3D Magneto-Optical Trap of Yttrium Monoxide

Blue-Detuned Magneto-optical Trap of CaF Molecules

A key method to produce trapped and laser-cooled molecules is the magneto-optical trap (MOT), which is conventionally created using light red detuned from an optical transition. In this work, we report a MOT for CaF molecules created using blue-detuned light. The blue-detuned MOT (BDM) achieves temperatures well below the Doppler limit and provides the highest densities and phase-space densities reported to date in CaF MOTs. Our results suggest that BDMs are likely achievable in many relatively light molecules including polyatomic ones, but our measurements suggest that BDMs will be challenging to realize in substantially heavier molecules due to sub-mK trap depths. In addition to record temperatures and densities, we find that the BDM substantially simplifies and enhances the loading of molecules into optical tweezer arrays, which are a promising platform for quantum simulation and quantum information processing. Notably, the BDM reduces molecular number requirements ninefold compared to a conventional red-detuned MOT, while not requiring additional hardware. Our work therefore substantially simplifies preparing large-scale molecular tweezer arrays, which are a novel platform for simulation of quantum many-body dynamics and quantum information processing with molecular qubits.

Imaging Rovibrational Excitation of Scattered YO Molecules in Inelastic Collisions with Kr and Ne

Energy transfer between atoms and molecules is fundamental to many physical and chemical processes, and understanding the mechanisms and outcomes of energy transfer is crucial for various applications in physics and chemistry. Here, the rovibrational excitation of YO(X 2Σ+) molecules with the collision of Kr and Ne has been studied in the laser-ablation crossed beam and time-sliced ion velocity map imaging setup in combination with the resonance enhanced multiphoton ionization scheme. Significant changes in the angular distribution for different rovibrational excitations of YO molecules are observed with the collision of Kr. The sharp forward distribution for low rovibrational excitation of YO(v' = 0, 1) molecules suggest that the weak attractive potential between Kr and YO is dominant at large impact parameters. Comparatively, the strong sideway distribution for highly rovibrationally excited YO(v' = 1, 2, 3, and 5) is due to rainbow scattering from the stronger attractive potential of Kr···YO at relatively small impact parameters. The more isotropic angular distribution in the highly rovibrationally excited YO(v' = 11) indicates the formation of a short-lived complex. A change in the angular distribution of scattered YO with different rovibrational excitations was also observed in the collisions of Ne. For YO as a heteronuclear diatomic molecule, collisions of the Y- and the O-end of YO with rare gases would affect the contribution of inelastic processes at different impact parameters.

High Density Loading and Collisional Loss of Laser-Cooled Molecules in an Optical Trap

We report optical trapping of laser-cooled molecules at sufficient density to observe molecule-molecule collisions for the first time in a bulk gas. SrF molecules from a red-detuned magneto-optical trap (MOT) are compressed and cooled in a blue-detuned MOT. Roughly 30% of these molecules are loaded into an optical dipole trap with peak number density n_{0}≈3×10^{10}  cm^{-3} and temperature T≈40  μK. We observe two-body loss with rate coefficient β=2.7_{-0.8}^{+1.2}×10^{-10}  cm^{3} s^{-1}. Achieving this density and temperature opens a path to evaporative cooling towards quantum degeneracy of laser-cooled molecules.

Numerical Equivalence of Diabatic and Adiabatic Representations in Diatomic Molecules

The (time-independent) Schrödinger equation for atomistic systems is solved by using the adiabatic potential energy curves (PECs) and the associated adiabatic approximation. In cases where interactions between electronic states become important, the associated nonadiabatic effects are taken into account via derivative couplings (DDRs), also known as nonadiabatic couplings (NACs). For diatomic molecules, the corresponding PECs in the adiabatic representation are characterized by avoided crossings. The alternative to the adiabatic approach is the diabatic representation obtained via a unitary transformation of the adiabatic states by minimizing the DDRs. For diatomics, the diabatic representation has zero DDR and nondiagonal diabatic couplings ensue. The two representations are fully equivalent and so should be the rovibronic energies and wave functions, which result from the solution of the corresponding Schrödinger equations. We demonstrate (for the first time) the numerical equivalence between the adiabatic and diabatic rovibronic calculations of diatomic molecules using the ab initio curves of yttrium oxide (YO) and carbon monohydride (CH) as examples of two-state systems, where YO is characterized by a strong NAC, while CH has a strong diabatic coupling. Rovibronic energies and wave functions are computed using a new diabatic module implemented in the variational rovibronic code Duo. We show that it is important to include both the diagonal Born-Oppenheimer correction and nondiagonal DDRs. We also show that the convergence of the vibronic energy calculations can strongly depend on the representation of nuclear motion used and that no one representation is best in all cases.

Entanglement Generation of Polar Molecules via Deep Reinforcement Learning

Polar molecules are a promising platform for achieving scalable quantum information processing because of their long-range electric dipole-dipole interactions. Here, we take the coupled ultracold CaF molecules in an external electric field with gradient as qubits and concentrate on the creation of intermolecular entanglement with the method of deep reinforcement learning (RL). After sufficient training episodes, the educated RL agents can discover optimal time-dependent control fields that steer the molecular systems from separate states to two-qubit and three-qubit entangled states with high fidelities. We analyze the fidelities and the negativities (characterizing entanglement) of the generated states as a function of training episodes. Moreover, we present the population dynamics of the molecular systems under the influence of control fields discovered by the agents. Compared with the schemes for creating molecular entangled states based on optimal control theory, some conditions (e.g., molecular spacing and electric field gradient) adopted in this work are more feasible in the experiment. Our results demonstrate the potential of machine learning to effectively solve quantum control problems in polar molecular systems.

