Radiative force from optical cycling on a diatomic molecule

Analytic gradients for relativistic exact-two-component equation-of-motion coupled-cluster singles and doubles method

A first implementation of analytic gradients for spinor-based relativistic equation-of-motion coupled-cluster singles and doubles method using an exact two-component Hamiltonian augmented with atomic mean-field spin-orbit integrals is reported. To demonstrate its applicability, we present calculations of equilibrium structures and harmonic vibrational frequencies for the electronic ground and excited states of the radium mono-amide molecule (RaNH2) and the radium mono-methoxide molecule (RaOCH3). Spin-orbit coupling is shown to quench Jahn-Teller effects in the first excited state of RaOCH3, resulting in a C3v equilibrium structure. The calculations also show that the radium atoms in these molecules serve as efficient optical cycling centers.

Fermat Principle, Ramsey Theory and Metamaterials

Reinterpretation of the Fermat principle governing the propagation of light in media within the Ramsey theory is suggested. Complete bi-colored graphs corresponding to light propagation in media are considered. The vertices of the graphs correspond to the points in real physical space in which the light sources or sensors are placed. Red links in the graphs correspond to the actual optical paths, emerging from the Fermat principle. A variety of optical events, such as refraction and reflection, may be involved in light propagation. Green links, in turn, denote the trial/virtual optical paths, which actually do not occur. The Ramsey theorem states that within the graph containing six points, inevitably, the actual or virtual optical cycle will be present. The implementation of the Ramsey theorem with regard to light propagation in metamaterials is discussed. The Fermat principle states that in metamaterials, a light ray, in going from point S to point P, must traverse an optical path length L that is stationary with respect to variations of this path. Thus, bi-colored graphs consisting of links corresponding to maxima or minima of the optical paths become possible. The graphs, comprising six vertices, will inevitably demonstrate optical cycles consisting of the mono-colored links corresponding to the maxima or minima of the optical path. The notion of the "inverse graph" is introduced and discussed. The total number of triangles in the "direct" (source) and "inverse" Ramsey optical graphs is the same. The applications of "Ramsey optics" are discussed, and an optical interpretation of the infinite Ramsey theorem is suggested.

Laser Scheme for Doppler Cooling of the Hydroxyl Cation (OH+)

We report on a cycling scheme for Doppler cooling of trapped OH+ ions using transitions between the electronic ground state X3Σ- and the first excited triplet state A3Π. We have identified relevant transitions for photon cycling and repumping, have found that coupling into other electronic states is strongly suppressed, and have calculated the number of photon scatterings required to cool OH+ to a temperature where Raman sideband cooling can take over. In contrast to the standard approach, where molecular ions are sympathetically cooled, our scheme does not require co-trapping of another species and opens the door to the creation of pure samples of cold molecular ions with potential applications in quantum information, quantum chemistry, and astrochemistry. The laser cooling scheme identified for OH+ is efficient despite the absence of near-diagonal Franck-Condon factors, suggesting that broader classes of molecules and molecular ions are amenable to laser cooling than commonly assumed.

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.

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.

Fully Saturated Hydrocarbons as Hosts of Optical Cycling Centers

Designing closed, laser-induced optical cycling transitions in trapped atoms or molecules is useful for quantum information processing, precision measurement, and quantum sensing. Larger molecules that feature such closed transitions are particularly desirable, as the increased degrees of freedom present new structures for optical control and enhanced measurements. The search for molecules with robust optical cycling centers is a challenge which requires design principles beyond trial-and-error. Two such principles are proposed for the particular M-O-R framework, where M is an alkaline earth metal radical, and R is a ligand: (1) Large, saturated hydrocarbons can serve as ligands, R, due to a substantial HOMO-LUMO gap that encloses the cycling transition, so long as the R group is rigid. (2) Electron-withdrawing groups, via induction, can enhance Franck-Condon factors (FCFs) of the optical cycling transition, as long as they do not disturb the locally linear structure in the M-O-R motif. With these tools in mind, larger molecules can be trapped and used as optical cycling centers, sometimes with higher FCFs than smaller molecules.

