# Exploring out-of-equilibrium quantum magnetism and thermalization in a spin-3 many-body dipolar lattice system

## TL;DR

This study investigates how a large ensemble of spin-3 atoms in an optical lattice thermalizes through dipolar interactions, demonstrating entanglement growth and local thermal equilibrium in an out-of-equilibrium quantum many-body system.

## Contribution

It provides experimental evidence of quantum thermalization and entanglement growth in a macroscopic spin-3 system, supported by advanced numerical methods and thermalization observations.

## Key findings

- System thermalizes to a steady state consistent with a thermal ensemble.
- Quantum correlation and entanglement entropy grow during dynamics.
- Experimental results agree with theoretical predictions of entanglement build-up.

## Abstract

Understanding quantum thermalization through entanglement build-up in isolated quantum systems addresses fundamental questions on how unitary dynamics connects to statistical physics. Here, we study the spin dynamics and approach towards local thermal equilibrium of a macroscopic ensemble of S = 3 spins prepared in a pure coherent spin state, tilted compared to the magnetic field, under the effect of magnetic dipole-dipole interactions. The experiment uses a unit filled array of 104 chromium atoms in a three dimensional optical lattice, realizing the spin-3 XXZ Heisenberg model. The buildup of quantum correlation during the dynamics, especially as the angle approaches pi/2, is supported by comparison with an improved numerical quantum phase-space method and further confirmed by the observation that our isolated system thermalizes under its own dynamics, reaching a steady state consistent with the one extracted from a thermal ensemble with a temperature dictated from the system's energy. This indicates a scenario of quantum thermalization which is tied to the growth of entanglement entropy. Although direct experimental measurements of the Renyi entropy in our macroscopic system are unfeasible, the excellent agreement with the theory, which can compute this entropy, does indicate entanglement build-up.