Structural and electronic trends of optical cycling centers in polyatomic molecules revealed by microwave spectroscopy of MgCCH, CaCCH, and SrCCH

The unique optical cycling efficiency of alkaline earth metal-ligand molecules has enabled significant advances in polyatomic laser cooling and trapping. Rotational spectroscopy is an ideal tool for probing the molecular properties that underpin optical cycling, thereby elucidating the design principles for expanding the chemical diversity and scope of these platforms for quantum science. We present a comprehensive study of the structure and electronic properties in alkaline earth metal acetylides with high-resolution microwave spectra of 17 isotopologues of MgCCH, CaCCH, and SrCCH in their 2Σ+ ground electronic states. The precise semiexperimental equilibrium geometry of each species has been derived by correcting the measured rotational constants for electronic and zero-point vibrational contributions calculated with high-level quantum chemistry methods. The well-resolved hyperfine structure associated with the 1,2H, 13C, and metal nuclear spins provides further information on the distribution and hybridization of the metal-centered, optically active unpaired electron. Together, these measurements allow us to correlate trends in chemical bonding and structure with the electronic properties that promote efficient optical cycling essential to next-generation experiments in precision measurement and quantum control of complex polyatomic molecules.

Intensity-Borrowing Mechanisms Pertinent to Laser Cooling of Linear Polyatomic Molecules

A study of the intensity-borrowing mechanisms important to optical cycling transitions in laser-coolable polyatomic molecules arising from non-adiabatic coupling, contributions beyond the Franck-Condon approximation, and Fermi resonances is reported. It has been shown to be necessary to include non-adiabatic coupling to obtain computational accuracy that is sufficient to be useful for laser cooling of molecules. The predicted vibronic branching ratios using perturbation theory based on the non-adiabatic mechanisms have been demonstrated to agree well with those obtained from variational discrete variable representation calculations for representative molecules including CaOH, SrOH, and YbOH. The electron-correlation and basis-set effects on the calculated transition properties, including the vibronic coupling constants, the spin-orbit coupling matrix elements, and the transition dipole moments, and on the calculated branching ratios have been thoroughly studied. The vibronic branching ratios predicted using the present methodologies demonstrate that RaOH is a promising radioactive molecule candidate for laser cooling.

Theoretical Investigation of Spectroscopic Properties of the Alkaline-Earth-Metal Monohydrides toward Laser Cooling and Magneto-Optical Trapping

Alkaline-earth-metal monohydrides MH (M = Be, Mg, Ca, Sr, Ba) have long been regarded as promising candidates toward laser cooling and trapping; however, their rich internal level structures that are amenable to magneto-optical trapping have not been completely explored. Here, we first systematically evaluated Franck-Condon factors of these alkaline-earth-metal monohydrides in the A²Π_1/2 ← X²Σ⁺ transition, exploiting three respective methods (the Morse potential, the closed-form approximation, and the Rydberg-Klein-Rees method). The effective Hamiltonian matrix was introduced for MgH, CaH, SrH, and BaH individually in order to figure out their molecular hyperfine structures of X²Σ⁺, the transition wavelengths in the vacuum, and hyperfine branching ratios of A²Π_1/2(J' = 1/2,+) ← X²Σ⁺(N = 1,-), followed by possible sideband modulation proposals to address all hyperfine manifolds. Lastly, the Zeeman energy level structures and associated magnetic g factors of the ground state X²Σ⁺(N = 1,-) were also presented. Our theoretical results here not only shed more light on the molecular spectroscopy of alkaline-earth-metal monohydrides toward laser cooling and magneto-optical trapping but also can contribute to research in molecular collisions involving few-atom molecular systems, spectral analysis in astrophysics and astrochemistry, and even precision measurement of fundamental constants such as the quest for nonzero detection of electron's electric dipole moment.

Blue-Detuned Magneto-optical Trap of Molecules

Direct laser cooling of molecules has reached a phase-space density exceeding 10^{-6} in optical traps but with rather small molecular numbers. To progress toward quantum degeneracy, a mechanism that combines sub-Doppler cooling and magneto-optical trapping would facilitate near unity transfer of ultracold molecules from the magneto-optical trap (MOT) to a conservative optical trap. Using the unique energy level structure of YO molecules, we demonstrate the first blue-detuned MOT for molecules that is optimized for both gray-molasses sub-Doppler cooling and relatively strong trapping forces. This first sub-Doppler molecular MOT provides an increase of phase-space density by 2 orders of magnitude over any previously reported molecular MOT.

Robust Nuclear Spin Entanglement via Dipolar Interactions in Polar Molecules

We propose a general protocol for on-demand generation of robust entangled states of nuclear and/or electron spins of ultracold ^{1}Σ and ^{2}Σ polar molecules using electric dipolar interactions. By encoding a spin-1/2 degree of freedom in a combined set of spin and rotational molecular levels, we theoretically demonstrate the emergence of effective spin-spin interactions of the Ising and XXZ forms, enabled by efficient magnetic control over electric dipolar interactions. We show how to use these interactions to create long-lived cluster and squeezed spin states.