Rydberg Atom-Enabled Spectroscopy of Polar Molecules via Förster Resonance Energy Transfer

Non-radiative energy transfer between a Rydberg atom and a polar molecule can be controlled by a static electric field. Here, we show how to exploit this control for state-resolved, non-destructive detection and spectroscopy of the molecules, where the lineshape reflects the type of molecular transition. Using the example of ammonia, we identify the conditions for collision-mediated spectroscopy in terms of the required electric field strengths, relative velocities, and molecular densities. Rydberg atom-enabled spectroscopy is feasible with current experimental technology, providing a versatile detection method as a basic building block for applications of polar molecules in quantum technologies and chemical reaction studies.

Laser Cooling and Electronic Structure of Be Halides Anions BeX- (X=Cl, Br, F, and I)

The adiabatic potential energy curves of the low lying electronic states of the Be halides anions BeX- (Cl, Br, F, and I) have been investigated in the representation 2s+1Ʌ(+/−) by using the complete active space self-consistent field (CASSCF) with multireference configuration interaction (MRCI+Q) method. The spectroscopic parameters Te,, Re, ωe, and Be, the static and transition dipole moment μe, and a rovibrational study of the investigated electronic states have been performed. New electronic states were investigated here for the first time. The highly diagonal FCF and the short radiative lifetime for the molecular anion BeF- prove its candidacy for direct Doppler laser cooling. The experimental proof of the stability and the calculated experimental parameters such as the vibrational branching ratio, the slowing distance, the recoil and Doppler temperatures with the experimental conditions of the buffer gas cell of this anion open the route for experimental work on the BeF- molecular ion.

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.

Theoretical investigation of laser cooling for BN- anion by ab inito calculation

A theoretical investigation for the feasibility of laser cooling BN^-anion is presented. An ab initio calculation on the three low-lying states Χ²Σ⁺, Α²Π and Β²Σ⁺ are performed at the CASSCF/MRCI + Q level. The calculated spectroscopic constants are in good agreement with the available theoretical and experimental data. Radiative properties including Franck-Condon factor, Einstein coefficients and radiative lifetimes are determined. The calculation shows that the transition B²Σ⁺(v^')↔X²Σ⁺(v^'') has highly diagonal FCFs, especially f₀₀ = 0.9898, and enough short radiative lifetimes. A cooling scheme by three laser beams is proposed, which requires one main pumping laser(λ₀₀ = 474.67 nm) and two repumping lasers (λ₀₁ = 514.64 nm, λ₁₂= 514.90 nm). The population dynamics of cooling is investigated with the rate equation approach. The simulation demonstrates that the population does not remain trapped within the intermediate Α²Π state. The resultant scattered photons are about2.5×10⁴, which is expected to stop BN^-anion molecule in a cryogenic beam theoretically.

Frequency-doubled Nd:YAG MOPA laser system with programmable rectangular pulses up to 200 microseconds

A compact frequency-doubled diode-pumped Nd:YAG master-oscillator power-amplifier laser system with programmable microsecond pulse length has been developed. Analog pulse shaping of the output from a single-frequency continuous-wave Nd:YAG oscillator, and subsequent amplification, allowed the generation of rectangular pulses with pulse lengths on the order of the Nd:YAG fluorescence lifetime. Temporally flat-top pulses of 1064 nm light with 520 mJ pulse energy, 2.6 kW peak power, and 200 μs duration, with linewidth below 10 kHz, were obtained at a repetition rate of 2 Hz. Second harmonic generation in a LBO crystal yielded pulses of 262 mJ and 1.3 kW peak power at 532 nm. The peak power can be maintained within 2.9% over the duration of the laser pulse, and long-term intensity stability of 1.1% was observed. The spatially flat-top beam at 1064 nm used in the amplifier is converted to a Gaussian beam at 532 nm with beam quality factor M² = 1.41(14) during the second harmonic generation. This system has potential as a pump source for Ti:sapphire, dye, or optical parametric amplifiers to generate tunable high-power single-frequency radiation for applications in precision measurements and laser slowing.

