Universal entanglement dynamics in quantum chaotic systems

We identify and analyze universal features of entanglement dynamics in quantum systems that are classically chaotic. We derive an expression for the evolution of the linear entropy in terms of the decomposition of the initial state in the basis of eigenstates of the Hamiltonian and analyze the power spectrum of the entanglement dynamics. We apply our analysis to the quantum kicked top system and also present results for an experimentally accessible system of cold atoms in a magneto-optical lattice. The entanglement exhibits quasiperiodic behavior for states initially localized in a regular island. For states in the chaotic region, there is a rapid increase of entanglement and no quasiperiodic behavior. We show that these features are universal and a result of the support of the initial state on ‘regular’ or ‘chaotic’ eigenstates. We present a detailed analysis of the regular quasi-periodic dynamics and the chaotic dynamics. We also estimate the initial rapid increase in the entanglement and compare our estimate to a previous result using semiclassical methods.