This thesis contributes to the field of collective effects in atomic ensembles. We explore synchronization of superradiant lasers in different coupling configurations and study superradiance in off-resonantly probed atomic ensembles, where we take into account the complete level structure of alkali metal atoms. In the first part we introduce the superradiant laser and extend the discussion of synchronization of symmetrically coupled superradiant lasers to unidirectional coupled superradiant lasers. We show that synchronization is also present when we replace the superradi- ant laser couplings with classical channels, meaning the synchronization can be considered a classical effect. In the second part we generalize a widely used approximation method taking into account lower order atom-atom correlations — the cumulant expansion method — to a basis independent formalism. We implement this formalism in a Python program allowing us to numerically calculate the n-atom reduced density matrix and two-time correlation functions for ensembles of multi-level atoms. This method allows us to study the stationary state of an ensemble of off-resonantly probed alkali metal atoms with a ground-state manifold consisting of many hyperfine levels. We show that collective effects in light-matter interaction depends on the tensor-polarizability of atoms and therefore cannot be explained on the basis of two-level-approximations.
This thesis contributes to the field of collective effects in atomic ensembles. We explore synchronization of superradiant lasers in different coupling configurations and study superradiance in off-resonantly probed atomic ensembles, where we take into account the complete level structure of alkali metal atoms. In the first part we introduce the superradiant laser and extend the discussion of synchronization of symmetrically coupled superradiant lasers to unidirectional coupled superradiant lasers. We show that synchronization is also present when we replace the superradi- ant laser couplings with classical channels, meaning the synchronization can be considered a classical effect. In the second part we generalize a widely used approximation method taking into account lower order atom-atom correlations — the cumulant expansion method — to a basis independent formalism. We implement this formalism in a Python program allowing us to numerically calculate the n-atom reduced density matrix and two-time correlation functions for ensembles of multi-level atoms. This method allows us to study the stationary state of an ensemble of off-resonantly probed alkali metal atoms with a ground-state manifold consisting of many hyperfine levels. We show that collective effects in light-matter interaction depends on the tensor-polarizability of atoms and therefore cannot be explained on the basis of two-level-approximations.
In the present thesis we investigate spatial and temporal intensity correlations which are created by statistically independent or by entangled light sources. Even though this classification may appear quite technical, the diverseness of the statistical properties of the considered photon sources naturally brings into our focus two different lines of research. In the first part of this thesis we will quantitatively study the non-classical and potentially entangled character of light fields which originate from a variety of different statistically independent light sources. To this end quantum correlations between light fields are analyzed which either stem from non-classical single-photon emitters (like ensembles of uncorrelated atoms) or from a mixture of non-classical and classical photon sources (like lasers with uncorrelated fluctuating initial phase). In the second part of this thesis we study correlations between initially entangled lightsources, namely localized atoms which share an entangled state. In the course of the investigations we physically reinterpret in particular the so called superradiance effect in a quantum-path formalism: superradiance denotes an enhanced mean radiated intensity in a particular direction, i.e., a focussing of the photons scattered by an atomic gas. This effect is commonly explained by a successive synchronization of the dipole moments of all participating atoms leading to a photon emission predominantly in one direction. For more than 60 years this focussing has been physically interpreted as a cooperative effect depending on the dipole-dipole interaction between the atoms. In contrast, we will show that it is rather a quantum-interference effect which is caused by non-synchronized and potentially widely separated entangled atoms.
The interaction between light and matter has captivated physicists for centuries, from early studies of vision and refraction in ancient Greece to the development of quantum mechanics and quantum electrodynamics in the past century. While the response of a single quantum emitter to light is well understood, the radiative properties of an ensemble of closely spaced emitters are far more intricate. Coupling to a shared electromagnetic environment induces coherent and dissipative interactions between emitters, giving rise to a collective response that cannot be captured by treating them independently. In the regime of few excitations, the system hosts delocalized subradiant states, that is, coherent superpositions that are largely decoupled from the electromagnetic field and thus decay at suppressed rates. While this weak coupling makes subradiant states attractive for quantum technologies, it also renders them difficult to manipulate. At higher excitation densities, the intrinsic nonlinearity of emitters and the exponential growth of the Hilbert space make theoretical and numerical descriptions of the system and its dynamics increasingly challenging. This thesis explores two fundamental questions: How can subradiant and dark states be selectively accessed and harnessed for practical applications in quantum technologies? And how can interacting ensembles of quantum emitters be efficiently simulated to uncover their many-body physics? The first part of the thesis develops protocols for controlling and addressing dark states in free-space and waveguide-coupled atomic arrays, demonstrating their utility in quantum storage and the deterministic generation of entangled photonic states. Incorporating atomic motion, we further show that collective subradiant states can enhance cooling in dense atomic arrays, offering new avenues for controlling motional dynamics. In the second part, we introduce cumulant expansions of the equations of motion as a powerful tool to analytically and numerically investigate collective decay in the many-body regime. We first examine the collective decay of fully excited atomic arrays in free space, characterizing the onset and scaling of the superradiant burst across different geometries. In collaboration with experiments on ultracold erbium atoms in optical lattices, we provide the first direct observations of many-body collective effects in free-space ordered arrays, including early-time superradiant bursts, late-time subradiant tails, and the emergence of atomic correlations throughout the dynamics. Finally, we theoretically and numerically explore the transient formation of multi-excitation subradiant states, and demonstrate how the existence of multiple dissipation channels suppresses steady-state superradiance in extended arrays.
