  We simulate the dynamics of a quantum dot coupled to the single resonating
mode of a metal nano-particle. Systems like this are known as metamolecules. In
this study, we consider a time-dependent driving field acting onto the
metamolecule. We use the Heisenberg equations of motion for the entire system,
while representing the resonating mode in Wigner phase space. A time-dependent
basis is adopted for the quantum dot. We integrate the dynamics of the
metamolecule for a range of coupling strengths between the quantum dot and the
driving field, while restricting the coupling between the quantum dot and the
resonant mode to weak values. By monitoring the average of the time variation
of the energy of the metamolecule model, as well as the coherence and the
population difference of the quantum dot, we observe distinct non-linear
behavior in the case of strong coupling to the driving field.
