We propose a scheme to induce weak-light nonlinearity in a double quantum
dot. The scheme positively utilizes locality and dissipation of an external
auxiliary system. As a plausible setup, we consider a complex system in which a
localized plasmon field from a metallic nanotip couples with only one of the
coupled quantum dots. The perturbative calculation with respect to the light
intensity shows that, even by a sufficiently weak light, a dipole-forbidden
two-exciton NOON state is prepared as the steady state. This result can be
explained by combining the two factors: decoherence-induced quantum state
preparation and two-photon resonance. The present work implies that the
positive usage of both the locality and the dissipation in the external
auxiliary system is promising for inducing two-photon processes effectively,
and provides one guideline to weak-light nonlinearities.Comment: 4 pages, 3 figure