# Dynamics of an itinerant spin-3 atomic dipolar gas in an optical lattice

## TL;DR

This study investigates the spin dynamics of a large ensemble of spin-3 bosonic chromium atoms in an optical lattice, revealing distinct regimes of behavior influenced by lattice depth, interactions, and magnetic field gradients, with implications for quantum simulation.

## Contribution

It provides a comprehensive analysis of spin dynamics across the superfluid to Mott insulator transition, highlighting the roles of long-range dipolar interactions and the necessity of beyond mean-field theories at high lattice depths.

## Key findings

- Spin dynamics are governed by particle motion, interactions, and magnetic gradients at low lattice depths.
- Long-range dipolar interactions dominate spin behavior at high lattice depths.
- Mean-field theory suffices at low depths, but beyond mean-field approaches are needed at high depths.

## Abstract

Arrays of ultra-cold dipolar gases loaded in optical lattices are emerging as powerful quantum simulators of the many-body physics associated with the rich interplay between long-range dipolar interactions, contact interactions, motion, and quantum statistics. In this work we report on our investigation of the quantum many-body dynamics of a large ensemble of bosonic magnetic chromium atoms with spin S = 3 in a three-dimensional lattice as a function of lattice depth. Using extensive theory and experimental comparisons we study the dynamics of the population of the different Zeeman levels and the total magnetization of the gas across the superfluid to the Mott insulator transition. We are able to identify two distinct regimes: At low lattice depths, where atoms are in the superfluid regime, we observe that the spin dynamics is strongly determined by the competition between particle motion, onsite interactions and external magnetic field gradients. Contact spin dependent interactions help to stabilize the collective spin length, which sets the total magnetization of the gas. On the contrary, at high lattice depths, transport is largely frozen out. In this regime, while the spin populations are mainly driven by long range dipolar interactions, magnetic field gradients also play a major role in the total spin demagnetization. We find that dynamics at low lattice depth is qualitatively reproduced by mean-field calculations based on the Gutzwiller ansatz; on the contrary, only a beyond mean-field theory can account for the dynamics at large lattice depths. While the cross-over between these two regimes does not correspond to sharp features in the observed dynamical evolution of the spin components, our simulations indicate that it would be better revealed by measurements of the collective spin length.