Floquet Recurrences in the Double Kicked Top

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.

9 pages (two-column) + 6 pages (one-column) + 16 figures. Accepted for publication in Physical Review E. Comments are welcome

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