Cooperative Interactions in Lattices of Atomic Dipoles

Abstract

Coherent radiation by an ensemble of scatterers can dramatically modify the ensemble's optical response. This can include, for example, enhanced and suppressed decay rates (superradiance and subradiance respectively), energy level shifts, and highly directional scattering. This behaviour is referred to as cooperative, since the scatterers in the ensemble behave as a collective rather than independently. In this Thesis, we investigate the cooperative behaviour of one- and two-dimensional arrays of interacting atoms.

We calculate the extinction cross-section of these arrays, analysing how the cooperative eigenmodes of the ensemble contribute to the overall extinction. Typically, the dominant eigenmode if the atoms are driven by a uniform or Gaussian light beam is the mode in which the atomic dipoles oscillate in phase together and with the same polarisation as the driving field. The eigenvalues of this mode become strongly resonant as the atom number is increased. For a one-dimensional array, the location of these resonances occurs when the atomic spacing is an integer or half integer multiple of the wavelength, thus behaving analogously to a single atom in a cavity. The interference between this mode and additional eigenmodes can result in Fano-like asymmetric lineshapes in the extinction. We find that the kagome lattice in particular exhibits an exceptionally strong interference lineshape, like a cooperative analog of electromagnetically induced transparency.

Triangular, square and hexagonal lattices however are typically dominated by one single mode which, for lattice spacings of the order of a wavelength, can be highly subradiant. This can result in near-perfect extinction of a resonant driving field, signifying a significant increase in the atom-light coupling efficiency. We show that this extinction is robust to possible experimental imperfections.