We study exact quantum resonances 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. By expressing the dynamics in terms of effective parameters $(k_r,k_{\theta })$, we analytically show the exact periodicity of the Floquet operator for integer and half-odd integer spin $j$ at $k_r=j\pi /2$. The analysis is further extended to $k_r=j\pi /4$ for integer spin $j$ and proves the absence of recurrences for half-odd-integer spin $j$. Remarkably, resonances are observed across the time-reversal symmetry (or its breaking) and generalize the QKT resonances. Spectral statistics and entanglement entropy in the pseudoclassical limit reveal qualitatively distinct behavior at the two resonances. Near $k_r=j\pi /2$, the level-spacing ratio distribution evolves from Poisson statistics (PS) to Gaussian orthogonal ensemble (GOE) statistics, indicating a crossover from resonant dynamics to quantum-chaotic behavior through an intermediate regime. No comparable intermediate-statistics regime is observed in the case of $k_r=j\pi /4$. In the time-reversal symmetric case $k_{\theta }=0$, our computations of the rate function associated with fidelity show the dynamical quantum phase transition (DQPT) only for half-odd-integer $j$ values. Our work demonstrates the DKT as a controllable platform where resonance, integrability, and quantum chaos can be tuned for any system size through the parameters $k_r$ and $k_{\theta }$, making the DKT a useful setting for quantum control and information processing applications.

Close

PrevNext

View figure in article

• Bifurcations
• Chaos
• Dynamical phase transitions
• Entanglement entropy
• Long-range interactions
• Quantum chaos
• Quantum entanglement
• Floquet systems
• Integrable systems