Entanglement across sliding-pinned transition of ion chains in optical cavities

TL;DR

This study investigates how steady-state entanglement in a small ion chain coupled to an optical cavity varies with spatial configurations, especially across a transition from sliding to pinned states induced by increased pumping.

Contribution

It provides a detailed analysis of the relationship between spatial structure, vibrational modes, and entanglement in a dissipative quantum system with a phase transition.

Findings

Entanglement varies with the ion chain's spatial configuration.

Pinned configurations can host entangled steady states.

Multipartite quantum correlations are present in the system.

Abstract

Dissipative quantum systems can under appropriate conditions exhibit bi- or multi-partite entanglement at the steady state. The presence and properties of these quantum correlations depend on the relevant model parameters. Here, we characterize the steady-state entanglement in connection with the spatial structure of a small chain of three ions dispersively coupled with a pumped optical cavity. Within a semiclassical approximation, we describe the relation between entanglement, spatial organization, and vibrational modes of the ion chain. Upon increasing the pumping strength, our system undergoes a transition from a sliding to a pinned configuration, in which ions are expelled from the maxima of the optical potential. The features of the steady-state entanglement strongly depend on the kind of pinned configuration reached. We identify scenarios leading to entangled steady states, analyze the effect of defect formation upon entanglement between different system partitions, and observe the presence of multipartite quantum correlations.