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Instabilities in the optical response of a semiconductor quantum dot - metal nanoparticle heterodimer: self - oscillations and chaos

We theoretically investigate the nonlinear optical response of a heterodimer comprising a semiconductor quantum dot strongly coupled to a metal nanoparticle. The quantum dot is considered as a three-level ladder system with ground, one-exciton, and bi-exction states. As compared to the case of a two-level quantum dot model, adding the third (bi-exciton) state produces fascinating effects in the optical response of the hybrid system. Specifically, we demonstrate that the system may exhibit picosecond and sub-picosecond self-oscillations and quasi-chaotic behaviour under {\it single}-frequency continuous wave excitation. An isolated semiconductor quantum dot does not show such features. The effects originate from competing one-exciton and bi-exciton transitions in the semiconductor quantum dot, triggered by the self-action of the quantum dot via the metal nanoparticle. The key parameter that governs the phenomena mentioned is the ratio of the self-action strength and the bi-exciton shift. The self-oscillation regime can be achieved in practice, in particular, in a heterodimer comprised of a closely spaced ZnS/ZnSe core-shell quantum dot and a spherical silver nanoparticle. The results may have applications in nanodevices for generating trains of ultrashort optical pulses.