one synthesize atomic positions that have correlation functions appropriate for the given type of atomic sample. We demonstrate how one may simulate both a Bose-Einstein condensate (BEC) and a zero-temperature noninteracting Fermi-Dirac gas. Results of simulations of light propagation in such quantum degenerate gases are compared with analytical density expansions obtained by adapting the approach of Morice, Castin, and Dalibard [Phys. Rev. A 51, 3896 (1995)] to the 1D electrodynamics. A BEC exhibits an optical resonance that narrows and stays somewhat below the atomic resonance frequency as collective effects set in with increasing atom density. The first two terms in the analytical density expansion are in excellent agreement with numerical results for a condensate. While fermions display a similar narrowing and shift of the resonance with increasing density, already in the limit of very dilute gas the linewidth is only half of the resonance linewidth of an isolated atom. We attribute this to the regular spacing between the atoms, which is enforced by the Pauli exclusion principle. The analytical density expansion successfully predicts the narrowing, and also gives the next term in the density expansion of the optical response in semiquantitative agreement with numerical simulations.
Understanding strong cooperative optical responses in dense and cold atomic ensembles is vital for fundamental science and emerging quantum technologies. Methodologies for characterizing light-induced quantum effects in such systems, however, are still lacking. Here we unambiguously identify significant quantum many-body effects, robust to position fluctuations and strong dipole-dipole interactions, in light scattered from planar atomic ensembles, by comparing full quantum simulations with a semiclassical model neglecting quantum fluctuations. We find pronounced quantum effects at high atomic densities, light close to saturation intensity, and around subradiant resonances. Such conditions also maximize spin-spin correlations and entanglement between atoms, revealing the microscopic origin of light-induced quantum effects. In several regimes of interest, our approximate model reproduces light transmission remarkably well, permitting analysis of otherwise numerically inaccessible large ensembles, in which we observe many-body analogues of resonance power broadening, vacuum Rabi splitting, and significant suppression in cooperative reflection from atomic arrays.
In the study of optical properties of large atomic systems, a weak laser driving is often assumed to simplify the system dynamics by linearly coupled equations. Here we investigate the light-scattering properties of atomic ensembles beyond weak-field excitation through the cumulant expansion method. By progressively incorporating higher-order correlations into the steady-state equations, an enhanced accuracy can be achieved in comparison to the exact solutions obtained by solving a full density matrix. Our analysis reveals that, in the regime of weak dipole-dipole interaction, the first-order expansion yields satisfactory predictions for optical depth, while denser atomic configurations necessitate consideration of higher-order correlations. As the intensity of incident light increases, atom saturation effects become noticeable, giving rise to significant changes in light transparency, energy shift, and decay rate. This saturation phenomenon extends to subradiant atom arrays even under weak driving conditions, leading to substantial deviations from the linear model. Our findings demonstrate that the mean-field model is a good extension to linear models as it balances both accuracy and computational complexity. However, the crucial role of higher-order cumulants in large and dense atom systems remains unclear, since it is challenging theoretically owing to the exponentially increasing Hilbert space in such light-matter interacting systems.
Abstract Understanding strong cooperative optical responses in dense and cold atomic ensembles is vital for fundamental science and emerging quantum technologies. Methodologies for characterizing light-induced quantum effects in such systems, however, are still lacking. Here we unambiguously identify significant quantum many-body effects, robust to position fluctuations and strong dipole–dipole interactions, in light scattered from planar atomic ensembles by comparing full quantum simulations with a semiclassical model neglecting quantum fluctuations. We find pronounced quantum effects at high atomic densities, light close to saturation intensity, and around subradiant resonances. Such conditions also maximize spin–spin correlations and entanglement between atoms, revealing the microscopic origin of light-induced quantum effects. In several regimes of interest, our approximate model reproduces light transmission remarkably well, permitting analysis of otherwise numerically inaccessible large ensembles, in which we observe many-body analogues of resonance power broadening, vacuum Rabi splitting, and significant suppression in cooperative reflection from atomic arrays.
We develop a general dressed-state framework for computing fluorescence spectra, probe absorption spectra, and photon-photon correlations of light scattered by ensembles of Nat two-level atoms with arbitrary Jg→Je transitions driven by intense coherent fields. The approach employs a full vectorial treatment of the electromagnetic field, handles any atomic geometries, illumination directions, and polarizations, and yields optical observables as explicit sums of Lorentzian lines whose positions, widths, and weights are directly tied to the eigenvalues and eigenvectors of the Lindbladian. The framework is implemented in an open-source Python package and benchmarked against exact single- and two-atom calculations. We identify geometries in which the full vectorial description is essential, and the scalar approximation fails qualitatively. Applying the method to pairs of atoms with a Jg=0→Je=1 transition, we show that elastic and inelastic scattered intensities collapse onto universal master curves controlled by a single collective saturation parameter built from the dominant superradiant mode, across several orders of magnitude in drive strength and interatomic distance. We identify collective phenomena that require a description beyond this single-mode picture. Extending the analysis to atoms with ground-state degeneracy, we find that most collective features carry over, while two qualitatively new effects emerge: an incoherent spontaneous Raman channel that modifies the scaling of inelastic emission, and a slow timescale in the time-delayed correlations g(2)(τ) governed by the competition between Raman scattering and subradiant decay, controlled by a single dimensionless parameter. These results provide both physical insight and practical computational tools for engineering collective optical responses in few-atom systems such as optical tweezer arrays.