  We present a quantum theoretical treatment of light-matter coupling in the
system consisting of a quantum dot and a spherical core-shell metal-dielectric
multilayer nanoparticle. It is shown that both weak and strong coupling regimes
can be realized in the set-up. Specifically, we demonstrate a strong coupling
regime between a quantum dot and a nanoparticle, when the quantum dot resonance
is tuned to the frequency at which normal component of effective nanoparticle
permittivity is crossing zero. Moreover, we demonstrate the regime at which the
quantum dot decays much faster than in vacuum (due to the large Purcell factor)
and at the same time radiates more power to the far field. This findings pave
the way towards more efficient control over radiation properties of quantum
emitters.
