Iterated dynamical maps in an ion trap

TL;DR

This paper explores how a single trapped ion subjected to periodic forces exhibits complex dynamical bifurcations, with entanglement patterns reflecting these bifurcations, providing insights into quantum dynamical systems.

Contribution

It demonstrates the occurrence of dynamical bifurcations in a trapped ion system modeled by the Jahn-Teller Hamiltonian, linking entanglement to bifurcation phenomena.

Findings

Rich structure of dynamical bifurcations observed

Entanglement reflects underlying bifurcations

Applicable to quantum computer implementations

Abstract

Iterated dynamical maps offer an ideal setting to investigate quantum dynamical bifurcations and are well adapted to few-qubit quantum computer realisations. We show that a single trapped ion, subject to periodic impulsive forces, exhibits a rich structure of dynamical bifurcations derived from the Jahn-Teller Hamiltonian flow model. We show that the entanglement between the oscillator and electronic degrees of freedom reflects the underlying dynamical bifurcation in a Floquet eigenstate.