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Geometric Control for High-Fidelity Entanglement of Individual Ultracold Molecules

Seejia Yu

Published Jan 1, 2026• 0 citations
OpenAlex

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.

Related papers

High-fidelity entanglement of polar molecules by dynamic geometric control

Scarlett S. Yu, Avikar Periwal, Jiaqi You +6 more

In quantum information systems made of optical tweezer arrays of ultracold molecules, thermal motion of molecules degrades the coherence of their interactions, which limits entanglement fidelity and the concomitant scientific applicability of these systems. We show that by controlling the geometry of the dipolar interaction, even when a molecule occupies many motional states in the tweezer, coherence can be preserved. We characterize several geometries that suppress sensitivity to thermal fluctuations. We further use programmable, coherence-preserving motion of the molecules during entanglement to refocus dephasing from relative positional jitter of the tweezers, which is relevant even on the 10 nm scale. These methods yield substantially improved dipolar coherence and enable generation of two-molecule entanglement with a Bell state fidelity of $\mathcal{F}= 0.976^{+0.008}_{-0.011}$ in directly laser-cooled molecules.

physics.atom-phCross-listedarXiv:2607.13008•Jul 15, 2026•0 citations

Ultracold molecules in an optical tweezer array: From dipolar interaction to ground state cooling

Yicheng Bao

Ultracold molecules are attractive candidates for various applications including ultracold chemistry, quantum information processing, quantum simulation and searches for physics beyond the standard model. Combined with optical tweezer techniques, an optical tweezer array of ultracold polar molecules holds promise for versatile quantum applications. Their long-lived molecular rotational states form robust qubits, while the long-range dipolar interaction between molecules provides quantum entanglement. In this thesis, we build a new generation experiment of optical tweezer array of ultracold CaF molecules. We optically transport the laser cooled and optically trapped molecules into a science glass cell using a hybrid method, where high numerical aperture optical access allows for tighter optical tweezers. In an array of these tight optical tweezers, we demonstrate dipolar spin-exchange interactions between single CaF molecules for the first time. We realize the spin-$\frac{1}{2}$ quantum XY model by encoding an effective spin-$\frac{1}{2}$ system into the rotational states of the molecules, and use it to generate a Bell state through an iSWAP operation. Conditioned on the verified existence of molecules in both tweezers at the end of the measurement, we obtain a Bell state fidelity of 0.89(6). Employing interleaved tweezer arrays, we demonstrate single site molecular addressability. To further improve the platform, cooling of the molecules to near the motional ground state is crucial for reducing various dephasings. We demonstrate Raman sideband cooling (RSC) of CaF molecules in optical tweezers to near their 3-D motional ground state, with a 3-D motional ground state probability of $54\pm18\%$ of the molecules that survive the RSC. This paves the way to increase molecular coherence times in optical tweezers for robust quantum information processing and simulation applications in the near future.

•Jan 1, 2024•0 citations

Deep laser cooling and coherent control of molecules

Luke Caldwell

Ultracold molecules can be used for a diverse set of exciting applications including controlled quantum chemistry, probes of physics beyond the standard model, simulation of many-body quantum systems and quantum information processing. However their rich internal structure makes the required control of their motional and internal states difficult. In the last decade, the field has made rapid progress on developing techniques for producing, cooling and trapping molecules and, whilst challenges remain, many of these applications are now being realised. This thesis presents my work on laser cooling and coherent control of calcium monofluoride (CaF) molecules. We load molecules into a three-dimensional magneto-optical trap (MOT), the first such trap for CaF and the second for any molecule. The MOT contains around 2×10⁴ molecules with an initial temperature of 12 mK. Lowering the laser intensity brings the temperature of the MOT down to 960 μK. To further cool the molecules we load them into a blue-detuned optical molasses, cooling them to 5.4(7) μK. This temperature is ~40 times below the Doppler limit and corresponds to a typical molecule moving at only a few times the single-photon recoil velocity. We optically pump the molecules into a single Zeeman sub-level and coherently transfer them between rotational states using microwave radiation. We load the molecules into a magnetic trap where they remain confined for about 5 s, the lifetime being limited by vibrational excitation due to room-temperature blackbody radiation. We show how to prepare the trapped molecules in a coherent superposition of two rotational states, and how to maintain this coherence for long periods, up to 6.4(8) ms. Detailed simulations of the remaining decoherence mechanisms suggest that it is possible to extend this to more than a second by compressing the sample to a smaller size, and using a magnetic trap geometry where the direction of the field is nearly uniform across the trapping volume. Finally we explore theoretically how Raman sideband cooling can be applied to molecules in optical tweezer traps, potentially providing a route to full quantum control.

