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Abstract

Mössbauer nuclei in thin film nanostructures are an established platform for X-ray quantum optics, and provide novel methods for the narrowband control of hard X-rays. However, quantum optical models for these nanostructures have so far only considered grazing incidence geometry, in a regime of idealized plane wave propagation, and homogeneous nuclear hyper-fine environments. We develop a theoretical description for the interaction of X-rays with Mössbauer nuclei in arbitrary geometries, including dispersive effects, using macroscopic quantum electrodynamics to derive Maxwell-Bloch equations. We use this formalism to study:

1. the effects of beam divergence and inhomogeneous hyper-fine distributions on energy spectra at grazing incidence. In particular, we demonstrate that the collective Lamb shift and broadening of single mode super-radiance can be used to overcome the effects of inhomogeneous broadening, and result in a single line spectrum in the large collective coupling limit.

2. the equations of motion for guided modes coupled to Mössbauer nuclei. We show that these modes obey equations of motion analogous to nuclear forward scattering. We study the interference of multiple modes coupled to a longitudinally structured layer of nuclei, and demonstrate selective super and sub radiant emission. This demonstrates that front coupling to thin film nanostructures opens the door for a vast new space of techniques for the control of hard X-rays.