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Analytical Model for Metamaterials with Quantum Ingredients

We present an analytical model for describing complex dynamics of a hybrid system consisting of interacting classical and quantum resonant structures. Classical structures in our model correspond to plasmonic nano-resonators of different geometries, as well as other types of nano- and micro-structures optical response of which can be described without invoking quantum-mechanical treatment. Quantum structures are represented by atoms or molecules, or their aggregates (for example, quantum dots and carbon nanotubes), which can be accurately modelled only with the use of quantum approach. Our model is based on the set of equations that combines well-established density matrix formalism appropriate for quantum systems, coupled with harmonic-oscillator equations ideal for modelling sub-wavelength plasmonic and optical resonators. This model can also be straightforwardly adopted for describing electromagnetic dynamics of various hybrid systems outside the photonics realm, such as Josephson-junction metamaterials, or SQUID elements coupled with an RF strip resonator.