  We present a theoretical analysis of the quantum dynamics of a
superconducting circuit based on a highly asymmetric Cooper pair transistor
(ACPT) in parallel to a dc-SQUID. Starting from the full Hamiltonian we show
that the circuit can be modeled as a charge qubit (ACPT) coupled to an
anharmonic oscillator (dc-SQUID). Depending on the anharmonicity of the SQUID,
the Hamiltonian can be reduced either to one that describes two coupled qubits
or to the Jaynes-Cummings Hamiltonian. Here the dc-SQUID can be viewed as a
tunable micron-size resonator. The coupling term, which is a combination of a
capacitive and a Josephson coupling between the two qubits, can be tuned from
the very strong- to the zero-coupling regimes. It describes very precisely the
tunable coupling strength measured in this circuit and explains the
'quantronium' as well as the adiabatic quantum transfer read-out.
