Collective spontaneous emission of two atoms near metal nanoparticle

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We present quantum-mechanical approach for collective spontaneous emission (superradiance) of emitters (as atoms) near metal nanoparticle, when frequencies of transitions of emitters coincide with frequency of localized plasmon resonance of the nanoparticle. Our approach is based on Schrodinger description and it uses wave functions of states of systems. Interactions between emitters and between the nanoparticle and emitters are taken into account. We consider an example of two emitters and show that radiation is occurred through symmetric states of emitters as it is in Dicke model of superradiance. The nanoparticle accelerates collective spontaneous emission similar how it accelerates spontaneous emission of single emitter. Radiation from two emitters near the nanoparticle is faster than the radiation from two separated and non-interacted "nanoparticle+single emitter" systems. Efficiency of superradiance, i.e. the ratio of emitted photons to total number initial excitations in the system, is smaller than 1 due to non-radiative losses in the nanoparticle. However the efficiency is the same for single and for two emitters near the nanoparticle. The approach can be straightforwardly generalized to the case of many emitters near the nanoparticle.