  We measure the state dynamics of a tunable anharmonic quantum system, the
Josephson phase circuit, under the excitation of a frequency-chirped drive. At
small anharmonicity, the state evolves like a wavepacket - a characteristic
response in classical oscillators; in this regime we report exponentially
enhanced lifetimes of highly excited states, held by the drive. At large
anharmonicity, we observe sharp steps, corresponding to the excitation of
discrete energy levels. The continuous transition between the two regimes is
mapped by measuring the threshold of these two effects.