•Feb 1, 2020•2 citations

Control, Readout, and Entanglement of Molecular Qubits

Lewis R. B. Picard

Ultracold polar molecules possess a manifold of long-lived molecular rotational states, which can be coherently controlled using microwave fields and entangled by the long-range dipole-dipole interactions between molecules. The ability to control these features at the individual molecule level provides a rich toolbox with which to engineer quantum simulations of exotic materials or build a molecular quantum computer. Until recently, this level of single molecule control has eluded researchers due to the challenges inherent in taming the complex internal structure of molecules. In this thesis, we demonstrate full control over the internal quantum states and coherent interactions of individual NaCs molecules in optical tweezers. This platform is based on coherent assembly of ultracold Na and Cs atoms trapped and cooled in separate arrays, before being magnetoassociated at a Feshbach resonance to form weakly-bound molecules. Using high-resolution spectroscopy of electronically excited molecular states, we identify an efficient two-photon pathway to the rovibrational ground state of NaCs that we use to prepare an array of ground state molecules in tweezers. We demonstrate a "magic ellipticity'' technique to eliminate differential light shifts between two molecular rotational states and achieve coherence times of up to 250(40) ms for a superposition of those states. We then show that we can rearrange molecules in an array to eliminate defects and perform single-shot readout of multiple rotational states using controlled molecule dissociation and imaging of constituent atoms at high magnetic field. Finally, we coherently control the dipole-dipole interactions between two molecules, producing a Bell state with a fidelity of 94(3) % and demonstrating a universal entangling iSWAP gate for qubits encoded in molecular hyperfine states.

•Jan 1, 2024•0 citations

Ultracold Molecules in Optical Arrays: From Laser Cooling to Molecular Collisions

Loïc Anderegg

Potential wide-ranging scientific applications, spanning fundamental physics to quantum engineering, has led to significant efforts in controlling molecules at the quantum level. The rich internal structure of molecules, that gives rise to these desirable properties also complicates the task of controlling such species. Over the past decade, our ability to produce, control, and detect molecules has advanced tremendously with direct laser-cooling and magneto-optical trapping of diatomic molecules realized by several groups around the world. In this thesis, we describe the creation of the first RF MOT of CaF, which at the time of the writing of this thesis, remains the largest and densest molecular MOT. New laser cooling techniques for molecules are demonstrated, allowing laser cooling of molecules to 4 uK, 50 times colder than the Doppler limit. Optical trapping of these molecules is also achieved, which, in combination with in-trap laser cooling increased the density of trapped molecules by five orders of magnitude compared to the density in the MOT. We developed methods to cool and detect single molecules with high fidelity, which aided us in the creation of an optical tweezer array of single, ultracold CaF molecules. The densities of molecules (10^12 cm^-3) attained inside the tweezer traps also enabled us to observe both light-assisted and ground state collisions of laser cooled molecules, for the first time. The phase space density within the merged tweezers reached 5x10^-4, 10 orders of magnitude larger than the initial MOT. We implemented internal quantum state control of the molecules and dynamical control of the tweezers to build a platform for exploring state-selective ultracold quantum chemistry.

•Jan 8, 2020•5 citations

A conveyor-belt magneto-optical trap of CaF

Scarlett S. Yu, Jiaqi You, Yicheng Bao +8 more

Abstract Achieving high-density samples of laser-cooled molecules is a critical step toward advancing applications in precision measurements, ultracold chemistry and quantum science. We report the experimental realization of a high-density conveyor-belt magneto-optical trap for calcium monofluoride (CaF) molecules. The obtained highly-compressed cloud has a mean radius of 64(5) μ m and a peak number density of 3.6(5) x 10 10 cm -3 , a 600-fold increase over the conventional red-detuned MOTs of CaF, and the densest molecular MOT observed to date. Subsequent loading of these molecules into an optical dipole trap yields up to 2.6 x 10 4 trapped molecules at a temperature of 14(2) μ K with a peak phase-space density of ~2.4 x 10 -6 . This opens new possibilities for a range of applications utilizing high-density, optically trapped ultracold molecules.

