We study a Rabi type Hamiltonian system in which a qubit and a
dd-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 found to
be of Greenberger-Horne-Zeilinger (GHZ) type. Therefore, despite the
qubit-qudit strong coupling, the nature of the specific tripartite
entanglement of the GHZ state suppresses 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 generation 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.