Minimal spin-rotor model for Barnett and Einstein--de Haas physics

TL;DR

This paper introduces a minimal quantum model coupling a spin-1/2 to a quantum rotor, revealing how quantization alters the classical Barnett effect and leads to spin-rotor entanglement.

Contribution

The authors present an exactly solvable quantum rotor model that captures quantum effects in the Barnett and Einstein--de Haas phenomena, highlighting the departure from classical effective-field descriptions.

Findings

Reproduces classical Barnett splitting in fixed angular-momentum sectors

Shows operator-valued Barnett field in superposition sectors

Demonstrates spin-rotor entanglement and coherence effects

Abstract

The Barnett effect is usually understood through an effective magnetic field generated by mechanical rotation, while its reciprocal Einstein--de Haas effect describes the transfer of spin angular momentum to mechanical motion. We show that this effective-field picture changes qualitatively once the mechanical degree of freedom itself is quantized. To demonstrate this, we introduce an exactly solvable minimal spin-rotor model in which a spin-$1/2$ is coupled to a quantum rotor. In a fixed angular-momentum sector, the model reproduces the conventional Barnett splitting and remains formally equivalent to a Zeeman problem. For a superposition of rotor sectors, however, the Barnett field becomes operator-valued and the resulting dynamics generates coherent spin-rotor entanglement. This is directly visible in the reduced spin purity, rotor coherence, and entanglement entropy. Our results identify a minimal quantum setting in which the Barnett effective-field picture departs from its classical form and acquires a reciprocal manifestation through spin-dependent rotor coherence.