Bipartite and tripartite entanglement in pure dephasing relativistic spin-boson model

TL;DR

This paper investigates how entanglement between two and three emitters is generated in a relativistic spin-boson model, revealing the conditions for high entanglement and the challenges in detecting tripartite entanglement.

Contribution

It provides an exact nonperturbative analysis of entanglement in a relativistic spin-boson model, highlighting the conditions for entanglement generation and the difficulties in observing tripartite entanglement.

Findings

High entanglement requires deep light cone interactions

Field mass can enhance entanglement

Tripartite entanglement is hard to detect or classify

Abstract

We study nonperturbatively the entanglement generation between two and three emitters in an exactly solvable relativistic variant of the spin-boson model, equivalent to the time-independent formulation of the Unruh-DeWitt detector model. We show that (i) (highly) entangled states of the two emitters require interactions very deep into the light cone, (ii) the mass of the field can generically improve the entanglement generation, (iii) while it is possible to find regimes with genuine Greenberger-Horne-Zeilinger-like tripartite entanglement, it is difficult find regimes where tripartite entanglement can be easily shown to be significant or classified. Result (iii), in particular, suggests that probing the multipartite entanglement of a relativistic quantum field nonperturbatively requires either different probe-based techniques or variants of the Unruh-DeWitt model. Along the way, we provide the regularity conditions for the $N$-emitter model to have well-defined ground states in the Fock space.