Abstract
We investigate the force between a plasmonic nanoparticle and a highly excited two-level system (molecule). Usually van der Waals' force between nanoscale electrically neutral systems is monotonic and attractive at moderate and larger distances and repulsive at small distances. In our system, the van der Waals' force acting on a molecule has a quantum-optical nature. At moderate distances it is attractive as usual but its strength highly increases in narrow distance ranges (lacunas). We show that quantum fluctuations of quasi-continuum of multipole plasmons of high, nearly infinite degree, altogether form an effective environment and determine the interaction force while their spectral peculiarities stand behind the large and narrow lacunas in force. We exactly solve the Hamiltonian problem and discuss the role of the dissipation.
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