Rovibronic States Research Articles

An electric-field-assisted magnetic trap for cold molecular evaporative cooling: Toward molecular Bose–Einstein condensation

Ultracold molecules provide fundamental new insights into molecular interaction dynamics in the quantum regime and represent a new platform for chemical physics where quantum behaviors play a dominant role in molecular interaction and dynamics. An electric-field-assisted magnetic trap for trapping and further evaporative cooling of cold molecules to ultracold regime is proposed utilizing the perturbation of the hyperfine levels in a mixed field, and the depth of the trap can be tuned by adjusting the assisted electric field rapidly. Thus, the evaporative cooling of [Formula: see text]I[Formula: see text]Br molecules in the [Formula: see text] state of the rovibronic ground state is simulated. It shows that IBr molecules would be cooled from 26[Formula: see text][Formula: see text]K to 556[Formula: see text]nK within 598.9[Formula: see text]ms and eventually we would obtain a number of [Formula: see text] molecules in a volume of [Formula: see text][Formula: see text]cm3 with the number density of [Formula: see text][Formula: see text]cm[Formula: see text]. The Bose–Einstein condensation of the alkali diatomic molecules would probably be realized in the proposed trap if the present experimentally available samples are loaded.

High-Resolution Diatomic Spectroscopy near the Dissociation Threshold

Current progress in and prospects for high-resolution molecular laser spectroscopy used for quantum-mechanical modeling of the energy and radiation properties of the rovibronic states of diatomic molecules near the dissociation threshold are discussed at the experimental (spectroscopic) level of accuracy, which is impossible without taking into account all types of intramolecular interactions. The weakly bound, quasibound, and continuum rovibronic states localized near the dissociation threshold actively participate in the formation of stable molecules during spontaneous or laser-stimulated association of colliding atoms, which leads to cooling of the initial reaction medium. Laser-induced fluorescence (LIF) combined with high-resolution Fourier transform spectroscopy is a unique experimental technique, which allows the study of all the three (bound, quasibound, and continuum) parts of the molecular spectrum simultaneously. LIF experiments combined with precision ab initio electronic structure calculations and global nonadiabatic analysis of quasidegenerate rovibronic states converging to the same dissociation limit make it possible to study the structural and dynamic properties of isolated molecules over a very wide range of their electronic-vibrational-rotational excitation.

An updated fluorescence emission model of CO+ for cometary science

ABSTRACT A new CO$^+$ fluorescence emission model for analysing cometary spectra is presented herein. Accurate line lists are produced using the PGOPHER software for all transitions between the three electronic states (X $^2\Sigma$, A $^2\Pi$, B $^2\Sigma$) with vibrational states up to $v_\textrm {max} = 9, 8, 6$, respectively, and maximum rotational states with rotational quantum numbers $N\le 20$. As a result of improved molecular constants and theoretical transition rates, an expansion of the utilized solar spectrum into the infrared, and the substantial expansion of the included rovibronic states, the model provides an update of the fluorescence efficiencies of the CO$^+$ cation. The dependencies on heliocentric velocity and distance are explicitly included. We report, for the first time, quantification of the fluorescence efficiencies for the ground state rovibrational transitions of CO$^+$ and predict the positions and relative intensities of CO$^+$ lines in windows accessible to both ground- and space-based observatories. The computed fluorescence efficiencies show excellent agreement with UV/optical observations of both C/2016 R2 (PanSTARRS) and 29P/Schwassmann-Wachmann 1. The updated fluorescence efficiencies allow for revised N$_2$/CO abundances for comets 1P/Halley, C/1987 P1 (Bradfield), and C/2016 R2 (PanSTARRS), which can change by up to 30 per cent when accounting for recent improvements to CO$^+$ and N$_2^+$ fluorescence efficiencies. The model code, input files, and fluorescence efficiencies are publicly available and distributed on permanent archives for future uses in cometary analyses.