Seemingly asymmetric atom-localized electronic densities following laser-dissociation of homonuclear diatomics

Recent experiments on laser-dissociation of aligned homonuclear diatomic molecules show an asymmetric forward-backward (spatial) electron-localization along the laser polarization axis. Most theoretical models attribute this asymmetry to interference effects between gerade and ungerade vibronic states. Presumably due to alignment, these models neglect molecular rotations and hence infer an asymmetric (post-dissociation) charge distribution over the two identical nuclei. In this paper, we question the equivalence that is made between spatial electron-localization, observed in experiments, and atomic electron-localization, alluded by these theoretical models. We show that (seeming) agreement between these models and experiments is due to an unfortunate omission of nuclear permutation symmetry, i.e., quantum statistics. Enforcement of the latter requires mandatory inclusion of the molecular rotational degree of freedom, even for perfectly aligned molecules. Unlike previous interpretations, we ascribe spatial electron-localization to the laser creation of a rovibronic wavepacket that involves field-free molecular eigenstates with opposite space-inversion symmetry i.e., even and odd parity. Space-inversion symmetry breaking would then lead to an asymmetric distribution of the (space-fixed) electronic density over the forward and backward hemisphere. However, owing to the simultaneous coexistence of two indistinguishable molecular orientational isomers, our analytical and computational results show that the post-dissociation electronic density along a specified space-fixed axis is equally shared between the two identical nuclei-a result that is in perfect accordance with the principle of the indistinguishability of identical particles.

Optical Cycling Functionalization of Arenes

Closed, laser-induced optical transitions ("optical cycling transitions") of molecules can be used for state preparation and measurement in quantum information science and quantum sensing. Increasingly complex molecular species supporting optical cycling can provide new capabilities for quantum science, and it is not clear if there is a limit on their size or complexity. We explore Ca-O-L molecular constructs to support the optical cycling center, Ca, with ligands, L, being arenes. We find that L can be as large as coronene (i.e., CaOC₂₄H₁₁) without losing the diagonality of the Franck-Condon factor (FCF). Furthermore, L can be substituted with electron-withdrawing groups to improve the FCF. Larger L, beyond ∼7 rings, can disrupt the diagonality of the FCF by closing the HOMO-LUMO ligand electronic state gap and reordering with the local states on the cycling center. Overall, we find that optical cycling can be retained for arenes, and we offer a principle for their design.

Franck-Condon Tuning of Optical Cycling Centers by Organic Functionalization

Laser induced electronic excitations that spontaneously emit photons and decay directly to the initial ground state ("optical cycling transitions") are used in quantum information and precision measurement for state initialization and readout. To extend this primarily atomic technique to large, organic compounds, we theoretically investigate optical cycling of alkaline earth phenoxides and their functionalized derivatives. We find that optical cycle leakage due to wave function mismatch is low in these species, and can be further suppressed by using chemical substitution to boost the electron-withdrawing strength of the aromatic molecular ligand through resonance and induction effects. This provides a straightforward way to use chemical functional groups to construct optical cycling moieties for laser cooling, state preparation, and quantum measurement.

Theoretical study of laser cooling of the TlF+ molecular ion

The feasibility of the thallium monofluoride TlF+ molecular ion towards laser cooling is brought into focus through an electronic structure study. Ab initio calculations are carried out to investigate the four lowest-lying electronic states, X2Σ+, (1)2Π, (2)2Σ+ and (2)2Π, including the spin-orbit coupling effect by employing the Complete Active Space Self Consistent Field (CASSCF) method at the Multireference Configuration Interaction (MRCI) level of theory while invoking Davidson correction (+Q). Potential energy and permanent dipole moment curves are used to determine the corresponding spectroscopic constants and some other equilibrium parameters. Vibrational parameters of vibrational states and transition dipole moments between possible transitions are computed. The calculated parameters are then used to conduct a theoretical study focusing on the potential possibility of TlF+ ionic molecule to be laser cooled on the (2)2Π1/2(ν')-X2Σ+1/2(ν'') transition based on Di Rosa's criteria. With the results obtained being promising, a laser cooling optical cycling scheme is proposed to illustrate the number of pump lasers needed with the corresponding wavelengths that were found to lie within the ranges covered by a specific scientific laser.

