Floquet Recurrences in the Double Kicked Top

TL;DR

This paper investigates exact quantum recurrences and dynamical quantum phase transitions in the double kicked top, revealing how tuning parameters controls the transition between regular and chaotic quantum regimes, with implications for quantum control.

Contribution

It analytically demonstrates exact Floquet recurrences in the double kicked top and explores their relation to quantum phase transitions and chaos control.

Findings

Exact Floquet recurrences at specific parameter values

Observation of dynamical quantum phase transitions

Transition from integrable to non-integrable behavior

Abstract

We study exact quantum recurrences in the double kicked top (DKT), a driven spin model that extends the quantum kicked top (QKT) by introducing an additional time-reversal symmetry-breaking kick. Reformulating its dynamics in terms of effective parameters $k_r$ and $k_\theta$, we analytically show exact periodicity of the Floquet operator for $k_r = j\pi/2$ and $k_r = j\pi/4$ with distinct periods for integer and half-odd integer $j$. These exact recurrences were found to be independent of $k_\theta$. The long-time-averaged entanglement and fidelity rate function show dynamical quantum phase transition (DQPT) for $k_r = j\pi/2$ at time-reversal symmetric cases $k_\theta = \pm k_r$. In the other time-reversal symmetric case $k_\theta = 0$, the DQPT exists only for a half-odd integer $j$. Using level statistics, a smooth transition is observed from integrable to non-integrable nature as $k_r$ is changed away from $j\pi/2$. Our work demonstrates that regular and chaotic regimes can be controlled for any system size by tuning $k_r$ and $k_\theta$, making the DKT a useful platform for quantum control and information processing applications.