CaF Molecules Research Articles

Raman Sideband Cooling of Molecules in an Optical Tweezer Array to the 3D Motional Ground State

Ultracold polar molecules are promising for quantum information processing and searches for physics beyond the standard model. Laser cooling to ultracold temperatures is an established technique for trapped diatomic and triatomic molecules. Further cooling of the molecules to near the motional ground state is crucial for reducing various dephasings in quantum and precision applications. In this work, we demonstrate Raman sideband cooling (RSC) of CaF molecules in optical tweezers to near their motional ground state, with average motional occupation quantum numbers of n¯x=0.16(12), n¯y=0.17(17) (radial directions), and n¯z=0.22(16) (axial direction), and a 3-D motional-ground-state probability of 54±18% of the molecules that survive the RSC. This process paves the way to increase molecular coherence times in optical tweezers for robust quantum computation and simulation applications. Published by the American Physical Society 2024

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.

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.

Shielding collisions of ultracold CaF molecules with static electric fields

Shielding collisions of ultracold CaF molecules with static electric fields

Bichromatic Imaging of Single Molecules in an Optical Tweezer Array.

We report on a novel bichromatic fluorescent imaging scheme for background-free detection of single CaF molecules trapped in an optical tweezer array. By collecting fluorescence on one optical transition while using another for laser cooling, we achieve an imaging fidelity of 97.7(2)% and a nondestructive detection fidelity of 95.5(6)%. Notably, these fidelities are achieved with a modest photon budget, suggesting that the method could be extended to more complex laser-coolable molecules with less favorable optical cycling properties. We also report on a framework and new methods to characterize various loss mechanisms that occur generally during fluorescent detection of trapped molecules, including two-photon decay and admixtures of higher excited states that are induced by the trapping light. In particular, we develop a novel method to dispersively measure transition matrix elements between electronically excited states. The method could also be used to measure arbitrarily small Franck-Condon factors between electronically excited states, which could significantly aid in ongoing efforts to laser cool complex polyatomic molecules.

Sticking Lifetime of Ultracold CaF Molecules in Triplet Interactions.

A six-dimensional potential energy surface is constructed for the spin-polarized triplet state of CaF-CaF by ab initio calculations at the CCSD(T) level of theory, followed by Gaussian process interpolation. The potential is utilized to calculate the density of states for this bialkaline-earth-halogen system where we find the value 0.038 μK-1, implying a mean resonance spacing of 26 μK in the collision complex. This value implies an associated Rice-Ramsperger-Kassel-Marcus lifetime of 1.8 μs, thus predicting long-lived complexes in collisions at ultracold temperatures.

Four-body singlet potential-energy surface for reactions of calcium monofluoride

A full six-dimensional Born-Oppenheimer singlet potential-energy surface is constructed for the reaction CaF $+$ CaF $\ensuremath{\rightarrow}\phantom{\rule{4pt}{0ex}}{\mathrm{CaF}}_{2} +$ Ca using a multireference configuration-interaction electronic structure calculation. The ab initio data thus calculated are interpolated by Gaussian process regression. The four-body potential-energy surface features one ${D}_{2h}$ global minimum and one ${C}_{s}$ local minimum, connected by a barrierless transition state that lends insight to the reaction mechanism. This surface is intended to be of use in understanding ultracold chemistry of CaF molecules.

Cryogenic buffer gas beams of AlF, CaF, MgF, YbF, Al, Ca, Yb and NO – a comparison

ABSTRACT Cryogenic buffer gas beams are central to many cold molecule experiments. Here, we use absorption and fluorescence spectroscopy to directly compare molecular beams of AlF, CaF, MgF and YbF molecules, produced by chemical reaction of laser ablated atoms with fluorine rich reagents. The beam brightness for AlF is measured as molecules per steradian per pulse in a single rotational state, comparable to an Al atomic beam produced in the same setup. The CaF, MgF and YbF beams show an order of magnitude lower brightness than AlF and far below the brightness of Ca and Yb beams. The addition of either or to the cell extinguishes the Al atomic beam, but has a minimal effect on the Ca and Yb beams. reacts more efficiently than , as a significantly lower flow rate is required to maximise the molecule production, which is particularly beneficial for long-term stability of the AlF beam. We use NO as a proxy for the reactant gas as it can be optically detected. We demonstrate that a cold, rotationally pure NO beam can be generated by laser desorption, thereby gaining insight into the dynamics of the reactant gas inside the buffer gas cell.

Engineering the sub-Doppler force in magneto-optical traps

Current dual-frequency magneto-optical traps for ultracold molecules are plagued by sub-Doppler heating effects, making them vastly inferior to standard atomic MOTs. Here we demonstrate theoretically that the sub-Doppler effects in such a MOT can be engineered to provide cooling instead of heating. We give an intuitive picture how to achieve such cooling and show the cooling and trapping force results of the 16 level optical Bloch equations for the case of CaF molecules. From three-dimensional Monte Carlo simulations we estimate the temperature and density of our MOT to be $40 \mu K$ and $4 \times 10^8 cm^{-3}$ respectively for a molecule number of $10^5$.

