Many-Body Dynamics of Dipolar Molecules in an Optical Lattice

We use Ramsey spectroscopy to experimentally probe the quantum dynamics of disordered dipolar-interacting ultracold molecules in a partially filled optical lattice, and we compare the results to theory. We report the capability to control the dipolar interaction strength. We find excellent agreement between our measurements of the spin dynamics and theoretical calculations with no fitting parameters, including the dynamics’ dependence on molecule number and on the dipolar interaction strength. This agreement verifies the microscopic model expected to govern the dynamics of dipolar molecules, even in this strongly correlated beyond-mean-field regime, and represents the first step towards using this system to explore many-body dynamics in regimes that are inaccessible to current theoretical techniques.

Figure 1

Probing dipolar spin-exchange interactions of molecules in a lattice with Ramsey spectroscopy. (a) Two pairs of rotational states in KRb molecules used to realize spin models. The states are labeled $|N,m_N⟩$, where $N$ is the total rotational angular momentum and $m_N$ its projection along the quantization axis set by the magnetic field $\mathbf{B}$. (b) A dilute gas of KRb molecules pinned in a deep optical lattice and experiencing long-range, anisotropic dipolar exchange interactions. (c) Ramsey protocol applied to initiate and probe the spin dynamics. (d) Schematic of the theoretical method employed in this Letter (MACE).

Figure 2

Measured contrast dynamics compared with theory. (a)–(c) Contrast versus time for the $\{|\uparrow ⟩=|1,-1⟩,|\downarrow ⟩=|0,0⟩\}$ rotational state choice, experimentally measured (red symbol) and theoretically calculated (red line) for all spins initially prepared along $\widehat{x}$, for increasing molecule number $N$ (left to right). Inset: Fourier transform of the simulated dynamics for $N=1.2\times 10^4$ and $|\uparrow ⟩=|1,-1⟩$. (d)–(f) Black symbols and black line, same as in (a)–(c), but choosing instead $|\uparrow ⟩=|1,0⟩$.

Figure 3

Contrast dynamics’ dependence on particle number (lattice filling) and rotational state pair choice. (a) Rescaled contrast dynamics for the two choices of spin states: the experimental times for the $|\uparrow ⟩=|1,-1⟩$ data (red circles) are rescaled by a factor of $J_{|1,-1⟩}/J_{|1,0⟩}\approx 1/2$ with respect to the $|\uparrow ⟩=|1,0⟩$ data (black squares), to show that the choice of rotational states only rescales the interaction timescale. Theoretically calculated dynamics (solid line) is shown for $N=12,000$. The two measurements have slightly different particle numbers: $N=1.1\times 10^4$ and $N=1.2\times 10^4$ for $|\uparrow ⟩=|1,0⟩$ and $|\uparrow ⟩=|1,-1⟩$, respectively. (b) Spin coherence time $\tau$ versus molecule number $N$, as determined by fitting the contrast data to a simple exponential decay, of the form $\mathcal{}C(t)=\exp (-t/\tau )$. (c) Root-mean-square residuals of the data from the exponential fit as a function of the molecule number $N$, quantifying the magnitude of all oscillations. Coherence times and residuals are shown for both sets of spin states, with theory predictions as well, with the same colors and symbols as in panel a.

Figure 4

Theoretically calculated contrast dynamics for (a) nearest-neighbor interactions and (b) interactions to next-nearest-neighbors for two fillings each (indicated) compared with the $N=1.2\times 10^4$, $|\uparrow ⟩=|1,0⟩$ measurement and dipolar theory (dashed line). The disagreement of the short-ranged calculations with experiment supports the necessity of including long-range interactions to describe the observed dynamics.