Surface chemical trapping of optical cycling centers

Quantum information processors based on trapped atoms utilize laser-induced optical cycling transitions for state preparation and measurement. These transitions consist of an electronic excitation from the ground to an excited state and a decay back to the initial ground state, associated with a photon emission. While this technique has been used primarily with atoms, it has also recently been shown to work for some divalent metal hydroxides (e.g. SrOH) and alkoxides (e.g. SrOCH3). This extension to molecules is possible because these molecules feature nearly isolated, atomic-like ground and first-excited electronic states centered on the radical metal atom. We theoretically investigate the extension of this idea to a larger scale by growing the alkyl group, R, beyond the initial methyl group, CH3, while preserving the isolated and highly vertical character of the electronic excitation on the radical metal atom, M. Theory suggests that in the limit as the size of the ligand carbon chain increases, it can be considered a functionalized diamond (or cubic boron nitride) surface. Several requirements must be observed for the cycling centers to function when bound to the surface. First, the surface must have a significant band gap that fully encapsulates both the ground and excited states of the cycling center. Second, while the surface lattice imposes strict limits on the achievable spacing between the SrO- groups, at high coverage, SrO- centers can interact, and show geometric changes and/or electronic state mixing. We show that the coverage of the diamond surface with SrO- cycling centers needs to be significantly sub-monolayer for the functionality of the cycling center to be preserved. Having the lattice-imposed spatial control of SrO- placements will allow nanometer-scale proximity between qubits and will eliminate the need for atom traps for localized cycling emitters. Our results also imply that a functionalization could be done on a scanning microscope tip for local quantum sensing or on photonic structures for optically-mediated quantum information processing.

Slow Decay Processes of Electrostatically Trapped Rydberg NO Molecules

Nitric oxide (NO) molecules initially traveling at 795  m/s in pulsed supersonic beams have been photoexcited to long-lived hydrogenic Rydberg-Stark states, decelerated and electrostatically trapped in a cryogenically cooled, chip-based transmission-line Rydberg-Stark decelerator. The decelerated and trapped molecules were detected in situ by pulsed electric field ionization. The operation of the decelerator was validated by comparison of the experimental data with the results of numerical calculations of particle trajectories. Studies of the decay of the trapped molecules on timescales up to 1 ms provide new insights into the lifetimes of, and effects of blackbody radiation on, Rydberg states of NO.

Multireference study of ionic/covalent electronic states of MF (M = Be, Mg and Ca)

Ultracold environments composed by atoms or molecules offer an opportunity to study chemical reactions at the quantum-state level, for simulation of solid-state systems, as qubits in quantum computing, and for test fundamental symmetries. Those ultracold conditions formed by molecules can be obtained from cryogenic buffer gas, via supersonic expansion, followed by deceleration or from the laser cooling process. Diatomic alkaline earth monofluoride molecules have been shown as great candidates for the laser cooling process. In this sense, the present work focuses on the characterization of the low-lying doublet electronic states correlated to the first dissociation channel of the alkaline earth monofluorides diatomic molecules MF (M = Be, Mg and Ca). The developed state-of-the-art methodology was based on a qualitative analysis of the diatomic electronic structure, employing a hypothetical potential energy curve or by a simple molecular orbital diagram combined with bond order analysis. The potential energy curves, excitation and dissociation energies, and various sets of spectroscopic parameters were calculated by the MRCI/cc-pV5Z methodology. Transition probabilities for emission and radiative lifetimes among the characterized electronic states were also calculated for the (A)²Π ⟶ (X)²Σ⁺ electronic transition. Comparing the spectroscopy properties, we were able to indicate the CaF molecule as the best candidate molecule for laser cooling devices among the studied 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.

Suppressed Spontaneous Emission for Coherent Momentum Transfer

Strong optical forces with minimal spontaneous emission are desired for molecular deceleration and atom interferometry applications. We report experimental benchmarking of such a stimulated optical force driven by ultrafast laser pulses. We apply this technique to accelerate atoms, demonstrating up to an average of 19ℏk momentum transfers per spontaneous emission event. This represents more than an order of magnitude improvement in suppression of spontaneous emission compared to radiative scattering forces. For molecular beam slowing, this technique is capable of delivering a many-fold increase in the achievable time-averaged force to significantly reduce both the slowing distance and detrimental losses to dark vibrational states.

