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arXiv:2408.14904 · Nature

Long-lived entanglement of molecules in magic-wavelength optical tweezers

Daniel K. Ruttley, Tom R. Hepworth, Alexander Guttridge, Simon L. Cornish

Published Jan 15, 2025• 48 citations
arXivHTMLPDF

Abstract

Abstract Realizing quantum control and entanglement of particles is crucial for advancing both quantum technologies and fundamental science. Substantial developments in this domain have been achieved in a variety of systems 1–5 . In this context, ultracold polar molecules offer new and unique opportunities because of their more complex internal structure associated with vibration and rotation, coupled with the existence of long-range interactions 6,7 . However, the same properties make molecules highly sensitive to their environment 8–10 , affecting their coherence and utility in some applications. Here we show that by engineering an exceptionally controlled environment using rotationally magic 11,12 optical tweezers, we can achieve long-lived entanglement between pairs of molecules using detectable hertz-scale interactions. We prepare two-molecule Bell states with fidelity $$0.92{4}_{-0.016}^{+0.013}$$ 0.92 4 − 0.016 + 0.013 , limited by detectable leakage errors. When correcting for these errors, the fidelity is $$0.97{6}_{-0.016}^{+0.014}$$ 0.97 6 − 0.016 + 0.014 . We show that the second-scale entanglement lifetimes are limited solely by these errors, providing opportunities for research in quantum-enhanced metrology 7,13 , ultracold chemistry 14 and the use of rotational states in quantum simulation, quantum computation and as quantum memories. The extension of precise quantum control to complex molecular systems will enable their additional degrees of freedom to be exploited across many domains of quantum science 15–17 .

DOI
10.1038/s41586-024-08365-1

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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.

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Abstract Realizing quantum control and entanglement of particles is crucial for advancing both quantum technologies and fundamental science. Substantial developments in this domain have been achieved in a variety of systems 1–5 . In this context, ultracold polar molecules offer new and unique opportunities because of their more complex internal structure associated with vibration and rotation, coupled with the existence of long-range interactions 6,7 . However, the same properties make molecules highly sensitive to their environment 8–10 , affecting their coherence and utility in some applications. Here we show that by engineering an exceptionally controlled environment using rotationally magic 11,12 optical tweezers, we can achieve long-lived entanglement between pairs of molecules using detectable hertz-scale interactions. We prepare two-molecule Bell states with fidelity 0.924−0.016+0.0130.92{4}_{-0.016}^{+0.013}0.924−0.016+0.013​ 0.92 4 − 0.016 + 0.013 , limited by detectable leakage errors. When correcting for these errors, the fidelity is 0.976−0.016+0.0140.97{6}_{-0.016}^{+0.014}0.976−0.016+0.014​ 0.97 6 − 0.016 + 0.014 . We show that the second-scale entanglement lifetimes are limited solely by these errors, providing opportunities for research in quantum-enhanced metrology 7,13 , ultracold chemistry 14 and the use of rotational states in quantum simulation, quantum computation and as quantum memories. The extension of precise quantum control to complex molecular systems will enable their additional degrees of freedom to be exploited across many domains of quantum science 15–17 .
Rotational states of ultracold polar molecules possess long lifetimes, microwave-domain coupling, and tunable dipolar interactions. The availability of numerous rotational states has inspired many applications, including simulating quantum magnetism, encoding high-dimensional qudits and generating large synthetic dimensions. However, engineering the coherent superpositions of multiple rotational states needed for these applications is difficult owing to strong differential light shifts. Here, we overcome this challenge using individual molecules confined in near-magic wavelength optical tweezers. Through precision Ramsey spectroscopy, we find the exact magic wavelengths and sensitivities to detuning errors for multiple rotational state superpositions. We find for traps polarised parallel to the quantisation axis, the magic wavelengths are closely clustered enabling long-lived coherence across multiple rotational states simultaneously. Using a generalised Ramsey sequence, we demonstrate second-scale coherent spin-1 dynamics encoded in three rotational states and perform multiparameter estimation. With modest experimental improvements, we predict second-scale coherence across ten rotational states is achievable.
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.
Polar molecules are a promising platform for quantum-enhanced sensing and precision tests of fundamental physics, owing to their strong long-range dipolar interactions, broad sensitivity to electromagnetic fields, and sensitivity to potential physics beyond the Standard Model. However, the creation of metrologically useful entangled states in molecular systems has remained elusive. Here, we report the first observation of a class of metrologically useful entangled states - spin-squeezed states - in polar CaF molecules trapped in an optical tweezer array. The spin degree of freedom is encoded in rotational levels which are directly coupled by dipolar exchange interactions. By harnessing appropriate dynamical decoupling schemes we observe up to 3.0(3)dB of metrological gain, (2.2(3)dB without measurement correction) from direct exchange interactions. Using Floquet engineering, we further realize richer Hamiltonians that preserve spin squeezing while enabling the development of longer-range quantum correlations. Using site- and spin-resolved measurements we demonstrate that these entangled states enhance sensitivity to both homogeneous and spatially varying fields, and reveal strong non-classical correlations, including bipartite entanglement and Einstein-Podolsky-Rosen steering. Finally, we transfer the spin-squeezed states into long-lived and non-interacting hyperfine states, where the metrological enhancement persists for up to 100ms. Our results establish molecular optical tweezer arrays as a scalable platform for generating, controlling, characterizing, and storing entangled states of molecules, opening new opportunities for quantum-enhanced sensing and precision tests of fundamental physics.
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.
Abstract Ultracold polar molecules combine a rich structure of long-lived internal states with access to controllable long-range anisotropic dipole–dipole interactions. In particular, the rotational states of polar molecules confined in optical tweezers or optical lattices may be used to encode interacting qubits for quantum computation or pseudo-spins for simulating quantum magnetism. As with all quantum platforms, the engineering of robust coherent superpositions of states is vital. However, for optically trapped molecules, the coherence time between rotational states is typically limited by inhomogeneous differential light shifts. Here we demonstrate a rotationally magic optical trap for 87 Rb 133 Cs molecules that supports a Ramsey coherence time of 0.78(4) s in the absence of dipole–dipole interactions. This is estimated to extend to >1.4 s at the 95% confidence level using a single spin-echo pulse. In our trap, dipolar interactions become the dominant mechanism by which Ramsey contrast is lost for superpositions that generate oscillating dipoles. By changing the states forming the superposition, we tune the effective dipole moment and show that the coherence time is inversely proportional to the strength of the dipolar interaction. Our work unlocks the full potential of the rotational degree of freedom in molecules for quantum computation and quantum simulation.
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.