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_θ, we analytically show exact periodicity of the Floquet operator for k_r = jπ/2 and k_r = jπ/4 with distinct periods for integer and half-odd integer j. These exact recurrences were found to be independent of k_θ. The long-time-averaged entanglement and fidelity rate function show dynamical quantum phase transition (DQPT) for k_r = jπ/2 at time-reversal symmetric cases k_θ = ± k_r. In the other time-reversal symmetric case k_θ = 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 jπ/2. Our work demonstrates that regular and chaotic regimes can be controlled for any system size by tuning k_r and k_θ, making the DKT a useful platform for quantum control and information processing applications.