In this paper we attempt to unify the theoretical treatment of a variety of cooperative interaction phenomena occurring in resonantly interacting radiation-matter systems. The system consists of a multimode optical field interacting with N resonant atoms in a region of large spatial extent. The field and atoms may or may not be coupled to reservoirs. We derive a set of coupled master equations for the reduced matter and radiation density operators of the composite system in the first Born approximation, using a method due to Bogoliubov. These equations describe within a single framework phenomena involving superradiant emission and coherent propagation. In the first place, our theory generalizes existing formulations of the superradiance problem by treating the radiation field as part of the dynamical system rather than as a reservoir. Hence, our equations describe stimulated interaction effects, which are entirely absent in the usual superradiance master equations. Moreover, our equations contain terms describing the self-consistent interaction of an average field with a set of polarizable atoms, as in the coupled Bloch and Maxwell equations of the theory of coherent pulse propagation, and enable us to describe fluctuations, arising from incoherent emission, about the average behavior described by the Bloch-Maxwell theory. We solve formally the dynamical equation for the radiation density operator and obtain a displaced multivariate Gaussian distribution centered on the solution of the Maxwell wave equation, which has as parameters the first and second moments of the matter density operator. Then we derive and discuss the field and atomic-moment equations, both in the wave-number and position representations. The moment equations enable us to show the relationship between descriptions of superradiant damping based on the Bloch equations and those based on the existence of correlated atomic states, including both as special cases. We introduce reduced matter moments, which allow us to separate incoherent- and coherent-emission effects and enable us to discuss the question of the closure of the moment equations. Then we consider cases where the behavior of the atomic system is dominated by a strong coherent pump wave or where the atoms are in a symmetric correlated state and show how the slowly-varying-envelope approximation simplifies the radiation-moment equations in these two cases. In the former case, we obtain an approximate theory which consists, in lowest order, of the Bloch-Maxwell equations with radiative-damping terms, plus an equation describing the time development of the correlation function for field fluctuations. Returning to our general formalism, we relate the usual parameters of the theory of radiative decay and of resonant interactions to the more general quantities appearing in our spatial analysis. Finally, we discuss the importance of the stimulated-emission terms appearing in our theory and describe several extensions, including the introduction of inhomogeneous broadening.
This thesis investigates two largely independent topics in many-body and quantum optical physics. The first concerns the thermalization of classical one-dimensional (1D) gases through three-body collisions, while the second explores collective light–matter interactions in atomic arrays and waveguide quantum electrodynamics, with an emphasis on subradiance, superradiance, and computational methods for many-body dynamics. The first part studies thermalization in dilute classical 1D gases, where conventional twobody collisions cannot establish thermal equilibrium. Using Monte Carlo calculations of the three-body collision kernel together with the Boltzmann equation and molecular dynamics simulations, we characterize the thermalization dynamics for particles interacting through inverse power-law and Lennard–Jones potentials. We show that the Boltzmann and molecular dynamics approaches agree in the dilute limit and derive the thermalization rate for inverse power-law interactions.The second part investigates realistic effects in collective light–matter systems. We first study the influence of finite trapping potentials on subradiant states in atomic arrays coupled through free space or a one-dimensional waveguide. We show that atomic motion fundamentally limits subradiant lifetimes through wavefunction delocalization, recoil heating, and dipole-force-induced motion, leading to decoherence and reduced quantum memory fidelity. These results identify optimal trapping and array configurations for long-lived collective excitations.The final chapters develop theoretical methods for describing photon emission in chiral and symmetric waveguide QED systems. Using higher-order mean-field approximations, we model collective emission in experimentally relevant chiral waveguides, obtaining agreement with recent experiments and deriving analytical expressions for photon statistics. We demonstrate that fourth-order correlations are required to capture the emergence of second-order coherence from a fully inverted state. Finally, in the thermodynamic limit of large atom number and fixed optical depth, we show that a second-order mean-field theory becomes exact, yielding analytical solutions for photon emission statistics in both chiral and symmetric waveguides. We characterize the crossover between enhanced superradiant and subradiant emission, establish the suppression of emission fluctuations in the large-system limit, and clarify the role of finite-size effects in generating nontrivial photon correlations.
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.
Subject of this thesis is the theoretical investigation of ensembles of atoms that are coherently laser-excited to a Rydberg state. Rydberg excited atoms interact with each other over large distances, which leads to strongly correlated many-body dynamics, demanding powerful numerical tools for their modeling. The first part of the thesis deals with effective two-level atoms consisting of a ground and a Rydberg state only. For resonant laser excitation a modified scaling behavior of the excitation number is observed, which is caused by effects of finite system size and coarse graining of the medium due to the finite atomic density. For off-resonant excitation, ordered structures arise out of an initially homogeneous gas, which are reflected in strongly peaked spatial correlations and modified excitation statistics. In the second part a fast decaying intermediate level is additionally taken into account. In this situation the phenomenon of electromagnetically induced transparency (EIT) is encountered. This effect is suppressed in the presence of strong interactions between the Rydberg atoms leading to an optical nonlinearity. A model predicting the properties of a cloud of Rydberg atoms in EIT configuration is developed. In both parts the models are validated by comparing their predictions to recent experimental observations.