Dipolar physics: a review of experiments with magnetic quantum gases

Since the achievement of quantum degeneracy in gases of chromium atoms in 2004, the experimental investigation of ultracold gases made of highly magnetic atoms has blossomed. The field has yielded the observation of many unprecedented phenomena, in particular those in which long-range and anisotropic dipole-dipole interactions (DDIs) play a crucial role. In this review, we aim to present the aspects of the magnetic quantum-gas platform that make it unique for exploring ultracold and quantum physics as well as to give a thorough overview of experimental achievements. Highly magnetic atoms distinguish themselves by the fact that their electronic ground-state configuration possesses a large electronic total angular momentum. This results in a large magnetic moment and a rich electronic transition spectrum. Such transitions are useful for cooling, trapping, and manipulating these atoms. The complex atomic structure and large dipolar moments of these atoms also lead to a dense spectrum of resonances in their two-body scattering behaviour. These resonances can be used to control the interatomic interactions and, in particular, the relative importance of contact over dipolar interactions. These features provide exquisite control knobs for exploring the few- and many-body physics of dipolar quantum gases. The study of dipolar effects in magnetic quantum gases has covered various few-body phenomena that are based on elastic and inelastic anisotropic scattering. Various many-body effects have also been demonstrated. These affect both the shape, stability, dynamics, and excitations of fully polarised repulsive Bose or Fermi gases. Beyond the mean-field instability, strong dipolar interactions competing with slightly weaker contact interactions between magnetic bosons yield new quantum-stabilised states, among which are self-bound droplets, droplet assemblies, and supersolids. Dipolar interactions also deeply affect the physics of atomic gases with an internal degree of freedom as these interactions intrinsically couple spin and atomic motion. Finally, long-range dipolar interactions can stabilise strongly correlated excited states of 1D gases and also impact the physics of lattice-confined systems, both at the spin-polarised level (Hubbard models with off-site interactions) and at the spinful level (XYZ models). In the present manuscript, we aim to provide an extensive overview of the various related experimental achievements up to the present.

Pathway toward Optical Cycling and Laser Cooling of Functionalized Arenes

Rapid and repeated photon cycling has enabled precision metrology and the development of quantum information systems using atoms and simple molecules. Extending optical cycling to structurally complex molecules would provide new capabilities in these areas, as well as in ultracold chemistry. Increased molecular complexity, however, makes realizing closed optical transitions more difficult. Building on already established strong optical cycling of diatomic, linear triatomic, and symmetric top molecules, recent work has pointed the way to cycling of larger molecules, including phenoxides. The paradigm for these systems is an optical cycling center bonded to a molecular ligand. Theory has suggested that cycling may be extended to even larger ligands, like naphthalene, pyrene, and coronene. Herein, we study optical excitation and fluorescent vibrational branching of CaO-[Formula: see text], SrO-[Formula: see text], and CaO-[Formula: see text] and find only weak decay to excited vibrational states, indicating a promising path to full quantum control and laser cooling of large arene-based molecules.

Seconds-Scale Coherence on Nuclear Spin Transitions of Ultracold Polar Molecules in 3D Optical Lattices

Ultracold polar molecules (UPMs) are emerging as a novel and powerful platform for fundamental applications in quantum science. Here, we report characterization of the coherence between nuclear spin levels of ultracold ground-state sodium-rubidium molecules loaded into a 3D optical lattice with a nearly photon scattering limited trapping lifetime of 9(1) seconds. After identifying and compensating the main sources of decoherence, we achieve a maximum nuclear spin coherence time of T_{2}^{*}=3.3(6)  s with two-photon Ramsey spectroscopy. Furthermore, based on the understanding of the main factor limiting the coherence of the two-photon Rabi transition, we obtain a Rabi line shape with linewidth below 0.8 Hz. The simultaneous realization of long lifetime and coherence time, and ultrahigh spectroscopic resolution in our system unveils the great potentials of Ultracold polar molecules in quantum simulation, computation, and metrology.

Magneto-optical trapping and sub-Doppler cooling of a polyatomic molecule

Laser cooling and trapping^1,2, and magneto-optical trapping methods in particular², have enabled groundbreaking advances in science, including Bose-Einstein condensation^3-5, quantum computation with neutral atoms^6,7 and high-precision optical clocks⁸. Recently, magneto-optical traps (MOTs) of diatomic molecules have been demonstrated^9-12, providing access to research in quantum simulation¹³ and searches for physics beyond the standard model¹⁴. Compared with diatomic molecules, polyatomic molecules have distinct rotational and vibrational degrees of freedom that promise a variety of transformational possibilities. For example, ultracold polyatomic molecules would be uniquely suited to applications in quantum computation and simulation^15-17, ultracold collisions¹⁸, quantum chemistry¹⁹ and beyond-the-standard-model searches^20,21. However, the complexity of these molecules has so far precluded the realization of MOTs for polyatomic species. Here we demonstrate magneto-optical trapping of a polyatomic molecule, calcium monohydroxide (CaOH). After trapping, the molecules are laser cooled in a blue-detuned optical molasses to a temperature of 110 μK, which is below the Doppler cooling limit. The temperatures and densities achieved here make CaOH a viable candidate for a wide variety of quantum science applications, including quantum simulation and computation using optical tweezer arrays^15,17,22,23. This work also suggests that laser cooling and magneto-optical trapping of many other polyatomic species^24-27 will be both feasible and practical.

