Probing spin dynamics from the Mott insulating to the superfluid regime in a dipolar lattice gas

We analyze the spin dynamics of an out-of-equilibrium large spin dipolar atomic Bose gas in an optical lattice. We observe a smooth crossover from a complex oscillatory behavior to an exponential behavior throughout the Mott-to-superfluid transition. While both of these regimes are well described by our theoretical models, we provide data in the intermediate regime where dipolar interactions, contact interactions, and superexchange mechanisms compete. In this strongly correlated regime, spin dynamics and transport are coupled, which challenges theoretical models for quantum magnetism.

Figure 1

(a) Simple representation of the system close to the Mott-to-superfluid transition. Atoms interact both due to intersite (white ellipse) and on-site (black ellipse) interactions. (b) Sketch illustrating the competition between exchange due to DDI ($V_{dd}$) and tunneling ($J$) assisted spin exchange due to contact interactions ($V_c$). (c) Measurement of the spin components as a function of time for $16E_r$. (d) Time evolution of observable $n_{-3}/n_{-2}$ for four different lattice depths ($27E_r, 16E_r, 11.5E_r$, and $3E_r$, from top to bottom). Lines are guides for the eye resulting from fits.

Figure 2

Spin dynamics amplitudes and frequencies as a function of the lattice depth. (a) Amplitude of the exponential dynamics (blue diamonds) and slow oscillation (red triangles). Green circles are results of numerical simulations. Inset: Variation of the magnetization over 20 ms. Solid lines are guides to the eye. (b) Frequency of fast (black points) and slow (red triangles) oscillations. The top black solid line corresponds to spin-exchange frequency associated with intrasite contact interactions, while the black open circles correspond to a numerical simulation of the Gross-Pitaevskii equation. The bottom red curve is a guide to the eye. The blue dotted-dashed line shows the prediction in the Mott regime (see text). The frequency of the superexchange process is given by the green solid line. Error bars in frequency and amplitude result from the statistical uncertainty in the fits.

Figure 3

Results of numerical simulations using the Gross-Pitaevskii equation. (a) Spin dynamics for the deepest lattice depth that could be simulated ($7E_r$, solid line). The red triangles are experimental data. (b) Spatial analysis of spin dynamics, showing a cut of the density of the atoms in the $m_s=-2$ state along a horizontal plane $z=0$ (with no lattice on).