Dynamics of an itinerant spin-3 atomic dipolar gas in an optical lattice. (arXiv:1905.06123v1 [cond-mat.quant-gas])

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.

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