An association sequence suitable for producing ground-state RbCs molecules in optical lattices

We identify a route for the production of ^{87}87Rb^{133}133Cs molecules in the X^1\Sigma^+X1Σ+ rovibronic ground state that is compatible with efficient mixing of the atoms in optical lattices. We first construct a model for the excited-state structure using constants found by fitting to spectroscopy of the relevant a\,^3 \Sigma^+ → b\, ^3\Pi_1a3Σ+→b3Π1 transitions at 181.5 G and 217.1 G. We then compare the predicted transition dipole moments from this model to those found for the transitions that have been successfully used for STIRAP at 181.5 G. We form molecules by magnetoassociation on a broad interspecies Feshbach resonance at 352.7 G and explore the pattern of Feshbach states near 305 G. This allows us to navigate to a suitable initial state for STIRAP by jumping across an avoided crossing with radiofrequency radiation. We identify suitable transitions for STIRAP at 305 G. We characterize these transitions experimentally and demonstrate STIRAP to a single hyperfine level of the ground state with a one-way efficiency of 85(4)%.

Mixed-field effect at the hyperfine level of 127I79Br in its rovibronic ground state: Toward field manipulation of cold molecules

The mixed-field effect at the hyperfine level of the rovibronic ground state of the 127I79Br (X1Σ, v = 0, J = 0) molecule is computed on the J–I uncoupled basis of |JMJI 1 M 1 I 2 M 2〉, where J is the molecular total angular momentum excluding nuclear spin, MJ is the projection number of J, I 1 and I 2 are the nuclear spins of the iodine and bromine atoms, and M 1 and M 2 are the projection numbers of I 1 and I 2, respectively. When the two applied electric and magnetic fields are parallel, the perturbations are rare and only one perturbation is observed in a relatively large field regime in our computation range. However, when the two fields are off-parallel, the perturbations increase significantly and some sublevels show the Feshbach-like resonance phenomenon. Therefore, such sublevels transit between weak-field seeking and strong-field seeking repeatedly, which can be utilized to enhance or suppress cold molecular collision and chemical reaction rates. Such behavior of the molecular hyperfine structure in the mixed off-parallel fields may also be utilized to construct an electric-field-assisted anti-Helmholtz magnetic trap for cold molecules and to realize evaporative cooling of cold molecules (sub-mK) into the ultracold regime (μK).

Nonequilibrium Scattering/Evaporation Dynamics at the Gas-Liquid Interface: Wetted Wheels, Self-Assembled Monolayers, and Liquid Microjets.

ConspectusWe often teach or are taught in our freshman courses that there are three phases of matter─gas, liquid and solid─where the ordering reflects increasing complexity and strength of interaction between the molecular constituents. But arguably there is also a fascinating additional "phase" of matter associated with the microscopically thin interface (<10 molecules thick) between the gas and liquid, which is still poorly understood and yet plays a crucial role in fields ranging from chemistry of the marine boundary layer and atmospheric chemistry of aerosols to the passage of O2 and CO2 through alveolar sacs in our lungs. The work in this Account provides insights into three challenging new directions for the field, each embracing a rovibronically quantum-state-resolved perspective. Specifically, we exploit the powerful tools of chemical physics and laser spectroscopy to pose two fundamental questions. (i) At the microscopic level, do molecules in all internal quantum-states (e.g., vibrational, rotational, electronic) colliding with the interface "stick" with unit probability? (ii) Can reactive, scattering, and/or evaporating molecules at the gas-liquid interface avoid collisions with other species and thereby be observed in a truly "nascent" collision-free distribution of internal degrees of freedom? To help address these questions, we present studies in three different areas: (i) reactive scattering dynamics of F atoms with wetted-wheel gas-liquid interfaces, (ii) inelastic scattering of HCl from self-assembled monolayers (SAMs) via resonance-enhanced photoionization (REMPI)/velocity map imaging (VMI) methods, and (iii) quantum-state-resolved evaporation dynamics of NO at the gas-water interface. As a recurring theme, we find that molecular projectiles reactively, inelastically, or evaporatively scatter from the gas-liquid interface into internal quantum-state distributions substantially out of equilibrium with respect to the bulk liquid temperatures (TS). By detailed balance considerations, the data unambiguously indicate that even simple molecules exhibit rovibronic state dependences to how they "stick" to and eventually solvate into the gas-liquid interface. Such results serve to underscore the importance of quantum mechanics and nonequilibrium thermodynamics in energy transfer and chemical reactions at the gas-liquid interface. This nonequilibrium behavior may well make this rapidly emergent field of chemical dynamics at gas-liquid interfaces more complicated but even more interesting targets for further experimental/theoretical exploration.

