  We investigate phase-sensitive interference effects in a periodically
$\sin(2\pi f_{\rm rf} t)$-driven, artificial two-state system connected to a
microwave resonator at $f_{LC} \simeq 800$ MHz. We observe two kinds of
multiphoton transitions in the two-state system, accompanied by: 1) Several
quanta from the drive at $f_{\rm rf}$ and 2) one quantum at $f_{\rm rf}$ and
several at $f_{LC}$. The former are described using phase-sensitive
Landau-Zener transitions, while the latter are discussed in terms of vibronic
transitions in diatomic molecules. Interference effects in the vibronic
transitions governed by Franck-Condon coefficients are also considered.