Nature Communications•Jan 7, 2026•8 citations
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 F=0.976−0.011+0.008\mathcal{F}=0.976^{+0.008}_{-0.011}F=0.976−0.011+0.008​ 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.
In quantum information systems made of optical tweezer arrays of ultracold molecules, thermal motion of molecules degrades the coherence of their interactions, which limits entanglement fidelity and the concomitant scientific applicability of these systems. We show that by controlling the geometry of the dipolar interaction, even when a molecule occupies many motional states in the tweezer, coherence can be preserved. We characterize several geometries that suppress sensitivity to thermal fluctuations. We further use programmable, coherence-preserving motion of the molecules during entanglement to refocus dephasing from relative positional jitter of the tweezers, which is relevant even on the 10 nm scale. These methods yield substantially improved dipolar coherence and enable generation of two-molecule entanglement with a Bell state fidelity of F=0.976−0.011+0.008\mathcal{F}= 0.976^{+0.008}_{-0.011}F=0.976−0.011+0.008​ in directly laser-cooled molecules.
Ultracold molecules are attractive candidates for various applications including ultracold chemistry, quantum information processing, quantum simulation and searches for physics beyond the standard model. Combined with optical tweezer techniques, an optical tweezer array of ultracold polar molecules holds promise for versatile quantum applications. Their long-lived molecular rotational states form robust qubits, while the long-range dipolar interaction between molecules provides quantum entanglement. In this thesis, we build a new generation experiment of optical tweezer array of ultracold CaF molecules. We optically transport the laser cooled and optically trapped molecules into a science glass cell using a hybrid method, where high numerical aperture optical access allows for tighter optical tweezers. In an array of these tight optical tweezers, we demonstrate dipolar spin-exchange interactions between single CaF molecules for the first time. We realize the spin-12\frac{1}{2}21​ quantum XY model by encoding an effective spin-12\frac{1}{2}21​ system into the rotational states of the molecules, and use it to generate a Bell state through an iSWAP operation. Conditioned on the verified existence of molecules in both tweezers at the end of the measurement, we obtain a Bell state fidelity of 0.89(6). Employing interleaved tweezer arrays, we demonstrate single site molecular addressability. To further improve the platform, cooling of the molecules to near the motional ground state is crucial for reducing various dephasings. We demonstrate Raman sideband cooling (RSC) of CaF molecules in optical tweezers to near their 3-D motional ground state, with a 3-D motional ground state probability of 54±18%54\pm18\%54±18% of the molecules that survive the RSC. This paves the way to increase molecular coherence times in optical tweezers for robust quantum information processing and simulation applications in the near future.
Ultracold molecules can be used for a diverse set of exciting applications including controlled quantum chemistry, probes of physics beyond the standard model, simulation of many-body quantum systems and quantum information processing. However their rich internal structure makes the required control of their motional and internal states difficult. In the last decade, the field has made rapid progress on developing techniques for producing, cooling and trapping molecules and, whilst challenges remain, many of these applications are now being realised. This thesis presents my work on laser cooling and coherent control of calcium monofluoride (CaF) molecules. We load molecules into a three-dimensional magneto-optical trap (MOT), the first such trap for CaF and the second for any molecule. The MOT contains around 2×10⁴ molecules with an initial temperature of 12 mK. Lowering the laser intensity brings the temperature of the MOT down to 960 μK. To further cool the molecules we load them into a blue-detuned optical molasses, cooling them to 5.4(7) μK. This temperature is ~40 times below the Doppler limit and corresponds to a typical molecule moving at only a few times the single-photon recoil velocity. We optically pump the molecules into a single Zeeman sub-level and coherently transfer them between rotational states using microwave radiation. We load the molecules into a magnetic trap where they remain confined for about 5 s, the lifetime being limited by vibrational excitation due to room-temperature blackbody radiation. We show how to prepare the trapped molecules in a coherent superposition of two rotational states, and how to maintain this coherence for long periods, up to 6.4(8) ms. Detailed simulations of the remaining decoherence mechanisms suggest that it is possible to extend this to more than a second by compressing the sample to a smaller size, and using a magnetic trap geometry where the direction of the field is nearly uniform across the trapping volume. Finally we explore theoretically how Raman sideband cooling can be applied to molecules in optical tweezer traps, potentially providing a route to full quantum control.
