Arresting Quantum Chaos Dynamically in Transmon Arrays

Ergodic quantum many-body systems evolving under unitary time dynamics typically lose memory of their initial state via information scrambling. Here we consider a paradigmatic translationally invariant many-body Hamiltonian of interacting bosons — a Josephson junction array in the transmon regime — in the presence of a strong Floquet drive. Generically, such a time-dependent drive is expected to heat the system to an effectively infinite temperature, featureless state in the late-time limit. However, using numerical exact-diagonalization we find evidence of special ratios of the drive amplitude and frequency where the system develops emergent conservation laws, and approximate integrability. Remarkably, at these same set of points, the Lyapunov exponent associated with the semi-classical dynamics for the coupled many-body equations of motion drops by at least an order of magnitude, arresting the growth of chaos. We supplement our numerical results with an analytical Floquet-Magnus expansion that includes higher-order corrections, and capture the slow dynamics that controls decay away from exact freezing.