The ground and low-lying excited states and feasibility of laser cooling for GaH+ and InH+ cations

The potential energy curves and transition dipole moments of 1²Σ⁺ and 1²Π states of GaH⁺ and InH⁺ cations are performed by employing ab initio calculations. Based on the potential energy curves, the rotational and vibrational energy levels of the two states are obtained by solving the Schrödinger equation of nuclear movement. The spectroscopic parameters are deduced with the obtained rovibrational energy levels. The spin-orbit coupling effect of the ²Π states for both the GaH⁺ and InH⁺ cations are also calculated. The feasibility of laser cooling of GaH⁺ and InH⁺ cations are examined by using the results of the electronic and spectroscopic properties. The highly diagonal Franck-Condon factors and appropriate radiative lifetimes are determined by using the potential energy curves and transition dipole moments for the ²Π_{1/2, 3/2}↔1²Σ⁺ transitions. The results indicate that the ²Π_{1/2, 3/2}↔1²Σ⁺ transitions of both GaH⁺ and InH⁺ cations are appropriate for the close cycle transition of laser cooling. The optical scheme of the laser cooling is constructed for the GaH⁺ and InH⁺ cations.

Coherent Bichromatic Force Deflection of Molecules

We demonstrate the effect of the coherent optical bichromatic force on a molecule, the polar free radical strontium monohydroxide (SrOH). A dual-frequency retroreflected laser beam addressing the X[over ˜]^{2}Σ^{+}↔A[over ˜]^{2}Π_{1/2} electronic transition coherently imparts momentum onto a cryogenic beam of SrOH. This directional photon exchange creates a bichromatic force that transversely deflects the molecules. By adjusting the relative phase between the forward and counterpropagating laser beams we reverse the direction of the applied force. A momentum transfer of 70ℏk is achieved with minimal loss of molecules to dark states. Modeling of the bichromatic force is performed via direct numerical solution of the time-dependent density matrix and is compared with experimental observations. Our results open the door to further coherent manipulation of molecular motion, including the efficient optical deceleration of diatomic and polyatomic molecules with complex level structures.

The low-lying electronic states and optical schemes for the laser cooling of the BH+ and BH- ions

The potential energy curves and transition dipole moments for the 1²Σ⁺, 2²Σ⁺, 1²Π and 2²Π electronic states of the two molecules are calculated using multi-reference configuration interaction and the large basis sets aug-cc-pwCV5Z. Based on the obtained potential energy curves, the rotational and vibrational energy levels of the states are obtained by solving the Schrödinger equation of nuclear motion, and the spectroscopic parameters are then obtained by fitting the energy levels to Dunham series expansions. The spin-orbit coupling effect of the ²Π states for both the BH⁺ cation and BH^- anion are calculated. Highly diagonally distributed Franck-Condon factors are determined for the 1²Σ⁺ (v″=0)↔1²Π (v'=0) transition, ƒ₀₀ (BH⁺)=0.943, while the Franck-Condon factors for the 1²Π (v″=0)↔1²Σ⁺ (v'=0) transition is ƒ₀₀ (BH^-)=0.942. Moreover, the radiative lifetime of 38.2ns for the excited 1²Π state of the BH⁺ and 91.8ns for the 1²Σ⁺ state of the BH^- are obtained, which are short enough for rapid laser cooling. A three-step optical scheme of the laser cooling is constructed for either the BH⁺ cation or the BH^- anion.

Sisyphus Laser Cooling of a Polyatomic Molecule

We perform magnetically assisted Sisyphus laser cooling of the triatomic free radical strontium monohydroxide (SrOH). This is achieved with principal optical cycling in the rotationally closed P(N^{''}=1) branch of either the X[over ˜]^{2}Σ^{+}(000)↔A[over ˜]^{2}Π_{1/2}(000) or the X[over ˜]^{2}Σ^{+}(000)↔B[over ˜]^{2}Σ^{+}(000) vibronic transitions. Molecules lost into the excited vibrational states during the cooling process are repumped back through the B[over ˜](000) state for both the (100) level of the Sr-O stretching mode and the (02^{0}0) level of the bending mode. The transverse temperature of a SrOH molecular beam is reduced in one dimension by 2 orders of magnitude to ∼750  μK. This approach opens a path towards creating a variety of ultracold polyatomic molecules by means of direct laser cooling.