Pre-Born–Oppenheimer energies, leading-order relativistic and QED corrections for electronically excited states of molecular hydrogen

For rovibronic states corresponding to the B and electronic states of the hydrogen molecule, the pre-Born–Oppenheimer (four-particle) non-relativistic energy is converged to a 1–3 parts-per-billion relative precision. The four-particle non-relativistic energy is appended with leading-order relativistic, leading- and estimated higher-order quantum-electrodynamics corrections. The resulting term values referenced to the rovibronic ground state are obtained in an excellent agreement with the experimental results. Further results are reported and discussed for other rovibronic states assignable to the and the and electronic states.

Black-body radiation-induced photodissociation and population redistribution of weakly bound states in H2 +

Molecular hydrogen ions in weakly bound states close to the first dissociation threshold are attractive quantum sensors for measuring the proton-to-electron mass ratio and hyperfine-induced ortho-para mixing. The experimental accuracy of previous spectroscopic studies relying on fast ion beams could be improved by using state-of-the-art ion trap setups. With the electric-dipole moment vanishing in H and preventing fast spontaneous emission, radiative lifetimes of the order of weeks are found. We include the effect of black-body radiation that can lead to photodissociation and rovibronic state redistribution to obtain effective lifetimes for trapped ion experiments. Rate coefficients for bound-bound and bound-continuum processes were calculated using adiabatic nuclear wave functions and nonadiabatic energies, including relativistic and radiative corrections. Effective lifetimes for the weakly bound states were obtained by solving a rate equation model and lifetimes in the range of 4–523 and >215 ms were found at room temperature and liquid nitrogen temperature, respectively. Black-body induced photodissociation was identified as the lifetime-limiting effect, which guarantees the purity of state-selectively generated molecular ion ensembles. The role of hyperfine-induced g/u-mixing, which allows pure rovibrational transitions, was found to be negligible.

Selecting lines for spectroscopic (re)measurements to improve the accuracy of absolute energies of rovibronic quantum states

Improving the accuracy of absolute energies associated with rovibronic quantum states of molecules requires accurate high-resolution spectroscopy measurements. Such experiments yield transition wavenumbers from which the energies can be deduced via inversion procedures. To address the problem that not all transitions contribute equally to the goal of improving the accuracy of the energies, the method of Connecting Spectroscopic Components (CSC) is introduced. Using spectroscopic networks and tools of graph theory, CSC helps to find the most useful target transitions and target wavenumber regions for (re)measurement. The sets of transitions suggested by CSC should be investigated by experimental research groups in order to select those target lines which they can actually measure based on the apparatus available to them. The worked-out examples, utilizing extensive experimental spectroscopic data on the molecules H_2^{~16}O, ^{32}S^{16}O_2, H_2^{~12}C^{16}O, and ^{14}NH_{3}, clearly prove the overall usefulness of the CSC method and provide suggestions how CSC can be used for various tasks and under different practical circumstances.

Hyperfine structures and the field effects of IBr molecule in its rovibronic ground state* *Project supported by the National Natural Science Foundation of China (Grant Nos. 12004199, U1810129, 52076145, and 11904252).

Hyperfine structures and the field effects of IBr molecule in its rovibronic ground state are theoretically studied by diagonalizing the effective Hamiltonian matrix. Perturbations of high-J levels up to 4 are taken into account when studying the hyperfine sub-levels of the J = 0 level, and thus, an 80 × 80 matrix is constructed and solved. Some of the experimentally absent molecular constants are computed using Dalton program. Our results will be helpful in the experimental investigation of manipulation and further cooling of cold IBr molecules.

