Geometric Control for High-Fidelity Entanglement of Individual Ultracold Molecules

Abstract

Ultracold polar molecules provide a powerful platform for quantum science because they combine long-lived rotational states, rich internal structure, and strong electric dipole-dipole interactions. Optical tweezer arrays provide a pristine way of controlling these molecules at single-particle level, in which molecules can be individually trapped, rearranged into programmable geometries, coherently manipulated by optical and microwave fields, and entangled through their native dipolar interactions. This dissertation describes the development of geometric control as a resource for improving interaction coherence and high fidelity of quantum entanglement between directly laser-cooled calcium monofluoride (CaF) molecules in optical tweezers. A central challenge in molecular tweezer systems is that dipolar interactions are intrinsically sensitive to the relative position of the molecules. Thermal motion in the traps, especially along the weakly confined axial direction, causes molecules to sample a distribution of intermolecular separations, degrading dipolar coherence and limiting entanglement fidelity. We show in this work that the interaction itself can be made robust by controlling its geometry. The experimental work begins with improvements to the production and optical trapping of dense CaF samples. We realize a blue-detuned conveyor-belt" magneto-optical trap (MOT) that compresses laser-cooled CaF to a mean cloud radius of $64(5)~\mu\mathrm{m}$ and a peak density of $3.6(5)\times10^{10}~\mathrm{cm}^{-3}$, a 600-fold density increase over conventional red-detuned CaF MOTs. Loading from this compressed source into an optical dipole trap yields up to $2.6\times10^4$ trapped molecules at $14(2)~\mu\mathrm{K}$, with a peak phase-space density of approximately $2.4\times10^{-6}$. This high-density source improves the transfer of laser-cooled molecules into conservative optical traps and provides the starting point for loading and manipulating single molecules in a hybrid SLM-AOD optical tweezer array. Using this platform, we prepare CaF molecules in selected rotational and hyperfine states to encode a rotational qubiyt. We show how to preserve the single-qubit coherence with a combination of techniques, including magic" polarization condition and microwave dynamical decoupling, as well as reduce motional quantum state of the trapped molecule with Raman sideband cooling. We then characterize coherent dipolar spin exchange between pairs of molecules and identify thermal motion and relative trap-center offsets as dominant sources of interaction dephasing. To suppress these effects, we engineer the three-dimensional interaction geometry between two individually trapped molecules. More specifically, we show that one can tune the \textit{static} geometric of the dipolar interaction to configurations where sensitivity to thermal fluctuations is strongly reduced while retaining a finite interaction strength. Furthermore, we show that a molecule can be moved during the interaction while preserving the coherence of ongoing entangling operations. We leverage programmable molecular motion to refocus dephasing arising from relative positional jitter of the optical tweezers. Combining static geometric insensitivity, programmable molecular motion, and partial Raman sideband cooling, we generate two-molecule entanglement with a Bell-state fidelity of $\mathcal{F}=0.976^{+0.008}_{-0.011}$ in directly laser-cooled molecules. Crucially, the high-fidelity molecular entanglement here is performed without ground-state preparation. Rather than relying on stringent cooling or species-specific trapping conditions, as in prior work, the methods demonstrated here are instead based on dynamic and static geometric control of interacting molecules and are therefore broadly applicable across molecular platforms. These results extend moving optical tweezers beyond assembly and rearrangement, opening routes to robust two-qubit gates, many-body dynamics, and dynamically programmable networks of interaction.