Molecular Laser Cooling in a Dynamically Tunable Repulsive Optical Trap

Recent work with laser-cooled molecules in attractive optical traps has shown that the differential ac Stark shifts arising from the trap light itself can become problematic, limiting collisional shielding efficiencies, rotational coherence times, and laser-cooling temperatures. In this Letter, we explore trapping and laser cooling of CaF molecules in a ring-shaped repulsive optical trap. The observed dependences of loss rates on temperature and barrier height show characteristic behavior of repulsive traps and indicate strongly suppressed average ac Stark shifts. Within the trap, we find that Λ-enhanced gray molasses cooling is effective, producing similar minimum temperatures as those obtained in free space. By combining in-trap laser cooling with dynamical reshaping of the trap, we also present a method that allows highly efficient and rapid transfer from molecular magneto-optical traps into conventional attractive optical traps, which has been an outstanding challenge for experiments to date. Notably, our method could allow nearly lossless transfer over millisecond timescales.

High Phase-Space Density of Laser-Cooled Molecules in an Optical Lattice

We report laser cooling and trapping of yttrium monoxide molecules in an optical lattice. We show that gray molasses cooling remains exceptionally efficient for yttrium monoxide molecules inside the lattice with a molecule temperature as low as 6.1(6)  μK. This approach has produced a trapped sample of 1200 molecules, with a peak spatial density of ∼1.2×10^{10}  cm^{-3}, and a peak phase-space density of ∼3.1×10^{-6}. By ramping down the lattice depth, we cool the molecules further to 1.0(2)  μK, 20 times colder than previously reported for laser-cooled molecules in a trap.

Zeeman-Sisyphus Deceleration of Molecular Beams

We present a robust, continuous molecular decelerator that employs high magnetic fields and few optical pumping steps. CaOH molecules are slowed, accumulating at low velocities in a range sufficient for loading both magnetic and magneto-optical traps. During the slowing, the molecules scatter only seven photons, removing around 8 K of energy. Because large energies can be removed with only a few spontaneous radiative decays, this method can in principle be applied to nearly any paramagnetic atomic or molecular species, opening a general path to trapping of complex molecules.

Rapid prototyping of grating magneto-optical traps using a focused ion beam

We have developed a rapid prototyping approach for creating custom grating magneto-optical traps using a dual-beam system combining a focused ion beam and a scanning electron microscope. With this approach we have created both one- and two-dimensional gratings of up to 400 µm × 400 µm in size with structure features down to 100 nm, periods of 620 nm, adjustable aspect ratios (ridge width : depth ∼ 1 : 0.3 to 1 : 1.4) and sidewall angles up to 71°. The depth and period of these gratings make them suitable for holographic trapping and cooling of neutral ytterbium on the ¹S₀ → ¹P₁ 399 nm transition. Optical testing of the gratings at this wavelength has demonstrated a total first order diffraction of 90% of the reflected light. This work therefore represents a fast, high resolution, programmable and maskless alternative to current photo and electron beam lithography-based procedures and provides a time efficient process for prototyping of small period, high aspect ratio grating magneto-optical traps and other high resolution structures.

Deceleration and Trapping of SrF Molecules

We report on the electrostatic trapping of neutral SrF molecules. The molecules are captured from a cryogenic buffer-gas beam source into the moving traps of a 4.5-m-long traveling-wave Stark decelerator. The SrF molecules in X^{2}Σ^{+}(v=0,N=1) state are brought to rest as the velocity of the moving traps is gradually reduced from 190  m/s to zero. The molecules are held for up to 50 ms in multiple electric traps of the decelerator. The trapped packets have a volume (FWHM) of 1  mm^{3} and a velocity spread of 5(1)  m/s, which corresponds to a temperature of 60(20) mK. Our result demonstrates a factor 3 increase in the molecular mass that has been Stark decelerated and trapped. Heavy molecules (mass>100  amu) offer a highly increased sensitivity to probe physics beyond the standard model. This work significantly extends the species of neutral molecules of which slow beams can be created for collision studies, precision measurement, and trapping experiments.

Polarization Enhanced Deep Optical Dipole Trapping of Λ-Cooled Polar Molecules

We demonstrate loading of SrF molecules into an optical dipole trap (ODT) via in-trap Λ-enhanced gray molasses cooling. We find that this cooling can be optimized by a proper choice of relative ODT and cooling beam polarizations. In this optimized configuration, we observe molecules with temperatures as low as 14(1)  μK in traps with depths up to 570  μK. With optimized parameters, we transfer ∼5% of molecules from our radio-frequency magneto-optical trap into the ODT, at a density of ∼2×10^{9}  cm^{-3}, a phase space density of ∼2×10^{-7}, and with a trap lifetime of ∼1  s.

