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We present quantum-mechanical approach for collective spontaneous emission(superradiance) of emitters (as atoms) near metal nanoparticle, whenfrequencies of transitions of emitters coincide with frequency of localizedplasmon resonance of the nanoparticle. Our approach is based on Schrodingerdescription and it uses wave functions of states of systems. Interactionsbetween emitters and between the nanoparticle and emitters are taken intoaccount. We consider an example of two emitters and show that radiation isoccurred through symmetric states of emitters as it is in Dicke model ofsuperradiance. The nanoparticle accelerates collective spontaneous emissionsimilar how it accelerates spontaneous emission of single emitter. Radiationfrom two emitters near the nanoparticle is faster than the radiation from twoseparated and non-interacted "nanoparticle+single emitter" systems. Efficiencyof superradiance, i.e. the ratio of emitted photons to total number initialexcitations in the system, is smaller than 1 due to non-radiative losses in thenanoparticle. However the efficiency is the same for single and for twoemitters near the nanoparticle. The approach can be straightforwardlygeneralized to the case of many emitters near the nanoparticle.

Collective spontaneous emission of two atoms near metal nanoparticle