  Josephson circuits have been ideal systems to study complex non-linear
dynamics which can lead to chaotic behavior and instabilities. More recently,
Josephson circuits in the quantum regime, particularly in the presence of
microwave drives, have demonstrated their ability to emulate a variety of
Hamiltonians that are useful for the processing of quantum information. In this
paper we show that these drives lead to an instability which results in the
escape of the circuit mode into states that are not confined by the Josephson
cosine potential. We observe this escape in a ubiquitous circuit: a transmon
embedded in a 3D cavity. When the transmon occupies these free-particle-like
states, the circuit behaves as though the junction had been removed, and all
non-linearities are lost. This work deepens our understanding of strongly
driven Josephson circuits, which is important for fundamental and application
perspectives, such as the engineering of Hamiltonians by parametric pumping.
