While typically designed to manipulate classical light, metamaterials have many potential applications for quantum optics as well. We argue why a quantum optical effective-medium theory is needed. We present such a theory for layered metamaterials that is valid for light propagation in all spatial directions, thereby generalizing earlier work for one-dimensional propagation. In contrast to classical effective-medium theory there is an additional effective parameter that describes quantum noise. Our results for metamaterials are based on a rather general Lagrangian theory for the quantum electrodynamics of media with both loss and gain. In the second part of this paper, we present a new application of transformation optics whereby local spontaneous-emission rates of quantum emitters can be designed. This follows from an analysis how electromagnetic Green functions trans- form under coordinate transformations. Spontaneous-emission rates can be either enhanced or suppressed using invisibility cloaks or gradient index lenses. Furthermore, the anisotropic material profile of the cloak enables the directional control of spontaneous emission.
Martijn Wubs, Ehsan Amooghorban, Jingjing Zhang, and N. Asger Mortensen, "Quantum optical effective-medium theory and transformation quantum optics for metamaterials," Proc. SPIE 9918, Metamaterials, Metadevices, and Metasystems 2016, 99180P (Presented at SPIE Nanoscience + Engineering: August 29, 2016; Published: 16 September 2016); https://doi.org/10.1117/12.2239328.
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