Optimizing pulsed-laser ablation production of AlCl molecules for laser cooling

Aluminum monochloride (AlCl) has been proposed as a promising candidate for laser cooling to ultracold temperatures, and recent spectroscopy results support this prediction. It is challenging to produce large numbers of AlCl molecules because it is a highly reactive open-shell molecule and must be generated in situ. Here we show that pulsed-laser ablation of stable, non-toxic mixtures of Al with alkali or alkaline earth chlorides, denoted XCl_n, can provide a robust and reliable source of cold AlCl molecules. Both the chemical identity of XCl_n and the Al : XCl_n molar ratio are varied, and the yield of AlCl is monitored using absorption spectroscopy in a cryogenic gas. For KCl, the production of Al and K atoms was also monitored. We model the AlCl production in the limits of nonequilibrium recombination dominated by first-encounter events. The non-equilibrium model is in agreement with the data and also reproduces the observed trend with different XCl_n precursors. We find that AlCl production is limited by the solid-state densities of Al and Cl atoms and the recondensation of Al atoms in the ablation plume. We suggest future directions for optimizing the production of cold AlCl molecules using laser ablation.

Rotational Coherence Times of Polar Molecules in Optical Tweezers

Qubit coherence times are critical to the performance of any robust quantum computing platform. For quantum information processing using arrays of polar molecules, a key performance parameter is the molecular rotational coherence time. We report a 93(7) ms coherence time for rotational state qubits of laser cooled CaF molecules in optical tweezer traps, over an order of magnitude longer than previous systems. Inhomogeneous broadening due to the differential polarizability between the qubit states is suppressed by tuning the tweezer polarization and applied magnetic field to a "magic" angle. The coherence time is limited by the residual differential polarizability, implying improvement with further cooling. A single spin-echo pulse is able to extend the coherence time to nearly half a second. The measured coherence times demonstrate the potential of polar molecules as high fidelity qubits.

Accurate prediction and measurement of vibronic branching ratios for laser cooling linear polyatomic molecules

We report a generally applicable computational and experimental approach to determine vibronic branching ratios in linear polyatomic molecules to the 10^-5 level, including for nominally symmetry-forbidden transitions. These methods are demonstrated in CaOH and YbOH, showing approximately two orders of magnitude improved sensitivity compared with the previous state of the art. Knowledge of branching ratios at this level is needed for the successful deep laser cooling of a broad range of molecular species.

Quantum Spin State Selectivity and Magnetic Tuning of Ultracold Chemical Reactions of Triplet Alkali-Metal Dimers with Alkali-Metal Atoms

We demonstrate that it is possible to efficiently control ultracold chemical reactions of alkali-metal atoms colliding with open-shell alkali-metal dimers in their metastable triplet states by choosing the internal hyperfine and rovibrational states of the reactants as well as by inducing magnetic Feshbach resonances with an external magnetic field. We base these conclusions on coupled-channel statistical calculations that include the effects of hyperfine contact and magnetic-field-induced Zeeman interactions on ultracold chemical reactions of hyperfine-resolved ground-state Na and the triplet NaLi(a^{3}Σ^{+}) producing singlet Na_{2}(^{1}Σ_{g}^{+}) and a Li atom. We find that the reaction rates are sensitive to the initial hyperfine states of the reactants. The chemical reaction of fully spin-polarized, high-spin states of rotationless NaLi(a^{3}Σ^{+},v=0,N=0) molecules with fully spin-polarized Na is suppressed by a factor of 10-100 compared to that of unpolarized reactants. We interpret these findings within the adiabatic state model, which treats the reaction as a sequence of nonadiabatic transitions between the initial nonreactive high-spin state and the final low-spin states of the reaction complex. In addition, we show that magnetic Feshbach resonances can similarly change reaction rate coefficients by several orders of magnitude. Some of these resonances are due to resonant trimer bound states dissociating to the N=2 rotational state of NaLi(a^{3}Σ^{+},v=0) and would thus exist in systems without hyperfine interactions.

Observation of microwave shielding of ultracold molecules

Harnessing the potential wide-ranging quantum science applications of molecules will require control of their interactions. Here, we used microwave radiation to directly engineer and tune the interaction potentials between ultracold calcium monofluoride (CaF) molecules. By merging two optical tweezers, each containing a single molecule, we probed collisions in three dimensions. The correct combination of microwave frequency and power created an effective repulsive shield, which suppressed the inelastic loss rate by a factor of six, in agreement with theoretical calculations. The demonstrated microwave shielding shows a general route to the creation of long-lived, dense samples of ultracold polar molecules and evaporative cooling.

An ion trap apparatus with high optical access in multiple directions

Optical controls provided by lasers are the most important and essential techniques in trapped ion and cold atom systems. It is crucial to increase the optical accessibility of the setup to enhance these optical capabilities. Here, we present the design and construction of a new segmented-blade ion trap integrated with a compact glass vacuum cell, in place of the conventional bulky metal vacuum chamber. The distance between the ion and four outside surfaces of the glass cell is 15 mm, which enables us to install four high-numerical-aperture (NA) lenses (with two NA ⩽ 0.32 lenses and two NA ⩽ 0.66 lenses) in two orthogonal transverse directions, while leaving enough space for laser beams in the oblique and longitudinal directions. The high optical accessibility in multiple directions allows the application of small laser spots for addressable Raman operations, programmable optical tweezer arrays, and efficient fluorescence collection simultaneously. We have successfully loaded and cooled a string of ¹⁷⁴Yb⁺ and ¹⁷¹Yb⁺ ions in the trap, which verifies the trapping stability. This compact high-optical-access trap setup not only can be used as an extendable module for quantum information processing but also facilitates experimental studies on quantum chemistry in a cold hybrid ion-atom system.

