Kicked fluxonium with quantum strange attractor

TL;DR

The paper analyzes the dissipative quantum dynamics of a kicked fluxonium, modeled by a time-dependent Hamiltonian with periodic kicks and described by the Lindblad equation. It shows that, at moderate to strong dissipation, the steady-state density matrix forms a quantum strange attractor whose Husimi representation mirrors the classical attractor, while its eigenstates localize and exhibit Schrödinger-cat–like structure; entropy grows while quantum negativity decays on dissipative timescales. The work connects the observed localization to the classical Lyapunov behavior and discusses regimes where weak dissipation could yield Ehrenfest-time–related delocalization, highlighting potential experimental realizations in fluxonium systems. Overall, the study provides a framework for observing quantum strange attractors in open quantum systems and guides future experimental exploration in superconducting qubits and related platforms.

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.

Figures (6)

• Figure 1: Time evolution of Husimi function (shown at different time moments $t$) in the phase plane $(x,p)$, $\hbar=\omega=1$, $k=K/\hbar =40$, $q=0.4$, $\gamma=0.05$, $N=2000$ ($\hbar_{eff} = \hbar q^2$, thus the classical chaos parameter rescaled to the case $q=1$ is $K_{cl}=K q^2 = 6.4$); here $t$ gives a number of kicks; $R=4$. Initial state at $t=0$ is a minimal coherent state located at $x=10, p=1$; color bars show Husimi function multiplied by factor $10^3$.
• Figure 2: Top panel: quantum Husimi function at the steady-state at $t=10^3$ with parameters and notations of Fig. \ref{['fig1']}; bottom panel: classical density distribution obtained with $4\times 10^6$ trajectories; all parameters are as in Fig. \ref{['fig1']}. Color density values are increased by a factor $10^3$.
• Figure 3: Collapse of density matrix eigenstate at maximal eigenvalue $\lambda_i$; Husimi function of eigenstate is shown at time moments $t$, color shows its values increased by a factor $\times 10^3$, system parameters are as in Fig. \ref{['fig1']}.
• Figure 4: Splitting $\Delta \lambda$ of largest eigenvalues $\lambda_i$ of density matrix $\rho(t)$ at different moments of time $t$ (given here in number of kicks); three quasi-degenerate pairs of largest eigenvalues are shown: $\lambda_0 -\lambda_1$, $\lambda_2 -\lambda_3$, $\lambda_4 -\lambda_5$; system parameters are as in Fig. \ref{['fig1']}.
• Figure 5: Entropy of entanglement $S_E$ vs time $t$, for system parameters $K=8$, $\hbar=q=1$, values of $\gamma$ are given in the panel.