Nonequilibrium Quantum Magnetism in a Dipolar Lattice Gas

We report on the realization of quantum magnetism using a degenerate dipolar gas in an optical lattice. Our system implements a lattice model resembling the celebrated $t\mathrm{\text{−}}J$ model. It is characterized by a nonequilibrium spinor dynamics resulting from intersite Heisenberg-like spin-spin interactions provided by nonlocal dipole-dipole interactions. Moreover, due to its large spin, our chromium lattice gases constitute an excellent environment for the study of quantum magnetism of high-spin systems, as illustrated by the complex spin dynamics observed for doubly occupied sites.

Figure 1

Long term spin dynamics. The ratio between two Zeeman spin components is plotted as a function of time. For this specific data, the lattice depth corresponds to lattice band gaps of $({\omega }_x^L,{\omega }_y^L,{\omega }_z^L)=2\pi \times (130,55,150)\mathrm{kH}z$. Experimental results are shown for singlons only (red diamonds) and for singlons plus doublons (black diamonds). Error bars show statistical uncertainties. The two dynamics show the same trend after 10 ms. The black line is a fit to the data (damped $\mathrm{\text{sinusoid}}+\mathrm{\text{exponential}}$) to guide the eye. The colored line are results of our simulation for spins 3 on a $3\times 3$ plaquette, for three different quadratic effects, and tunneling rates $J_{(x,z)}=(11,3)\mathrm{Hz}$ (deduced from lattice calibrations).

Figure 2

Fast spin exchange dynamics due to contact interactions. The experimental evolution of the different spin components shows damped oscillations. For this specific data, the lattice depth was reduced, corresponding to lattice band gaps of $({\omega }_x^L,{\omega }_y^L,{\omega }_z^L)=2\pi \times (100,50,145)\mathrm{kH}z$. The value of the pseudo period for $m_s=-3$, $-2$ is in good agreement with theory. Full lines are results of fits with exponentially damped sinusoids.

Figure 3

Slow spin exchange dynamics due to dipole-dipole interactions. The experimental evolution of different spin components shows oscillations on a few ms time scale. Lines are results of fits with exponentially damped sinusoids.