Quantum-State Control and Manipulation of Paramagnetic Molecules with Magnetic Fields

Since external magnetic fields were first employed to deflect paramagnetic atoms in 1921, a range of magnetic field-based methods have been introduced to state-selectively manipulate paramagnetic species. These methods include magnetic guides, which selectively filter paramagnetic species from all other components of a beam, and magnetic traps, where paramagnetic species can be spatially confined for extended periods of time. However, many of these techniques were developed for atomic-rather than molecular-paramagnetic species. It has proven challenging to apply some of these experimental methods developed for atoms to paramagnetic molecules. Thanks to the emergence of new experimental approaches and new combinations of existing techniques, the past decade has seen significant progress toward the manipulation and control of paramagnetic molecules. This review identifies the key methods that have been implemented for the state-selective manipulation of paramagnetic molecules-discussing the motivation, state of the art, and future prospects of the field. Key applications include the ability to control chemical interactions, undertake precise spectroscopic measurements, and challenge our understanding of chemical reactivity at a fundamental level.

Entanglement via rotational blockade of MgF molecules in a magic potential

Diatomic polar molecules are one of the most promising platforms of quantum computing due to their rich internal states and large electric dipole moments. Here, we propose entangling rotational states of MgF molecules in an optical tweezer array via strong electric dipole-dipole interactions. We employ two rotational states with the projection quantum number of the total angular momentum MF = 0 to maximize the dipole-dipole interaction with a given separation distance. The splitting of 1.27 kHz between two entangled states is predicted for MgF molecules separated by 1 μm. The resolution of the entangled states can be achieved in a magic optical potential where the rotational states have the same trap frequencies. The magic potential can be formed by tuning the angle between the molecules' quantization axis and the linear polarization of trapping light to a "magic angle". We calculate the magic angle for MgF molecules under reasonable experimental conditions and obtain that the trap frequencies of the two involved states can be matched within a few 10s of Hz. By establishing an entanglement scheme for the molecules, our results provide a first step towards quantum computing using MgF molecules.

Infrared Comb Spectroscopy of Buffer-Gas-Cooled Molecules: Toward Absolute Frequency Metrology of Cold Acetylene

We review the recent developments in precision ro-vibrational spectroscopy of buffer-gas-cooled neutral molecules, obtained using infrared frequency combs either as direct probe sources or as ultra-accurate optical rulers. In particular, we show how coherent broadband spectroscopy of complex molecules especially benefits from drastic simplification of the spectra brought about by cooling of internal temperatures. Moreover, cooling the translational motion allows longer light-molecule interaction times and hence reduced transit-time broadening effects, crucial for high-precision spectroscopy on simple molecules. In this respect, we report on the progress of absolute frequency metrology experiments with buffer-gas-cooled molecules, focusing on the advanced technologies that led to record measurements with acetylene. Finally, we briefly discuss the prospects for further improving the ultimate accuracy of the spectroscopic frequency measurement.

Magnetic properties and quench dynamics of two interacting ultracold molecules in a trap

We theoretically investigate the magnetic properties and nonequilibrium dynamics of two interacting ultracold polar and paramagnetic molecules in a one-dimensional harmonic trap in external electric and magnetic fields. The molecules interact via a multichannel two-body contact potential, incorporating the short-range anisotropy of intermolecular interactions. We show that various magnetization states arise from the interplay of the molecular interactions, electronic spins, dipole moments, rotational structures, external fields, and spin-rotation coupling. The rich magnetization diagrams depend primarily on the anisotropy of the intermolecular interaction and the spin-rotation coupling. These specific molecular properties are challenging to calculate or measure. Therefore, we propose the quench dynamics experiments for extracting them from observing the time evolution of the analyzed system. Our results indicate the possibility of controlling the molecular few-body magnetization with the external electric field and pave the way towards studying the magnetization of ultracold molecules trapped in optical tweezers or optical lattices and their application in quantum simulation of molecular multichannel many-body Hamiltonians and quantum information storing.

Enhancing Dipolar Interactions between Molecules Using State-Dependent Optical Tweezer Traps

We show how state-dependent optical potentials can be used to trap a pair of molecules in different internal states at a separation much smaller than the wavelength of the trapping light. This close spacing greatly enhances the dipole-dipole interaction and we show how it can be used to implement two-qubit gates between molecules that are 100 times faster than existing protocols and than rotational coherence times already demonstrated. We analyze complications due to hyperfine structure, tensor light shifts, photon scattering, and collisional loss, and conclude that none is a barrier to implementing the scheme.

