Robert J. Bettles

Absolute absorption on the rubidium D1 line including resonant dipole?dipole interactions

Here we report on measurements of the absolute absorption spectra of dense rubidium vapour on the D1 line in the weak-probe regime for temperatures up to 170 °C and number densities up to 3 × 1014 cm−3. In such vapours, modifications to the homogeneous linewidth of optical transitions arise due to dipole–dipole interactions between identical atoms, in superpositions of the ground and excited states. Absolute absorption spectra were recorded with a deviation of 0.1% between experiment and a theory incorporating resonant dipole–dipole interactions. The manifestation of dipole–dipole interactions is a self-broadening contribution to the homogeneous linewidth, which grows linearly with number density of atoms. Analysis of the absolute absorption spectra allows us to ascertain the value of the self-broadening coefficient for the rubidium D1 line: β/2π = (0.69 ± 0.04) × 10−7 Hz cm3, in excellent agreement with the theoretical prediction.

Enhanced Optical Cross Section via Collective Coupling of Atomic Dipoles in a 2D Array.

Enhancing the optical cross section is an enticing goal in light-matter interactions, due to its fundamental role in quantum and nonlinear optics. Here, we show how dipolar interactions can suppress off-axis scattering in a two-dimensional atomic array, leading to a subradiant collective mode where the optical cross section is enhanced by almost an order of magnitude. As a consequence, it is possible to attain an optical depth which implies high-fidelity extinction, from a monolayer. Using realistic experimental parameters, we also model how lattice vacancies and the atomic trapping depth affect the transmission, concluding that such high extinction should be possible, using current experimental techniques.

Cooperative ordering in lattices of interacting two-level dipoles.

We investigate the cooperative behavior of regular monolayers of driven two-level dipoles, using classical electrodynamics simulations. The dipolar response results from the interference of many cooperative eigenmodes, each frequency-shifted from the single resonant dipole case, and with a modified lifetime, due to the interactions between dipoles. Of particular interest is the kagome lattice, where the semiregular geometry permits simultaneous excitation of two dominant modes, one strongly subradiant, leading to an electromagnetically induced transparencylike interference in a two-level system. The interfering modes are associated with ferroelectric and antiferroelectric ordering in alternate lattice rows with long-range interactions.

Topological properties of a dense atomic lattice gas.

We investigate the existence of topological phases in a dense two-dimensional atomic lattice gas. The coupling of the atoms to the radiation field gives rise to dissipation and a non-trivial coherent long-range exchange interaction whose form goes beyond a simple power-law. The far-field terms of the potential -- which are particularly relevant for atomic separations comparable to the atomic transition wavelength -- can give rise to energy spectra with one-sided divergences in the Brillouin zone. The long-ranged character of the interactions has another important consequence: it can break the standard bulk-boundary relation in topological insulators. We show that topological properties such as the transport of an excitation along the edge of the lattice are robust with respect to the presence of lattice defects and dissipation. The latter is of particular relevance as dissipation and coherent interactions are inevitably connected in our setting.

Cooperative eigenmodes and scattering in one-dimensional atomic arrays.

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.

Eigenmodes in a Two-Dimensional Atomic Monolayer

In Sect. 7.2 we calculate the extinction cross-section and eigenmode behaviour for 2D ensembles of just a few atoms.

Single Two-Level Atom

We will start our discussion with the most simple system: a single two-level atom interacting with an electromagnetic field.

One-Dimensional Atom Array

In this Chapter, we move beyond considering just a pair of atoms to considering N atoms arranged in a one-dimensional chain.

Extinction in a Two-Dimensional Atomic Monolayer

In the Chap. 7 we investigated the eigenmode behaviour of different 2D lattices and the resulting extinction cross-section. In this Chapter, we consider how this extinction might be measured experimentally.

Multiple Four-Level Atoms

In Chap. 2, we discussed the interaction between a single two-level atom and an electromagnetic (EM) field.