Domainal Investigation of a Quartz-Fluorite Composite Using Spectroscopic Techniques

The analysis of geological samples that have several chemically diffused zones which formed under certain physico-chemical condition is difficult to achieve. The quantitative estimations of the minerals in such samples are tedious. The present work demonstrates the application of LIBS for qualitative and quantitative analyses of a quartz-fluorite composite which was procured from an amygdaloidal basalt from Deccan Traps, India. The presence of weak emission lines of F in the spectral range of 200–900 nm makes it challenging to quantify the fluorine. This study has addressed a promising alternative to quantify the fluorine using electronic bands of CaF molecules observed in the Laser-induced Breakdown Spectroscopy (LIBS) spectrum. In addition to this spectroscopic technique, the authors also have used Photoacoustic Spectroscopy (PAS) and UV-VIS spectroscopy technique to obtain molecular information from the geological sample. Principal Component Analysis (PCA) was applied to a truncated spectral region of the CaF molecule, and it showed 99% variance. Further, the obtained results with these spectroscopic techniques were compared with the results that were obtained from X-ray diffraction and Electron Probe Micro Analyzer, and they show good agreement. Thus, the LIBS technique can be promising for in situ profile section (varies from few microns to centimeters size) studies without the sample’s destruction using the point detection capability of LIBS.

Determination of bromine and fluorine via sequential vaporization of TlBr and CaF molecules from the same aliquot by high-resolution continuum source graphite furnace molecular absorption spectrometry

This work describes the development of a multielement method for determination of bromine and fluorine, via sequential vaporization of TlBr and CaF molecules, from the same sample aliquot, using high resolution molecular absorption spectrometry. The molecular absorption of TlBr and CaF was measured at 342.9797 nm and 606.4322 nm, respectively. Studies were conducted by injecting 10 μL of sample or standard of bromine and fluorine into the graphite furnace. The source of the molecule-forming agents was 10 μL of solutions at 8.0 g L−1 of thallium and calcium, individually prepared from TlNO3 and Ca(NO3)2·4 H2O. The optimized vaporization temperatures were at 900 °C (TlBr) and 2100 °C (CaF). No chemical modifiers were used, and calibration against aqueous standard was employed. The limits of detection (LOD) were 2 ng (Br) and 0.02 ng (F). The linear ranges were 5–5000 ng (Br) and 0.5–100 ng (F). The evaluation of potentially interfering species showed no interference due to the presence of bromide over the signal for CaF or fluorine over the signal for TlBr. No interference was observed for TlBr with up to 20 μg of chlorine. However, for the CaF molecule, significant depreciation of the signal for 5 ng of fluorine was observed in the presence of 10 μg of chlorine. This interference is visually indicated by the appearance of a structured background, relative to the formation of CaCl, in the region next to CaF absorption. To verify the accuracy and performance of the proposed method, drug samples were analyzed with reported values for bromine or fluorine, sea lettuce reference material BCR 279 with informed value for bromine and road dust sample CW7 with no reported values. The determined values closely agreed with the reference values for the drugs and BCR 279 samples. However, for the road dust sample, non-spectral interference was observed. Nevertheless, the results here are promising and indicate the way to develop similar studies.

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.

Calcium monofluoride as a target molecule for determination of organic fluorine in gasoline and its components using high-resolution continuum source flame molecular absorption spectrometry

High-resolution continuum source molecular absorption spectrometry (HR-CS MAS) is widely applied to determine fluorine in various materials, and its graphite furnace option with calcium monofluoride as a target molecule is popular. However, up to now, the idea of using the molecule in flame molecular absorption spectrometry seemed impossible or impractical due to the expected low sensitivity and detectability. The following paper completely changes this view. The CaF molecule has been proven to be an excellent tool for determining organic fluorine in gasoline using flame molecular absorption spectrometry, giving benefits over previously used gallium monofluoride. The following favourable circumstances decide about it: 1) relatively high population of CaF molecules in preferable air-acetylene flame, 2) possibility of using oil calcium “standard” as a source of calcium, which is well dissoluble in both xylene (solvent) and gasoline, 3) extremely good stability of baseline in the used spectrum range, 4) relatively high freedom from spectral and chemical interferences and 5) possibility of summing of many pixels response. The analysis relies on simple sample dilution in xylene, with the addition of oil calcium “standard” to obtain 1500 mg L−1 Ca in measured solutions. Simplified standard addition calibration is used to overcome the effect of variability of samples (various physical properties and combustion characteristics). The signals of four CaF rotational “lines” are summed. The only undesirable spectral effect is a molecular absorption at the second “line” (606.0368 nm), which is attributed to the absorption by the CaOH molecule formed in the flame. The effect can be easily overcome by using the least square background correction, LSBC. The characteristic concentration and the detection limit for solutions are 6 and 0.6 mg L−1, respectively. The detection limit recalculated for the original sample is 2 mg kg−1 in the case of alkalyte, reformate and gasoline, while it is 6 mg kg−1 in the case of volatile isomerizate, mainly due to necessary higher sample dilution. The calibration curve is linear over at least two orders of magnitude. Heptafluorobutanol has been found a suitable standard. The agreement of the results of the proposed method and standard combustion ion chromatography is satisfactory.

