Quantum Chaos and Entanglement for Two Coupled Spins

Recent work suggests that there is a connection between the rate of entanglement generation of a bipartite quantum mechanical system and the existence of chaos in the classical limit of that system. This work further explores this connection for the case of two spins in an atom, electron and nuclear, coupled by the hyperfine interaction and driven by a time varying external magnetic field. In contrast to other work, we are considering a system which is chaotic only when coupling exists between the subsystems, rather than one made of two independently chaotic subsystems. We have studied numerical simulations of the classical limit of this system and explore the parameter space that shows the appearance or lack of chaos for a variety of different fields and initial conditions. For a quantum mechanical wave packet placed in the regular and chaotic regions of a mixed space, we compare the rate of entanglement generation.