Title: Arrays of strongly-coupled atoms in a one-dimensional waveguide,
Abstract: We study the cooperative optical coupling between regularly spaced atoms in a
one-dimensional waveguide using decompositions to subradiant and superradiant
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 superradiant 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 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.