Cooperative scattering in cold atoms has gained renewed interest, in particular in the context of single-photon superradiance, with the recent experimental observation of super- and subradiance in dilute atomic clouds. Numerical simulations to support experimental signatures of cooperative scattering are often limited by the number of dipoles which can be treated, well below the number of atoms in the experiments. In this paper, we provide systematic numerical studies aimed at matching the regime of dilute atomic clouds. We use a scalar coupled-dipole model in the low excitation limit and an exclusion volume to avoid density-related effects. Scaling laws for super- and subradiance are obtained and the limits of numerical studies are pointed out. We also illustrate the cooperative nature of light scattering by considering an incident laser field, where half of the beam has a π phase shift. The enhanced subradiance obtained under such condition provides an additional signature of the role of coherence in the detected signal.
Cooperative scattering in cold atoms has gained renewed interest, in particular in the context of single-photon superradiance, with the recent experimental observation of super- and subradiance in dilute atomic clouds. Numerical simulations to support experimental signatures of cooperative scattering are often limited by the number of dipoles which can be treated, well below the number of atoms in the experiments. In this paper, we provide systematic numerical studies aimed at matching the regime of dilute atomic clouds. We use a scalar coupled-dipole model in the low excitation limit and an exclusion volume to avoid density-related effects. Scaling laws for super- and subradiance are obtained and the limits of numerical studies are pointed out. We also illustrate the cooperative nature of light scattering by considering an incident laser field, where half of the beam has a π phase shift. The enhanced subradiance obtained under such condition provides an additional signature of the role of coherence in the detected signal.
The problem of the interaction of N atoms with a laser beam and vacuum modes can give rise to many interesting phenomena concerning the spontaneous emission of light and its propagation in the medium. The cooperative effects, for example, such as superadiance and subradiance, are effects related to the coherence created between the atoms when a photon is emitted spontaneously by a single excited atom. Superradiance can be defined as the enhancement of the spontaneous emission due to constructive interference of the scattered light. Its counterpart, subradiance, is the trapping of some remaining light due to destructive interference. In cold atoms, some previous theoretical works predict and characterize these two cooperative effects in a large and diluted atomic cloud, in the regime of low intensities and large detunings of the incident laser. The theoretical model is a coupled-dipole model for two-level atoms driven by a low-intensity field and in the scalar approach. The experiment consists in measuring the super- and subradiant decay rates from the temporal emitted intensity after the switch off of the incident laser in the steady state. Our experimental setup consists in a magneto-optical trap of rubidium 87 atoms at large resonant optical thicknesses. A probe beam excites the atoms close to the D2 line. The intensity emitted is detected by a single photon detector with no afterpulsing and a calibration procedure allows us to determine the resonant optical thickness of the cloud and its temperature. In this work, we report the experimental observation of super- and subradiance in a large cloud of cold atoms. For subradiance, the main result is the linear evolution of the characteristic time with the resonant optical thickness of the cloud and its independence of the detuning. For superradiance, we observe superradiance out of the forward direction. We verify the validity of our interpretations with the predictions of the coupled-dipole model. Finally, we discuss the interplay of subradiance and radiation trapping, as well as theoretical predictions for: a setup of a phased cloud, to control the subradiant amplitude emission; and temperature effects, where subradiance is shown to be robust in a large range of temperatures.
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.
Since Dicke's seminal paper on coherence in spontaneous radiation by atomic ensembles, superradiance has been extensively studied. Subradiance, on the contrary, has remained elusive, mainly because subradiant states are weakly coupled to the environment and are very sensitive to nonradiative decoherence processes. Here, we report the experimental observation of subradiance in an extended and dilute cold-atom sample containing a large number of particles. We use a far detuned laser to avoid multiple scattering and observe the temporal decay after a sudden switch-off of the laser beam. After the fast decay of most of the fluorescence, we detect a very slow decay, with time constants as long as 100 times the natural lifetime of the excited state of individual atoms. This subradiant time constant scales linearly with the cooperativity parameter, corresponding to the on-resonance optical depth of the sample, and is independent of the laser detuning, as expected from a coupled-dipole model.
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.
We investigate numerically the role of near-field dipole-dipole interactions on the late-emission dynamics of large disordered cold atomic samples driven by a weak field. Previous experimental and numerical studies of subradiance in macroscopic samples have focused on low-density samples of pure two-level atoms, without internal structure, which corresponds to a scalar representation of the light. The cooperative nature of the late emission of light is then governed by the resonant optical depth. Here, by considering the vectorial nature of the light, we show the detrimental role of the near-field terms on cooperativity in higher-density samples. The observed reduction in the subradiant lifetimes is interpreted as a signature of the inhomogeneous broadening due to the near-field contributions, in analogy with the van der Waals dephasing phenomenon for superradiance.
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 22N in the full quantum model to N2. 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.