Abstract
Collective effects in the interaction of light with ensembles of identical scatterers play an important role in many fields of physics. However, often the term ``identical'' is not accurate due to the presence of hyperfine fields which induce inhomogeneous transition shifts and splittings. Here we develop a formalism based on the Green's-function method to model the linear response of such inhomogeneous ensembles in one-dimensional waveguides. We obtain a compact formula for the collective spectrum, which exhibits deviations from the uniform frequency shift and broadening expected of two-level systems. In particular, if the coherent contribution to the collective coupling is large, the effect of inhomogeneous broadening can be suppressed, with the linewidth approaching that of the superradiant value. We apply this formalism to describe collective effects in x-ray scattering off thin-film waveguides for inhomogeneous hyperfine parameters.
Highlights
When an ensemble of identical atoms interacts with light of wavelength much larger than the size of the ensemble, the atoms absorb and emit radiation collectively, resulting in the phenomenon of superradiance
In this paper we have examined an extension of the Dicke model for inhomogeneous atoms
We found a compact formula for the susceptibility in the weak-excitation regime, in terms of the coherently averaged nuclear or atomic responses, and the collective coupling constants J and
Summary
When an ensemble of identical atoms interacts with light of wavelength much larger than the size of the ensemble, the atoms absorb and emit radiation collectively, resulting in the phenomenon of superradiance. The atomic excitations propagate through the waveguide as a polariton and the waveguide structure restricts the propagation of the scattered light to onedimensional plane-wave propagation This results in uniform illumination, with translational symmetry playing the role of permutational symmetry, achieving superradiance without. This allows the effects of inhomogeneities and of the collective interaction to be analyzed separately, allowing for a better understanding of their respective contributions to the collective spectrum We apply this formalism to the concrete example of x-ray quantum optics systems that comprise ensembles of Mössbauer nuclei in thin-film x-ray cavities. The latter are a suitable platform for exploring superradiance and collective interaction between emitters.
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