Quantum ergodicity and entanglement in kicked coupled-tops

TL;DR

This paper investigates how chaos in a periodically kicked coupled-tops system leads to the generation of entanglement, revealing a strong correlation between classical phase space structures and quantum entanglement patterns.

Contribution

It provides a detailed analysis linking classical chaos with quantum entanglement, including new analytic results for typical entanglement in symmetric subspaces and the role of random states.

Findings

Entanglement correlates with classical phase space structures.

Chaotic dynamics produce highly entangled pseudo-random states.

Analytic predictions match long-time entanglement measurements.

Abstract

We study the dynamical generation of entanglement as a signature of chaos in a system of periodically kicked coupled-tops, where chaos and entanglement arise from the same physical mechanism. The long-time averaged entanglement as a function of the position of an initially localized wave packet very closely correlates with the classical phase space surface of section -- it is nearly uniform in the chaotic sea, and reproduces the detailed structure of the regular islands. The uniform value in the chaotic sea is explained by the random state conjecture. As classically chaotic dynamics take localized distributions in phase space to random distributions, quantized versions take localized coherent states to pseudo-random states in Hilbert space. Such random states are highly entangled, with an average value near that of the maximally entangled state. For a map with global chaos, we derive that value based on new analytic results for the typical entanglement in a subspace defined by the symmetries of the system. For a mixed phase space, we use the Percival conjecture to identify a "chaotic subspace" of the Hilbert space. The typical entanglement, averaged over the unitarily invariant Haar measure in this subspace, agrees with the long-time averaged entanglement for initial states in the chaotic sea. In all cases the dynamically generated entanglement is predicted by a unitary ensemble of random states, even though the system is time-reversal invariant, and the Floquet operator is a member of the circular orthogonal ensemble.