Assembly of a Rovibrational Ground State Molecule in an Optical Tweezer.

We demonstrate the coherent creation of a single NaCs molecule in its rotational, vibrational, and electronic (rovibronic) ground state in an optical tweezer. Starting with a weakly bound Feshbach molecule, we locate a two-photon transition via the |c^{3}Σ_{1},v^{'}=26⟩ excited state and drive coherent Rabi oscillations between the Feshbach state and a single hyperfine level of the NaCs rovibronic ground state |X^{1}Σ,v^{''}=0,N^{''}=0⟩ with a binding energy of D_{0}=h×147044.63(11) GHz. We measure a lifetime of 3.4±1.6 s for the rovibronic ground state molecule, which possesses a large molecule-frame dipole moment of 4.6D and occupies predominantly the motional ground state. These long-lived, fully quantum-state-controlled individual dipolar molecules provide a key resource for molecule-based quantum simulation and information processing.

Frequency comb referenced spectroscopy of A-X 0-0 transitions in SH.

We report absolute transition frequencies for the allowed transitions from the X2Π3/2, v″ = 0, J″ = 3/2 rovibronic ground state of 32S1H to the A2Σ+, v' = 0 vibronic state. The frequencies have been determined with an uncertainty of less than 1 MHz, representing a more than 1000-fold improvement over previous measurements. Spectral traces are measured by scanning a frequency comb stabilized continuous-wave spectroscopy laser over the molecular transitions and detecting laser-induced fluorescence from SH molecules in a highly collimated molecular beam. To determine the absolute transition frequencies, the traces are fit with a quantum-mechanical model that accounts for saturation effects and shifts due to quantum interference. The model also provides estimates of the predissociation rate of the excited-state levels. Weighted averages of the hyperfine-resolved transition frequencies are computed in order to enable comparisons to measurements where the hyperfine structure is not resolved. These hyperfine-averaged frequencies indicate that the absolute transition frequencies determined in previous measurements were about ∼2.1 GHz (0.07 cm-1) too high. Finally, the measured transition frequencies are fit using an effective Hamiltonian model, resulting in more precise estimates of the spectroscopic constants.

Photon-excitation photon-emission maps (PhexPhem maps) with rovibronic resolution as a data base for theory and astrophysics part I: method and first results for H2

Dispersed fluorescence of wavelengths between 75 and 180 nm has been recorded after excitation of room temperature by narrow bandwidth monochromatized synchrotron radiation. Spectra have been taken in the exciting-photon energy range between 11 and 18 eV for discrete energy steps of 2.5 meV at a bandwidth of about 10 meV. The exciting-photon energy bandwidth has been narrow enough to induce transitions between individual rovibronic states. The resolution in the dispersed fluorescence detection was partly sufficient to resolve fluorescent transitions between individual rovibronic states. The recorded intensities are presented as two-dimensional photon-excitation photon-emission (PhexPhem) maps. They give a complete overview of experimental dispersed VUV/ FUV fluorescence spectra of H2 for these excitation energies, covering excitation from to all known singly excited states. The presented proof of principle experiments show a way to generate spectroscopic reference data for theory benchmarking and the interpretation of astrophysical observations.

The effect of the electric trapping field on state-selective loading of molecules into rf ion traps

Trapped molecular ions in pure rovibronic states are desirable in experiments ranging from cold chemistry to searches for physics beyond the Standard Model. Resonance-enhanced multiphoton ionisation (REMPI) can be used to prepare molecular ions in specific internal states with high fidelities. However, in the presence of electric fields, ionisation spectra exhibit frequency shifts and the ionisation thresholds are broadened. For this reason, REMPI studies are normally conducted in low and highly homogeneous electric fields, whereas the operating principle of rf ion traps requires electric fields that vary in space and time. In order to investigate the impact of this on the state-selectivity of REMPI in ion traps, we have simulated the expected broadening of the ionisation threshold under various operating conditions of a typical linear Paul trap. In many cases, the width of the ionisation threshold exceeds the separation between rotational energy levels, preventing state-selective ionisation. Careful choice of the trapping and laser parameters during loading can reduce this broadening, enabling state-selective ionisation in some instances. Where this strategy is not sufficient, the broadening can be reduced further by rapidly switching the trapping voltages off and on again during loading. This has been demonstrated experimentally for a Coulomb crystal of ^{40}hbox {Ca}^+ ions without descrystallising it.

