Quantum-classical correspondence in entanglement production: Entropy and classical tori

We analyze the connections between entanglement dynamics and classical trajectories in a semiclassical regime for two systems: A pair of coupled oscillators and the Jaynes-Cummings model. We find that entanglement production depends on classical invariant tori and such phenomenon is closely related to the power spectra of classical trajectories. Classical power spectrum with a larger number of frequency components corresponds to larger entanglement. We introduce a frequency entropy to describe the classical frequency distribution. It is found that there is good correspondence between the classical frequency entropies and the maximum von Neumann entropies.