Collective coupling between dipoles can dramatically modify the optical response of a medium. Such effects depend strongly on the geometry of the medium and the polarization of the light. Using a classical coupled dipole model, here we investigate the simplest case of one-dimensional arrays of interacting atomic dipoles driven by a weak laser field. Changing the polarization and direction of the driving field allows us to separately address superradiant, subradiant, redshifted, and blueshifted eigenmodes, as well as observe strong Fano-like interferences between different modes. The cooperative eigenvectors can be characterized by the phase difference between nearest-neighbor dipoles, ranging from all oscillating in phase to all oscillating out of phase with their nearest neighbors. Investigating the eigenvalue behavior as a function of atom number and lattice spacing, we find that certain eigenmodes of an infinite atomic chain have the same decay rate as a single atom between two mirrors. The effects we observe provide a framework for collective control of the optical response of a medium, giving insight into the behavior of more complicated geometries, as well as providing further evidence for the dipolar analog of cavity QED.
Collective coupling between dipoles can dramatically modify the optical response of a medium. Such effects depend strongly on the geometry of the medium and the polarization of the light. Using a classical coupled dipole model, here we investigate the simplest case of one-dimensional arrays of interacting atomic dipoles driven by a weak laser field. Changing the polarization and direction of the driving field allows us to separately address superradiant, subradiant, redshifted, and blueshifted eigenmodes, as well as observe strong Fano-like interferences between different modes. The cooperative eigenvectors can be characterized by the phase difference between nearest-neighbor dipoles, ranging from all oscillating in phase to all oscillating out of phase with their nearest neighbors. Investigating the eigenvalue behavior as a function of atom number and lattice spacing, we find that certain eigenmodes of an infinite atomic chain have the same decay rate as a single atom between two mirrors. The effects we observe provide a framework for collective control of the optical response of a medium, giving insight into the behavior of more complicated geometries, as well as providing further evidence for the dipolar analog of cavity QED.
The coherent photon scattering of atoms in an atomic array is studied. It is found that due to cooperative photon exchanges, the excitation probability of an atom in an array parallel to the direction of laser propagation ($\stackrel{\ifmmode \hat{}\else \^{}\fi{}}{\mathbit{k}}$) will either grow or decay along $\stackrel{\ifmmode \hat{}\else \^{}\fi{}}{\mathbit{k}}$, depending on the detuning of the laser. The symmetry of the system for atomic separations of $a=j\ensuremath{\lambda}/2$ causes the excitation distribution and scattered radiation to abruptly become symmetric about the center of the array, where j is an integer and $\ensuremath{\lambda}$ is the transition wavelength. For atomic separations of $a<\ensuremath{\lambda}/2$, a collection of nonradiating states ($\mathrm{\ensuremath{\Gamma}}\ensuremath{\sim}0$) disrupts the described trend. In order to interpret this surprising result, a band-structure calculation in the $N\ensuremath{\rightarrow}\ensuremath{\infty}$ limit is conducted, where the decay rates and the collective Lamb shifts of the eigenmodes versus quasimomentum are obtained. This calculation shows that the collective exchange of photons in an array strongly affects its scattered radiation, allowing one to easily manipulate the collective Lamb shift and directly excite either superradiant or subradiant eigenmodes by correctly choosing the angle of the driving laser.
We study the cooperative optical coupling between regularly spaced atoms in a one-dimensional waveguide using decompositions to subradiant and super-radiant collective excitation eigenmodes, direct numerical solutions, and analytical transfer-matrix methods. We illustrate how the spectrum of transmitted light through the waveguide, including the emergence of narrow Fano resonances, can be understood by the resonance features of the eigenmodes. We describe a method based on super-radiant and subradiant modes to engineer the optical response of the waveguide and to store light. The stopping of light is obtained by transferring an atomic excitation to a subradiant collective mode with the zero radiative resonance linewidth by controlling the level shift of an atom in the waveguide. Moreover, we obtain an exact analytic solution for the transmitted light through the waveguide for the case of a regular lattice of atoms and provide a simple description of how the light transmission may present large resonance shifts when the lattice spacing is close, but not exactly equal, to half of the wavelength of the light. Experimental imperfections such as fluctuations of the positions of the atoms and loss of light from the waveguide are easily quantified in the numerical simulations, which produce the natural result that the optical response of the atomic array tends toward the response of a gas with random atomic positions.
An ensemble of atoms coupled to the radiation field exhibits collective behaviours when the interatomic separation is comparable to the wavelength of photons emitted by the atoms. The collective coupling of the atoms with the electromagnetic field gives rise to coherent exchange interactions between the atoms. In addition, the spontaneous decay of photons from the ensemble becomes a collective process that can happen at a much faster (superradiant) or slower (subradiant) rate than that of a single atom. These processes affect the way that fluorescence light is scattered from the system when it is driven by a laser. However, little is known about the response of a dense atomic gas beyond the linear regime of very weak driving, due to the involved complexity of the problem. The first part of this thesis investigates how the presence of strong laser driving affects properties of the far-field fluorescence light emitted by the ensemble, such as the power spectrum and second order coherence. Depending on the strength of the driving laser and the particular arrangement of the atoms, the laser can modify considerably how the collective behaviours of the atomic ensemble are manifested in the fluorescence. The relative strengths of the coherent interaction and collective decay process are intrinsically linked to the way that the atoms couple to the radiation field; one cannot be changed without modifying the other. Altering the environment by, for example, placing the atoms near a surface or a waveguide, can change this relation significantly from that for atoms in free space. Therefore, modified environments represent a platform for the generation of otherwise inaccessible regimes of collective behaviour, with potential applications in quantum state engineering. The second part of this thesis provides a numerical investigation into how the collective properties of a dense atomic system can be manipulated by placing the atoms close to planar surfaces or an optical nanofiber. These structures modify the light-matter coupling by altering the electric field experienced by the atoms. It is shown that surfaces of metallic and dielectric materials can be used to either enhance or suppress the collective behaviours, depending on the particular system arrangement. In particular, the coupling of atoms with bound surface modes, such as the surface plasmon polaritons that are formed at an air-metal interface, is demonstrated to have a strong effect on the interactions. An optical nanofiber supports a set of fundamental guided modes, that propagate along the fiber. If the atoms are suitably polarised, then they will emit primarily into the guided modes travelling in one direction. By calculating and analysing the collective decay states of a chain of atoms placed near a nanofiber, it is demonstrated that the atom-fiber coupling leads to the formation of a superradiant mode that is preserved at large atomic separations. The presence of chiral emission is shown to introduce phase gradients to the collective modes.
We study strong, light-mediated, resonant dipole-dipole interactions in two-dimensional planar lattices of cold atoms. We provide a detailed analysis for the description of the dipolar point emitter lattice plane as a ``superatom'' whose response is similar to electromagnetically induced transparency but which exhibits an ultranarrow collective size-dependent subradiant resonance linewidth. The superatom model provides intuitively simple descriptions for the spectral response of the array, including the complete reflection, full transmission, narrow Fano resonances, and asymptotic expressions for the resonance linewidths of the collective eigenmodes. We propose a protocol to transfer almost the entire radiative excitation to a single correlated subradiant eigenmode in a lattice and show that the medium obtained by stacked lattice arrays can form a cooperative magnetometer. Such a magnetometer utilizes similar principles as magnetometers based on the electromagnetically induced transparency. The accuracy of the cooperative magnetometer, however, is not limited by the single-atom resonance linewidth but the much narrower collective linewidth that results from the strong dipole-dipole interactions.
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.
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.