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.
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.
The objective of this thesis is to expand our understanding of collective light-scattering phenomena, which manifest themselves in the strong suppression of radiation from the scattering medium. In particular, we are interested in subradiance, a collective effect in spontaneous emission which, as a result of the dissipative coupling of atoms through common electromagnetic modes, creates long-lived excitation modes in an ensemble of cold atoms, with lifetimes much longer than those of individual, isolated atoms. Previously, subradiance had been well-characterized for dilute cold-atom scattering media and the low-intensity limit of the driving laser (linear-optics regime). In this thesis, we study this collective phenomenon beyond the linear-optics and dilute regimes.To study experimentally subradiance beyond the linear-optics regime, we varied the saturation parameter of the excitation laser up to relatively large values and we have observed the increase of the subradiant population with increasing saturation parameter. More importantly, we have identified the super-linear scaling of the subradiant population beyond the linear-optics regime, due to a process similar to optical pumping via multi-excitation superradiant states. This study showed that the increase in the intensity of the driving laser beyond the linear-optics regime can overcome the weak coupling of subradiant modes with the external world.Moreover, we have numerically studied subradiance using the vectorial coupled-dipole model, with a focus on understanding the effect of the near-field dipole-dipole interaction. For that, we extensively compared the vectorial and scalar (which does not contain near-field interaction terms) models and studied the subradiant lifetime as a function of the density and optical thickness of the cold-atom cloud. We observed that the near-field terms are detrimental for subradiance, which was seen in the reduction of the subradiant lifetimes with increasing density. This detrimental character of near-field terms can be interpreted as being due to an effective inhomogeneous broadening induced by the near-field interaction, which reduces the subradiant lifetimes as the density increases.The detrimental character of near-field interaction has also been previously numerically identified for Anderson localization of light waves (Anderson localization is a coherent multiple-scattering wave phenomenon in a strongly scattering medium that results in a cessation of a diffusive wave transport; it also yields long-lived modes): the scalar coupled-dipole model predicts Anderson localization of light waves, but not the vectorial one. However, adding a strong magnetic field allows one to recover localized modes for vectorial light. In this context, we numerically studied a possible signature of Anderson localization of light in cold atoms, based on the measurement of intensity fluctuations of the scattered light. We have shown that at the transition to the localized regime, the fluctuations are enhanced. In particular, for vectorial light, we have demonstrated the absence and recovery of enhanced intensity fluctuations without and with the applied magnetic field, which further corroborates that the intensity fluctuations could serve as an experimental way to probe the localized states.
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 study numerically the slow (subradiant) decay of the fluorescence of motionless atoms after a weak pulsed excitation. We show that, in the linear-optics regime and for an excitation detuned by several natural linewidths, the slow decay rate can be dominated by close pairs of atoms (dimers) forming superradiant and subradiant states. However, for a large-enough resonant optical depth and at later time, the dynamics is dominated by collective many-body effects. In this regime, we study the polarization and the spectrum of the emitted light, as well as the spatial distribution of excitation inside the sample, as a function of time during the decay dynamics. The behavior of these observables is consistent with what would be expected for radiation trapping of nearly resonant light. This finding sheds light on subradiance in dilute samples by providing an interpretation based on the light behavior of the system (multiple scattering) which is complementary to the more commonly used picture of the collective atomic Dicke state.
Dipole-dipole interactions are at the origin of long-lived collective atomic states, often called subradiant, which are explored for their potential use in novel photonic devices or in quantum protocols. Here, we study subradiance beyond the single-excitation regime and experimentally demonstrate a 200-fold increase in the population of these modes, as the saturation parameter of the driving field is increased. We attribute this enhancement to a mechanism similar to optical pumping through the well-coupled superradiant states. The lifetimes are unaffected by the pump strength, as the system is ultimately driven toward the single-excitation sector. Our study is a new step in the exploration of the many-body dynamics of large open systems.
We experimentally and numerically study the temporal dynamics of light scattered by large clouds of cold atoms after the exciting laser is switched off, in the low intensity (linear-optics) regime. Radiation trapping due to multiple scattering as well as subradiance lead to decay much slower than the single atom fluorescence decay. These two effects have already been observed separately, but the interplay between them remained to be understood. Here, we show that with well chosen parameters of the driving field, the two effects can occur at the same time, but follow different scaling behaviors. The subradiant decay is observed at late time and its rate is independent of the detuning, while the radiation trapping decay is observed at intermediate time and depends on the detuning through the optical depth of the sample. Numerical simulations based on random walk process and coupled-dipole equations support our interpretations. Our study clarifies the different interpretations and physical mechanisms at the origin of slow temporal dynamics of light in cold atoms.
The collective scattering of light by a large number of coupled scatterers yields a rich many-body physics, yet treating such a problem in the quantum regime is a challenge.In this thesis, we consider a large atomic cloud in free space and driven by a monochromatic light, where the vacuum modes induce long-range dipole-dipole interactions.In order to study clouds of hundreds of particles, higher order correlation terms are neglected, keeping only quantum correlations between pair of atoms: this allows to reduce the number of degrees of freedom from 2 2N in the full quantum model to N 2 .Most of the works in the literature on dipole-dipole interactions have been performed in the linear optics limit, and our techniques allow to compare classical to beyond-semi-classical results.In particular, superradiance and subradiance have been reported in the decay dynamics of the cloud.Differently, by considering a system in the ground state and switching on the pump, we show that superradiance is also present in the Rabi oscillations at a rate obtained from using a single-dipole model for the radiated intensity.A frequency shift in the Rabi oscillations is also reported, which can be interpreted, in a linear dispersion theory, as a signature of a collective multimode vacuum Rabi splitting.While the classical dipoles model captures correctly the dynamics in the low-intensity regime, it fails for higher saturation, where semi-classical methods can be applied successfully.In particular, we observe a quantum subradiant decay in the intensity of the radiated field in the saturated regime.Furthermore, considering the decay dynamics starting from an initially strongly driven cloud, we observed that the states with n < N/2 excited atoms decays much slower than the ones with n > N/2: in other words, the upper part of the Dicke ladder is characterized by a superradiant emission, and the lower part by a subradiant one.Finally, investigating the fluorescence spectrum, we obtained quantum cooperative effects that modify the steady-state spectrum: additional sidebands at twice the Rabi frequency for the system driven at resonance and, out of resonance, an asymmetry in the peaks at the generalized Rabi frequency, and for all detection angles.We also present preliminary results of a sensor model that can capture the time evolution of the spectrum in the decay dynamics, a situation that the quantum regression theorem fails to describe.Several of these results were discussed in parallel with experimental data obtained by an experimental group of collaborators, and others aim to guide future experiments.