Probing Coherent Many-Body Spin Dynamics in a Molecular Tweezer Array Quantum Simulator

Abstract

Models of interacting quantum spins are used in many areas of physics ranging from the study of magnetism and strongly correlated materials to quantum sensing. In this work, we study coherent many-body dynamics of interacting spin models realized using polar molecules trapped in rearrangeable optical tweezer arrays. Specifically, we encode quantum spins in long-lived rotational states and use the electric dipolar interaction between molecules, together with Floquet Hamiltonian engineering, to realize $1/r^3$ XXZ and XYZ models. We microscopically probe several types of coherent dynamics in these models, including quantum walks of single spin excitations, the emergence of magnon bound states, and coherent creation and annihilation of magnon pairs. Our results establish molecular tweezer arrays as a new quantum simulation platform for interacting quantum spin models.

Figures (4)

• Figure 1: Realizing $1/r^3$ XXZ/XYZ Spin Models in a Molecular Tweezer Array. (a) Polar CaF molecules are laser-cooled and trapped in a rearrangeable optical tweezer array. A spin-1/2 degree of freedom is encoded in two molecular rotational states and electric dipolar interactions provide a native $1/r^3$ XY Hamiltonian $\hat{H}_{\rm XY}$. Floquet engineering using microwave pulses converts $\hat{H}_{\rm XY}$ into $\hat{H}_{\rm XYZ}$. Specifically, $\pi/2$ pulses toggle the instantaneous spin frame, providing two additional terms: (1) an Ising term $\hat{S}_i^z \hat{S}_j^z$ with strength $\Delta$, and (2) a pair creation/annihilation interaction term $\hat{S}_i^+ \hat{S}_j^++\hat{S}_i^- \hat{S}_j^-$ with strength $\gamma$. (b) The blue shaded region indicates the accessible parameter space of $\gamma$ and $\Delta$. The red (green) data points show the parameters explored in this work. (c) Normalized depolarization time $J_{\rm ex}T_1$ (blue circles) and decoherence time $J_{\rm ex}T_2$ (red triangles) for the XXZ sequences, together with $J_{\rm ex}T_1$ (green squares) and $J_{\rm ex}T_2$ (yellow diamonds) for the XYZ sequences. The data is corrected for blackbody leakage. These times are generally on the scale of $10^2$. (d) Experimentally measured Ising strength $\Delta$ with isolated molecular pairs versus the theoretically predicted value $\Delta_{\text{th}}$. The red line indicates $\Delta = \Delta_{\text{th}}$.
• Figure 2: Single Magnon Dynamics in the $1/r^3$ XXZ Model. (a) Evolution of $\langle P_i^\uparrow\rangle$ at Ising strengths $\Delta=0.012(11), 0.361(8), 0.686(10), 1.00(12), 1.329(11), 1.741(19)$ versus time $J t$, where $J$ is the nearest-neighbor spin-exchange strength. The initially localized $\ket{\uparrow}$ spin excitation performs a coherent quantum walk. Top row shows experimental data, which are qualitatively consistent with exact diagonalization simulations shown in the bottom row. (b) Spin up probability of the center site $\langle P_4^\uparrow\rangle$ versus time $Jt$ (c) Spin up probability of the leftmost site $\langle P_1^\uparrow\rangle$ versus time $Jt$. For (b,c), solid lines show numerical simulations of the ideal model. Dashed lines include a phenomenological exponential damping envelope with damping constant obtained by fitting to $\langle P_4^\uparrow\rangle$. The data and corresponding fits are ordered by increasing $\Delta$ from bottom to top and vertically offset by 0.8 for clarity. The values of $\Delta$ are the same as (a).
• Figure 3: Two-Magnon Dynamics in the $1/r^3$ XXZ Model. (a) For nearest-neighbor interactions and $\Delta\gg1$, breaking a spin pair creates domain walls with energy $\Delta J$. Energy conservation implies domain wall conservation, leading to magnon bound states. (b) $\ket{\uparrow}$-$\ket{\uparrow}$ separation probability $P_b(d,t)$ versus time $t$. (c) $P_{B}$, the equilibrium value of $P_b(1,t)$, versus $\Delta$. The green (blue) curve shows exact diagonalization results with (without) interaction disorder and state preparation/detection infidelities, with the shaded region showing error bands from fitting Supplement. (d) Measured spatial correlators $\langle P^{\uparrow}_i P^{\uparrow}_j\rangle$ for $\Delta=1.741\,(19)$ versus time. Significant weight on the first off-diagonals indicates the two spins propagating as a bound pair. Color scales are normalized to the measured peak value. (e) Center-of-mass distribution $P_{{\rm CM}, i}(t)$ versus time for $\Delta=1.329\,(11)$ (left) and $\Delta=1.741\,(19)$ (right). Revival at the central site indicates coherent dynamics. (f) For $1/r^3$ interactions, pair hopping includes both a second-order and a first-order contribution. (g) Pair hopping rate ${\tilde{t}_{\rm{eff}}}$ versus $\Delta$. Green points show measured values for $\Delta$ above the thermodynamic bound state threshold ($\Delta\approx 1.03$) Supplement. The dashed red (blue) line shows perturbation theory for nearest-neighbor ($1/r^3$) interactions; the solid red (blue) line shows the exact-diagonalization result for nearest-neighbor ($1/r^3$) interactions.
• Figure 4: Coherent Magnon Pair Creation and Annihilation in the $1/r^3$ XYZ Model. (a) For $\hat{H}_{\text{XYZ}}$ under a nearest-neighbor approximation, adjacent spins are flipped pairwise, creating domain walls with energy $J\Delta/2$. (b) $\langle \hat{S}_i^z\rangle$ versus time $\gamma Jt$ for an initial state $\ket{\downarrow}^{\otimes N_{\rm mol}}$, with $\Delta=1.033(11)$ and $\gamma=0.466(5)$. (c) Full counting statistics $P_\text{FC}(N_\uparrow)$ versus $\gamma Jt$. (d) The parity $\langle\mathcal{P}\rangle$ (blue circles) and total spin $-2 \langle \hat{S}^z\rangle/N_{\rm mol}$ (red squares) versus time. The blue solid line is an exponential fit to $\langle\mathcal{P}\rangle$ with a time constant of $9.6(8)/J_{\text{ex}}$. The red solid (dashed) line shows exact diagonalization simulations with (without) a fitted exponential envelope. (e) Energy diagram for $\hat{H}_{\text{XYZ}}$ with $\Delta\gg 1$ and nearest-neighbor approximation. Pair creation is mapped onto a quantum walk of a domain wall. (f) Simulated $\langle \hat{S}_i^z\rangle$ versus time for a coherent quantum walk (left) and an incoherent random walk (right). (g) $\langle \hat{S}_i^z\rangle$ versus time for the initial state $\ket{\downarrow\downarrow \uparrow \uparrow\uparrow\uparrow\uparrow\uparrow}$ with $\Delta=1.860\,(13)$ and $\gamma=0.290(3)$. (h) Measured microstate population $P$ versus time for data in (g). (i) Population $P$ of the 3 most occupied microstates versus time. Dashed lines are exact diagonalization results. Solid lines include an exponential envelope with a time constant of $36.8(4)/J_{\text{ex}}$.