Kicked fluxonium with quantum strange attractor

TL;DR

This paper investigates the quantum dissipative dynamics of a fluxonium system under pulsed fields, revealing a quantum strange attractor analogous to the classical chaotic attractor, with implications for localization, delocalization, and experimental realization.

Contribution

It introduces the concept of a quantum strange attractor in a dissipative fluxonium system and analyzes its properties both numerically and analytically, connecting classical chaos with quantum behavior.

Findings

Quantum steady-state density matrix forms a strange attractor similar to the classical one.

Eigenstates localization depends on dissipation strength, with delocalization at weak dissipation.

Relation between Lyapunov exponent, Ehrenfest time, and quantum wave packet behavior.

Abstract

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 for the density matrix in the frame of Lindblad equation. In the case of dissipative quantum evolution the steady-state density matrix is converged to a quantum strange attractor being similar to the classical one. It is shown that depending on the dissipation strength there is a regime when the eigenstates of density matrix are localized at a strong or moderate dissipation. At a weak dissipation the eigenstates are argued to be delocalized being linked to the Ehrenfest explosion of quantum wave packet. This phenomenon is related with the Lyapunov exponent and Ehrenfest time for the quantum strange attractor. Possible experimental realisations of this quantum strange attractor with fluxonium are discussed.