Entangled three-particle states in magnetic field: Periodic correlations and density matrices

TL;DR

This paper investigates the periodic evolution of three-particle entangled spin states under magnetic and electric fields, revealing new classifications and detailed dynamical behaviors of such quantum systems.

Contribution

It introduces a comprehensive analysis of three-particle entangled states in magnetic fields, including periodic correlations, density matrix evolution, and a novel classification scheme based on angular momentum coupling.

Findings

Periodic correlations depend on initial states and magnetic field parameters.

Electric field effects are incorporated via Lorentz transformations and Wigner rotations.

A systematic classification of three-particle entangled states is proposed.

Abstract

We present a novel study of the time evolutions of entangled states of three spin-1/2 particles in the presence of a constant external magnetic field, which causes the individual spins to precess and leads to remarkable periodicities in the correlations and density matrices. The emerging patterns of periodicity are studied explicitly for different entangled states and in detail for a particular initial configuration of the velocities. Contributions to precession of anomalous magnetic moments are analysed and general results are also obtained. We then introduce an electric field orthogonal to the magnetic field, linking to the preceding case via a suitable Lorentz transformation, and obtain the corresponding Wigner rotations of the spin states. Finally, we point out for the first time that the entangled states corresponding to well-known ones in the study of 3-particle entanglements, may be classified systematically using a particular coupling of three angular momenta.