# Quantum Spin Stabilized Magnetic Levitation

## TL;DR

This paper demonstrates theoretically that quantum spin effects enable stable magnetic levitation of a non-rotating nanoparticle in static magnetic fields, revealing new stable phases and quantum properties.

## Contribution

It introduces a quantum spin-based stabilization mechanism for magnetic levitation, overcoming classical limitations and predicting entanglement and squeezing at equilibrium.

## Key findings

- Stable levitation via quantum spin effects despite Earnshaw's theorem
- Existence of two stable phases related to Einstein--de Haas and Larmor precession
- Quantum state at equilibrium exhibits entanglement and squeezing

## Abstract

We theoretically show that, despite Earnshaw's theorem, a non-rotating single magnetic domain nanoparticle can be stably levitated in an external static magnetic field. The stabilization relies on the quantum spin origin of magnetization, namely the gyromagnetic effect. We predict the existence of two stable phases related to the Einstein--de Haas effect and the Larmor precession. At a stable point, we derive a quadratic Hamiltonian that describes the quantum fluctuations of the degrees of freedom of the system. We show that in the absence of thermal fluctuations, the quantum state of the nanomagnet at the equilibrium point contains entanglement and squeezing.