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.

Collisions in a dual-species magneto-optical trap of molecules and atoms

We study inelastic collisions between CaF molecules and 87Rb atoms in a dual-species magneto-optical trap. The presence of atoms increases the loss rate of molecules from the trap. By measuring the loss rates and density distributions, we determine a collisional loss rate coefficient k 2 = (1.43 ± 0.29) × 10−10 cm3 s−1 at a temperature of 2.4 mK. We show that this is not substantially changed by light-induced collisions or by varying the populations of excited-state atoms and molecules. The observed loss rate is close to the universal rate expected in the presence of fast loss at short range, and can be explained by rotation-changing collisions in the ground electronic state.

Caffeine modulates the intercalation of drugs on DNA: A study at the single molecule level

We use optical tweezers to characterize the ability of Caffeine (Caf) to modulate the intercalation of drugs into the DNA double-helix at the single molecule level. When previously bound to the double-helix, Caf hinders ethidium bromide (EtBr) intercalation, decreasing its effective equilibrium binding constant with DNA. The dominant mechanism of such singular ability is a direct binding of Caf to the intercalating drugs in solution, which decreases the effective concentration of such compounds available to interact with DNA. When EtBr intercalation into the DNA double-helix occurs firstly, on the other hand, the measured cooperativity between Caf molecules interacting with DNA can be modulated, a feature also correlated to the Caf-EtBr interaction in solution. The results achieved here unveil many peculiarities about the details of such interactions at the molecular level and provide new insights on the use of Caf in therapeutic applications.

Collisions between Ultracold Molecules and Atoms in a Magnetic Trap.

We prepare mixtures of ultracold CaF molecules and Rb atoms in a magnetic trap and study their inelastic collisions. When the atoms are prepared in the spin-stretched state and the molecules in the spin-stretched component of the first rotationally excited state, they collide inelastically with a rate coefficient k_{2}=(6.6±1.5)×10^{-11} cm^{3}/s at temperatures near 100 μK. We attribute this to rotation-changing collisions. When the molecules are in the ground rotational state we see no inelastic loss and set an upper bound on the spin-relaxation rate coefficient of k_{2}<5.8×10^{-12} cm^{3}/s with 95%confidence. We compare these measurements to the results of a single-channel loss model based on quantum defect theory. The comparison suggests a short-range loss parameter close to unity for rotationally excited molecules, but below 0.04 for molecules in the rotational ground state.

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.

Laser-assisted Stark deceleration of CaF in its rovibronic ground (high-field-seeking) state**Project supported by the National Natural Science Foundation of China (Grant No. 11604164).

A near-resonant, red-detuning laser-assisted Stark deceleration scheme is proposed to slow CaF in its high-field-seeking rovibronic ground state. The assisting Gaussian laser beam can confine CaF molecules transversely owing to the optical Stark effect. Simulations suggest that the present scheme is superior to previous Stark decelerators. Under typical experimental conditions, when the assisting laser frequency is red-detuned to the molecular transition (λ ∼606.3 nm) by 5.0 GHz and the laser power is about 5.6 W, the proposed decelerator can achieve a total number at the order of 104 CaF molecules with a number density at the order of 108 cm−3. The equivalent temperature of the obtained cold CaF molecules is 2.3 mK. Additionally, the desired assisting laser power can be as low as about 1.2 W if keeping the red-detuning value to be 1.0 GHz, which further suggests its experimental feasibility.

Collision of cold CaF molecules: Towards evaporative cooling**Project supported by the National Natural Science Foundation of China (Grant Nos. 11604164 and U1810129), the Fund for Shanxi “1331 Project” Key Innovation Research Team, China (Grant No. 1331KIRT), and Excellent Youth Academic Leader in Higher Education of Shanxi Province, China (2018).

Long range intermolecular interaction potential surface of CaF (2Σ+) was simulated by employing the MOLPRO program and using the RCCSD(T)/def2-TZVP theory. The predicted data were further fitted to obtain the collision cross-section. The elastic collision cross-section of CaF at the temperature around 2 mK is as high as 6.5×10−9 cm2 and the collision rate is over 4.1×106 Hz. Additionally, we found that an orientation electric field will simplify the intermolecular interaction potential function from quaternary into ternary and the collision cross-section will be raised by about three orders. All-optical evaporative cooling of cold CaF is discussed in the conclusion.