Extensive theoretical study on electronically excited states of calcium monochloride: Molecular laser cooling and production of ultracold chlorine atoms

Nine doublet Λ-S states of calcium monochloride (CaCl) are calculated using the internally contracted multireference configuration interaction method with the Davidson correction. Both the core subvalence and spin-orbit coupling effects are taken into account. Laser cooling of CaCl and production of ultracold chlorine atoms are investigated and assessed. Our computed spectroscopic constants and radiative lifetimes match the available experimental data very well. The determined Franck-Condon factors and vibrational branching ratios of the A(2)Π1/2(ν('))←X(2)Σ1/2 (+)(ν) transition are highly diagonally distributed and the evaluated radiative lifetime for the A(2)Π1/2(ν' = 0) state is 28.2 ns, which is short enough for rapid laser cooling. Subsequently, detection of cold molecules via resonance enhanced multiphoton ionization to determine the final quantum state populations is discussed and the ionization energy calculated. A multi-pulse excitation scheme is proposed for producing ultracold chlorine atoms from zero-energy photodissociation of the cooled CaCl. Our results demonstrate the possibility of producing ultracold CaCl molecules and Cl atoms.

Laser cooling of the AlCl molecule with a three-electronic-level theoretical model

Feasibility of laser-cooling AlCl molecule is investigated using ab initio quantum chemistry. Potential energy curves, permanent dipole moments, and transition dipole moments for the X(1)Σ(+), a(3)Π, and A(1)Π states are studied based on multi-reference configuration interaction plus Davidson corrections (MRCI+Q) method with ACVQZ basis set, spin-orbit coupling effects are considered at the MRCI+Q level. Highly diagonally distributed Franck-Condon factors (f00 = 0.9988 and f11 = 0.9970) and branching ratios (R00 = 0.9965, R01 = 2.85 × 10(-3), R02 = 6.35 × 10(-4), and R03 = 2.05 × 10(-6)) for the A(1)Π1(ν(')=0)→X(1)Σ0(+) (+)(ν(″)=0) transition are determined. A sufficiently radiative lifetime τ (A(1)Π1) = 4.99 ns is predicted for rapid laser cooling. The proposed cooling wavelength is deep in the ultraviolet region at λ00 = 261.75 nm. Total emission rates for the a(3)Π0(+) →X(1)Σ0(+) (+), a(3)Π1→X(1)Σ0(+) (+), A(1)Π1 → a(3)Π0(+) , and A(1)Π1 → a(3)Π1 transitions are particularly small (∼10 s(-1)-650 s(-1)). The calculated vibrational branching loss ratio to the intermediate a(3)Π0(+) and a(3)Π1 states can be negligible. The results imply the probability of laser cooling AlCl molecule with three-electronic-level.

Dependences of Q-branch integrated intensity of linear-molecule pendular spectra on electric-field strength and rotational temperature and its potential applications

We calculate the pendular-state spectra of cold linear molecules, and investigated the dependences of “Q-branch” integrated intensity of pendular spectra on both electric-field strength and molecular rotation-temperature. A new multi-peak structure in the “Q-branch” spectrum is appearing when the Stark interaction strength ω = μE/B equal to or larger than the critical value. Our study shows that the above results can be used not only to measure the electric-field vector and its spatial distribution in some electrostatic devices, such as the Stark decelerator, Stark velocity filter and electrostatic trap and so on, but also to survey the orientation degree of cold linear molecules in a strong electrostatic field.

