  We study a Rabi type Hamiltonian system in which a qubit and a d-level
quantum system (qudit) are coupled through a common resonator. In the weak and
strong coupling limits the spectrum is analysed through suitable perturbative
schemes. The analysis show that the presence of the multilevels of the qudit
effectively enhance the qubit-qudit interaction. The ground state of the
strongly coupled system is a found of Greenberger-Horne-Zeilinger (GHZ) type.
Therefore, despite the qubit-qudit strong coupling, the nature of the specific
tripartite entanglement of the GHZ state suppress the bipartite entanglement.
We analyze the system dynamics under quenching and adiabatic switching of the
qubit-resonator and qudit-resonator couplings. In the quench case, we found
that the non-adiabatic generations of photons in the resonator is enhanced by
the number of levels in the qudit. The adiabatic control represents a possible
route for preparation of GHZ states. Our analysis provides relevant information
for future studies on coherent state transfer in qubit-qudit systems.