Towards accurate prediction for laser-coolable molecules: relativistic coupled-cluster calculations for yttrium monoxide and prospects for improving its laser cooling efficiencies

Benchmark relativistic coupled-cluster calculations for yttrium monoxide (YO) with accurate treatment of relativistic and electron correlation effects are reported. The spin-orbit mixing of 2Π and 2Δ is found to be an order of magnitude smaller than previously reported in the literature. Together with the measurement of the lifetime of the A'2Δ3/2 state, it implies an enhanced capability of a narrow-line cooling scheme to bring YO to sub-recoil temperature. The computed electronic transition properties also support a four-photon scheme to close the leakage of the A2Π1/2 ↔ X2Σ1/2+ cycle through the A'2Δ3/2 state by repumping the A'2Δ3/2 state to the B2Σ1/2+ state, which subsequently decays back to X2Σ1/2+. Relativistic coupled-cluster methods, capable of providing accurate spectroscopic parameters that characterize the local potential curves and hence of providing accurate Franck-Condon factors, appear to be promising candidates for accurate calculation of properties for laser-coolable molecules.

Electron Electric Dipole Moment Searches Using Clock Transitions in Ultracold Molecules

Permanent electric dipole moments (EDMs) of fundamental particles such as the electron are signatures of parity and time-reversal violation occurring in physics beyond the standard model. EDM measurements probe new physics at energy scales well beyond the reach of present-day colliders. Recent advances in assembling molecules from ultracold atoms have opened up new opportunities for improving the reach of EDM experiments. However, the magnetic field sensitivity of such ultracold molecules means that new measurement techniques are needed before these opportunities can be fully exploited. We present a technique that takes advantage of magnetically insensitive hyperfine clock transitions in polar molecules, offering a way to improve both the precision and accuracy of EDM searches with ultracold assembled molecules.

Direct laser cooling of a symmetric top molecule

Ultracold polyatomic molecules have potentially wide-ranging applications in quantum simulation and computation, particle physics, and quantum chemistry. For atoms and small molecules, direct laser cooling has proven to be a powerful tool for quantum science in the ultracold regime. However, the feasibility of laser-cooling larger, nonlinear polyatomic molecules has remained unknown because of their complex structure. We laser-cooled the symmetric top molecule calcium monomethoxide (CaOCH3), reducing the temperature of ~104 molecules from 22 ± 1 millikelvin to 1.8 ± 0.7 millikelvin in one dimension and state-selectively cooling two nuclear spin isomers. These results demonstrate that the use of proper ro-vibronic transitions enables laser cooling of nonlinear molecules, thereby opening a path to efficient cooling of chiral molecules and, eventually, optical tweezer arrays of complex polyatomic species.

Toward Ultracold Organic Chemistry: Prospects of Laser Cooling Large Organic Molecules

Ultracold organic chemistry enables studies of reaction dynamics and mechanisms in the quantum regime. Access to ultracold molecules hinges on the ability to efficiently scatter multiple photons via quasi-closed cycling transitions. Optical cycling in polyatomic molecules is challenging due to their complex electronic structure. Using equation-of-motion coupled-cluster calculations, we demonstrate that an alkaline earth metal attached to various aromatic ligands (such as benzene, phenol, cyclopentadienyl, and pyrrolide) offers nearly closed cycling transitions with only a few additional repump lasers. We also show that aromatic ligands such as benzene can accommodate multiple cycling centers in various geometrical arrangements, opening new avenues in quantum information science, precision measurements, and ultracold chemistry.

Observation of Collisions between Two Ultracold Ground-State CaF Molecules

We measure inelastic collisions between ultracold CaF molecules by combining two optical tweezers, each containing a single molecule. We observe collisions between ^{2}Σ CaF molecules in the absolute ground state |X,v=0,N=0,F=0⟩, and in excited hyperfine and rotational states. In the absolute ground state, we find a two-body loss rate of 7(4)×10^{-11}  cm^{3}/s, which is below, but close to, the predicted universal loss rate.

Loss of Ultracold ^{87}Rb^{133}Cs Molecules via Optical Excitation of Long-Lived Two-Body Collision Complexes

We show that the lifetime of ultracold ground-state ^{87}Rb^{133}Cs molecules in an optical trap is limited by fast optical excitation of long-lived two-body collision complexes. We partially suppress this loss mechanism by applying square-wave modulation to the trap intensity, such that the molecules spend 75% of each modulation cycle in the dark. By varying the modulation frequency, we show that the lifetime of the collision complex is 0.53±0.06  ms in the dark. We find that the rate of optical excitation of the collision complex is 3_{-2}^{+4}×10^{3}  W^{-1} cm^{2} s^{-1} for λ=1550  nm, leading to a lifetime of <100  ns for typical trap intensities. These results explain the two-body loss observed in experiments on nonreactive bialkali molecules.

1D Magneto-Optical Trap of Polyatomic Molecules

We demonstrate a 1D magneto-optical trap of the polar free radical calcium monohydroxide (CaOH). A quasiclosed cycling transition is established to scatter ∼10^{3} photons per molecule, predominantly limited by interaction time. This enables radiative laser cooling of CaOH while compressing the molecular beam, leading to a significant increase in on axis beam brightness and reduction in temperature from 8.4 to 1.4 mK.

Long-Range N-N Bonding by Rydberg Electrons

By using high-level ab initio methods, we examine the nature of bonding between Rydberg electrons hosted by two four-coordinate nitrogen centers embedded in a hydrocarbon scaffold. The electronic structure of these species resembles that of diradicals, yet the diffuse nature of the orbitals hosting the unpaired electrons results in unusual features. The unpaired Rydberg electrons exhibit long-range bonding interactions, leading to stabilization of the singlet state (relative to the triplet) and a reduced number of effectively unpaired electrons. However, thermochemical gains due to through-space bonding are offset by strong Coulomb repulsion between positively charged nitrogen cores. The kinetic stability of these Rydberg diradicals may be controlled by a judicious choice of the molecular scaffold, suggesting possible strategies for their experimental characterization.