Laser cooling of BeCl and BeBr molecules in an ab initio method

In this study, the feasibility of laser-cooling of BeCl and BeBr molecules is studied using ab initio quantum chemistry. The potential energy curves for the X(2)Σ(+), A(2)Π, and 2(2)Π electronic states of BeCl and BeBr are plotted based on multi-reference configuration interaction plus Davidson corrections (MRCI + Q), and the spin-orbit coupling (SOC) effects are considered at the MRCI + Q level. The calculated spectroscopic parameters agree with the experimental data. Highly diagonally distributed Franck-Condon factors are determined for the A(2)Π(ν' = 0) ← X(2)Σ(+)(ν'' = 0) transition: f00(BeCl) = 0.947 and f00(BeBr) = 0.966. Moreover, the suitable radiative lifetimes τ of the A(2)Π(ν' = 0) state are determined for rapid laser cooling: τ(BeCl) = 18.38 ns and τ(BeBr) = 27.09 ns. The proposed cooling wavelengths of both BeCl and BeBr are within the ultraviolet region at λ00(BeCl) = 358.51 nm and λ00(BeBr) = 379.38 nm. Laser cooling schemes for BeCl and BeBr molecules are also developed in consideration of the SOC effects. These results indicate that the inclusion of SOC effects does not affect the judgment of the feasibility of laser cooling of BeCl and BeBr molecules, even for the given BeBr molecules in which the SOC effect is significant.

Laser cooling of copper monofluoride: a theoretical study including spin–orbit coupling

A laser cooling scheme is proposed for CuF by including the spin–orbit coupling effects, and based on our calculated radiative lifetimes and vibrational branching ratios.

Low-temperature kinetics and dynamics with Coulomb crystals

Coulomb crystals-as a source of translationally cold, highly localized ions-are being increasingly utilized in the investigation of ion-molecule reaction dynamics in the cold regime. To develop a fundamental understanding of ion-molecule reactions, and to challenge existing models that describe the rates, product branching ratios, and temperature dependence of such processes, investigators need to exercise full control over the experimental reaction parameters. This requires not only state selection of the reactants, but also control over the collision process (e.g., the collisional energy and angular momentum) and state-selective product detection. The combination of Coulomb crystals in ion traps with cold neutral-molecule sources is enabling the measurement of state-selective reaction rates in a diverse range of systems. With the development of appropriate product detection techniques, we are moving toward the ultimate goal of examining low-energy, state-to-state ion-molecule reaction dynamics.

Laser cooling of BH and GaF: insights from an ab initio study

The feasibility of laser cooling BH and GaF is investigated usingab initioquantum chemistry.

A linewidth-narrowed and frequency-stabilized dye laser for application in laser cooling of molecules

We demonstrate a robust and versatile solution for locking the continuous-wave dye laser for applications in laser cooling of molecules which need linewidth-narrowed and frequency-stabilized lasers. The dye laser is first stabilized with respect to a reference cavity by Pound-Drever-Hall (PDH) technique which results in a single frequency with the linewidth 200 kHz and short-term stabilization, by stabilizing the length of the reference cavity to a stabilized helium-neon laser we simultaneously transfer the ± 2 MHz absolute frequency stability of the helium-neon laser to the dye laser with long-term stabilization. This allows the dye laser to be frequency chirped with the maximum 60 GHz scan range while its frequency remains locked. It also offers the advantages of locking at arbitrary dye laser frequencies, having a larger locking capture range and frequency scanning range to be implemented via software. This laser has been developed for the purpose of laser cooling a molecular magnesium fluoride beam.

Magnetic trapping of molecules via optical loading and magnetic slowing

Calcium monofluoride (CaF) is magnetically slowed and trapped using optical pumping. Starting from a collisionally cooled slow beam, CaF with an initial velocity of ∼ 30 m/s is slowed via magnetic forces as it enters a 800 mK deep magnetic trap. Employing two-stage optical pumping, CaF is irreversibly loaded into the trap via two scattered photons. We observe a trap lifetime exceeding 500 ms limited by background collisions. This method paves the way for cooling and magnetic trapping of chemically diverse molecules without closed cycling transitions.

Cold state-selected molecular collisions and reactions

Over the past decade, and particularly the past five years, a quiet revolution has been building at the border between atomic physics and experimental quantum chemistry. The rapid development of techniques for producing cold and even ultracold molecules without a perturbing rare-gas cluster shell is now enabling the study of chemical reactions and scattering at the quantum scattering limit with only a few partial waves contributing to the incident channel. Moreover, the ability to perform these experiments with nonthermal distributions comprising one or a few specific states enables the observation and even full control of state-to-state collision rates in this computation-friendly regime: This is perhaps the most elementary study possible of scattering and reaction dynamics.