Entanglement, Berry Phases, and Level Crossings for the Atomic Breit-Rabi Hamiltonian

TL;DR

This paper explores how entanglement, Berry phases, and level crossings are interconnected in the Breit-Rabi Hamiltonian for hydrogen and sodium atoms, revealing that maximum entanglement occurs at avoided crossings and is linked to Berry phase behavior.

Contribution

It demonstrates the relationship between entanglement, Berry phases, and level crossings in atomic hyperfine interactions, highlighting the significance of avoided crossings.

Findings

Maximum entanglement occurs at avoided crossings.

Marginal Berry phase signals avoided crossing points.

Nodal points of Berry phase correspond to avoided crossings.

Abstract

The relation between level crossings, entanglement, and Berry phases is investigated for the Breit-Rabi Hamiltonian of hydrogen and sodium atoms, describing a hyperfine interaction of electron and nuclear spins in a magnetic field. It is shown that the entanglement between nuclear and electron spins is maximum at avoided crossings. An entangled state encircling avoided crossings acquires a marginal Berry phase of a subsystem like an instantaneous eigenstate moving around real crossings accumulates a Berry phase. Especially, the nodal points of a marginal Berry phase correspond to the avoided crossing points.