Kicked Fluxonium with a Quantum Strange Attractor

The quantum dissipative time evolution of a fluxonium under a pulsed field (kicks) is studied numerically and analytically. In the classical limit, the system dynamics is converged to a strange chaotic attractor. The quantum properties of this system are studied using the density matrix within the framework of the Lindblad equation. In the case of dissipative quantum evolution, the steady-state density matrix is converged to a quantum strange attractor that is similar to the classical one. It is shown that depending on the dissipation strength, there is a regime when the eigenstates of the density matrix are localized at a strong or moderate dissipation. At weak dissipation, the eigenstates are argued to be delocalized, which is linked to the Ehrenfest explosion of the quantum wave packet. This phenomenon is related to the Lyapunov exponent and Ehrenfest time for the quantum strange attractor. Possible experimental realizations of this quantum strange attractor with fluxonium are discussed.