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.
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.
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.
Waveguide QED with cold atoms provides a potent platform for the study of non-equilibrium, many-body, and open-system quantum dynamics. Even with weak coupling and strong photon loss, the collective enhancement of light-atom interactions leads to strong correlations of photons arising in transmission, as shown in recent experiments. Here we apply an improved mean-field theory based on higher-order cumulant expansions to describe the experimentally relevant, but theoretically elusive, regime of weak coupling and strong driving of large ensembles. We determine the transmitted power, squeezing spectra and the degree of second-order coherence, and systematically check the convergence of the results by comparing expansions that truncate cumulants of few-particle correlations at increasing order. This reveals the important role of many-body and long-range correlations between atoms in steady state. Our approach allows to quantify the trade-off between anti-bunching and output power in previously inaccessible parameter regimes. Calculated squeezing spectra show good agreement with measured data, as we present here.
Waveguide QED with cold atoms provides a potent platform for the study of non-equilibrium, many-body, and open-system quantum dynamics. Even with weak coupling and strong photon loss, the collective enhancement of light-atom interactions leads to strong correlations of photons arising in transmission, as shown in recent experiments. Here we apply an improved mean-field theory based on higher-order cumulant expansions to describe the experimentally relevant, but theoretically elusive, regime of weak coupling and strong driving of large ensembles. We determine the transmitted power, squeezing spectra and the degree of second-order coherence, and systematically check the convergence of the results by comparing expansions that truncate cumulants of few-particle correlations at increasing order. This reveals the important role of many-body and long-range correlations between atoms in steady state. Our approach allows to quantify the trade-off between anti-bunching and output power in previously inaccessible parameter regimes. Calculated squeezing spectra show good agreement with measured data, as we present here.
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.
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.
Atoms subject to weak coherent incident light can be treated as coupled classical linear oscillators, supporting subradiant and superradiant collective excitation eigenmodes. We identify the limits of validity of this linear classical oscillator model at increasing intensities of the drive by solving the quantum many-body master equation for coherent and incoherent scattering from a chain of trapped atoms. We show that deviations from the linear classical oscillator model depend sensitively on the resonance linewidths υα of the collective eigenmodes excited by light, with the intensity at which substantial deviation occurs scaling as a power law of υα. The linear classical oscillator model then becomes inaccurate at much lower intensities for subradiant collective excitations than superradiant ones, with an example system of seven atoms resulting in critical incident light intensities differing by a factor of 30 between the two cases. By individually exciting eigenmodes, we find that this critical intensity has a υα2.5 scaling for narrower resonances and more strongly interacting systems, while it approaches a υα3 scaling for broader resonances and when the dipole-dipole interactions are reduced. The υα3 scaling also corresponds to the semiclassical result whereby quantum fluctuations between the atoms have been neglected. We study both the case of perfectly mode-matched drives and the case of standing-wave drives, with significant differences between the two cases appearing only at very subradiant modes and positions of Fano resonances.