Two Cycling Centers in One Molecule: Communication by Through-Bond Interactions and Entanglement of the Unpaired Electrons

Many applications in quantum information science (QIS) rely on the ability to laser-cool molecules. The scope of applications can be expanded if laser-coolable molecules possess two or more cycling centers, i.e., moieties capable of scattering photons via multiple absorption-emission events. Here we employ the equation-of-motion coupled-cluster method for double electron attachment (EOM-DEA-CCSD) to study the electronic structure of hypermetallic molecules with two alkaline-earth metals connected by an acetylene linker. The electronic structure of the molecules is similar to that of two separated alkali metals; however, the interaction between the two electrons is weak and largely dominated by through-bond interactions. The communication between the two cycling centers is quantified by the extent of the entanglement of the two unpaired electrons associated with the two cycling centers. This contribution highlights the rich electronic structure of hypermetallic molecules that may advance various applications in QIS and beyond.

Long Rotational Coherence Times of Molecules in a Magnetic Trap

Polar molecules in superpositions of rotational states exhibit long-range dipolar interactions, but maintaining their coherence in a trapped sample is a challenge. We present calculations that show many laser-coolable molecules have convenient rotational transitions that are exceptionally insensitive to magnetic fields. We verify this experimentally for CaF where we find a transition with sensitivity below 5  Hz G^{-1} and use it to demonstrate a rotational coherence time of 6.4(8) ms in a magnetic trap. Simulations suggest it is feasible to extend this to more than 1 s using a smaller cloud in a biased magnetic trap.

Second-Scale Coherence Measured at the Quantum Projection Noise Limit with Hundreds of Molecular Ions

Cold molecules provide an excellent platform for quantum information, cold chemistry, and precision measurement. Certain molecules have enhanced sensitivity to beyond standard model physics, such as the electron's electric dipole moment (eEDM). Molecular ions are easily trappable and are therefore particularly attractive for precision measurements where sensitivity scales with interrogation time. Here, we demonstrate a spin precession measurement with second-scale coherence at the quantum projection noise (QPN) limit with hundreds of trapped molecular ions, chosen for their sensitivity to the eEDM rather than their amenability to state control and readout. Orientation-resolved resonant photodissociation allows us to simultaneously measure two quantum states with opposite eEDM sensitivity, reaching the QPN limit and fully exploiting the high count rate and long coherence.

Sub-Doppler Cooling and Compressed Trapping of YO Molecules at μK Temperatures

Complex molecular structure demands customized solutions to laser cooling by extending its general set of principles and practices. Compared with other laser-cooled molecules, yttrium monoxide (YO) exhibits a large electron-nucleus interaction, resulting in a dominant hyperfine interaction over the electron spin-rotation coupling. The YO ground state is thus comprised of two manifolds of closely spaced states, with one of them possessing a negligible Landé g factor. This unique energy level structure favors dual-frequency dc magneto-optical trapping (MOT) and gray molasses cooling (GMC). We report exceptionally robust cooling of YO at 4 μK over a wide range of laser intensity, detunings (one- and two-photon), and magnetic field. The magnetic insensitivity enables the spatial compression of the molecular cloud by alternating GMC and MOT under the continuous operation of the quadrupole magnetic field. A combination of these techniques produces a laser-cooled molecular sample with the highest phase space density in free space.

In search of molecular ions for optical cycling: a difficult road

Optical cycling, a continuous photon scattering off atoms or molecules, is the key tool in quantum information science.

Spectroscopy of YO from first principles

We report an ab initio study on the spectroscopy of the open-shell diatomic molecule yttrium oxide, YO. The study considers the six lowest doublet states, X2Σ+, A'2Δ, A2Π, B2Σ+, C2Π, D2Σ+, and a few higher-lying quartet states using high levels of electronic structure theory and accurate nuclear motion calculations. The coupled cluster singles, doubles, and perturbative triples, CCSD(T), and multireference configuration interaction (MRCI) methods are employed in conjunction with a relativistic pseudopotential on the yttrium atom and a series of correlation-consistent basis sets ranging in size from triple-ζ to quintuple-ζ quality. Core-valence correlation effects are taken into account and complete basis set limit extrapolation is performed for CCSD(T). Spin-orbit coupling is included through the use of both MRCI state-interaction with spin-orbit (SI-SO) approach and four-component relativistic equation-of-motion CCSD calculations. Using the ab initio data for bond lengths ranging from 1.0 to 2.5 Å, we compute 6 potential energy, 12 spin-orbit, 8 electronic angular momentum, 6 electric dipole moment and 12 transition dipole moment (4 parallel and 8 perpendicular) curves which provide a complete description of the spectroscopy of the system of six lowest doublet states. The Duo nuclear motion program is used to solve the coupled nuclear motion Schrödinger equation for these six electronic states. The spectra of 89Y16O simulated for different temperatures are compared with several available high resolution experimental studies; good agreement is found once minor adjustments are made to the electronic excitation energies.