Ultracold polar molecules possess a manifold of long-lived molecular rotational states, which can be coherently controlled using microwave fields and entangled by the long-range dipole-dipole interactions between molecules. The ability to control these features at the individual molecule level provides a rich toolbox with which to engineer quantum simulations of exotic materials or build a molecular quantum computer. Until recently, this level of single molecule control has eluded researchers due to the challenges inherent in taming the complex internal structure of molecules. In this thesis, we demonstrate full control over the internal quantum states and coherent interactions of individual NaCs molecules in optical tweezers. This platform is based on coherent assembly of ultracold Na and Cs atoms trapped and cooled in separate arrays, before being magnetoassociated at a Feshbach resonance to form weakly-bound molecules. Using high-resolution spectroscopy of electronically excited molecular states, we identify an efficient two-photon pathway to the rovibrational ground state of NaCs that we use to prepare an array of ground state molecules in tweezers. We demonstrate a "magic ellipticity'' technique to eliminate differential light shifts between two molecular rotational states and achieve coherence times of up to 250(40) ms for a superposition of those states. We then show that we can rearrange molecules in an array to eliminate defects and perform single-shot readout of multiple rotational states using controlled molecule dissociation and imaging of constituent atoms at high magnetic field. Finally, we coherently control the dipole-dipole interactions between two molecules, producing a Bell state with a fidelity of 94(3) % and demonstrating a universal entangling iSWAP gate for qubits encoded in molecular hyperfine states.
Potential wide-ranging scientific applications, spanning fundamental physics to quantum engineering, has led to significant efforts in controlling molecules at the quantum level. The rich internal structure of molecules, that gives rise to these desirable properties also complicates the task of controlling such species. Over the past decade, our ability to produce, control, and detect molecules has advanced tremendously with direct laser-cooling and magneto-optical trapping of diatomic molecules realized by several groups around the world. In this thesis, we describe the creation of the first RF MOT of CaF, which at the time of the writing of this thesis, remains the largest and densest molecular MOT. New laser cooling techniques for molecules are demonstrated, allowing laser cooling of molecules to 4 uK, 50 times colder than the Doppler limit. Optical trapping of these molecules is also achieved, which, in combination with in-trap laser cooling increased the density of trapped molecules by five orders of magnitude compared to the density in the MOT. We developed methods to cool and detect single molecules with high fidelity, which aided us in the creation of an optical tweezer array of single, ultracold CaF molecules. The densities of molecules (10^12 cm^-3) attained inside the tweezer traps also enabled us to observe both light-assisted and ground state collisions of laser cooled molecules, for the first time. The phase space density within the merged tweezers reached 5x10^-4, 10 orders of magnitude larger than the initial MOT. We implemented internal quantum state control of the molecules and dynamical control of the tweezers to build a platform for exploring state-selective ultracold quantum chemistry.
Abstract Achieving high-density samples of laser-cooled molecules is a critical step toward advancing applications in precision measurements, ultracold chemistry and quantum science. We report the experimental realization of a high-density conveyor-belt magneto-optical trap for calcium monofluoride (CaF) molecules. The obtained highly-compressed cloud has a mean radius of 64(5) μ m and a peak number density of 3.6(5) x 10 10 cm -3 , a 600-fold increase over the conventional red-detuned MOTs of CaF, and the densest molecular MOT observed to date. Subsequent loading of these molecules into an optical dipole trap yields up to 2.6 x 10 4 trapped molecules at a temperature of 14(2) μ K with a peak phase-space density of ~2.4 x 10 -6 . This opens new possibilities for a range of applications utilizing high-density, optically trapped ultracold molecules.