  With advanced fabrication techniques it is possible to make nanoscale
electronic structures that have discrete energy levels. Such structures are
called artificial atoms because of analogy with true atoms. Examples of such
atoms are quantum dots in semiconductor heterostructures and Josephson-junction
qubits. It is also possible to have artificial atoms interacting with each
other. This is an artificial molecule in the sense that the electronic states
are analogous to the ones in a molecule. In this letter we present a different
type of artificial molecule that, in addition to electronic states, also
includes the analog of nuclear vibrations in a diatomic molecule. Some of the
earlier experiments could be interpreted using this analogy, including qubits
coupled to oscillators and qubits driven by an intense field. In our case the
electronic states of the molecule are represented by a Josephson-junction
qubit, and the nuclear separation corresponds to the magnetic flux in a loop
containing the qubit and an LC oscillator. We probe the vibronic transitions,
where both the electronic and vibrational states change simultaneously, and
find that they are analogous to true molecules. The vibronic transitions could
be used for sideband cooling of the oscillator, and we see damping up to
sidebands of order 10.
