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Lacunas in the optical force induced by quantum fluctuations of quasicontinuum of multipole plasmons

We investigate the force between plasmonic nanoparticle and 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 molecule has optical nature. At moderate distances it is attractive as usual but its strength highly increases in a narrow distance ranges ("lacunas"). We show that quantum fluctuations of (quasi)continuum of multipole plasmons of high, nearly infinite degree altogether form effective environment and determine the interaction force while their spectral peculiarities stand behind the large and narrow lacunas in force. We solve exactly the Hamiltonian problem and discuss the role of the dissipation.