Three-player polaritons: nonadiabatic fingerprints in an entangled atom–molecule–photon system

A quantum system composed of a molecule and an atomic ensemble, confined in a microscopic cavity, is investigated theoretically. The indirect coupling between atoms and the molecule, realized by their interaction with the cavity radiation mode, leads to a coherent mixing of atomic and molecular states, and at strong enough cavity field strengths hybrid atom–molecule–photon polaritons are formed. It is shown for the Na2 molecule that by changing the cavity wavelength and the atomic transition frequency, the potential energy landscape of the polaritonic states and the corresponding spectrum could be changed significantly. Moreover, an unforeseen intensity borrowing effect, which can be seen as a strong nonadiabatic fingerprint, is identified in the atomic transition peak, originating from the contamination of the atomic excited state with excited molecular rovibronic states.

Photodissociation branching ratios of 12C16O from 108000 cm−1 to 113200 cm-1 measured by two-color VUV-VUV laser pump-probe time-slice velocity-map ion imaging method: Observation of channels for producing O(1D)

The photoabsorption and photodissociation of carbon monoxide (CO) in the vacuum ultraviolet (VUV) region is one of the most important photochemical processes in the interstellar medium, thus it has attracted numerous experimental and theoretical studies. Here, we employed the two-color VUV-VUV laser pump-probe time-slice velocity-map ion imaging method to measure the relative branching ratios [C(3P0)+O(1D)]/ {[C(3P0)+O(3P)]+ [C(3P0)+O(1D)]} and [C(3P2)+O(1D)]/ {[C(3P2)+O(3P)]+[C(3P2)+O(1D)]} in the VUV photoexcitation energy range of 108000−113200 cm−1. Here, one tunable VUV laser beam is used to excite CO to specific rovibronic states, and a second independently tunable VUV laser beam is used to state-selectively ionize C(3P0) and C(3P2) for detection. State-selective photoionization through the 1VUV+1UV/visible resonance-enhanced multiphoton ionization scheme has greatly enhanced the detection sensitivity, which makes many new weak absorption bands observable in the current study. The branching ratio measurement shows that the spin-forbidden channels C(3P0)+O(1D) and C(3P2)+O(1D) only open at several discrete narrow energy windows. This might be caused by certain accidental resonance-enhanced spin-orbit interactions between the directly excited Rydberg states and valence states of triplet type which finally dissociate into the spin-forbidden channels.

A pathway to ultracold bosonic 23Na39K ground state molecules

We spectroscopically investigate a pathway for the conversion of 23Na39K Feshbach molecules into rovibronic ground state molecules via stimulated Raman adiabatic passage. Using photoassociation spectroscopy from the diatomic scattering threshold in the a3Σ+ potential, we locate the resonantly mixed electronically excited intermediate states and which, due to their singlet–triplet admixture, serve as an ideal bridge between predominantly a3Σ+ Feshbach molecules and pure X1Σ+ ground state molecules. We investigate their hyperfine structure and present a simple model to determine the singlet–triplet coupling of these states. Using Autler–Townes spectroscopy, we locate the rovibronic ground state of the 23Na39K molecule () and the second rotationally excited state N = 2 to unambiguously identify the ground state. We also extract the effective transition dipole moment from the excited to the ground state. Our investigations result in a fully characterized scheme for the creation of ultracold bosonic 23Na39K ground state molecules.

Imaging the [1+1] two-photon dissociation dynamics of Br2+ in a cold ion beam

The [1+1] two-photon dissociation dynamics of mass-selected 79Br2+ has been studied in a cold ion beam using a cryogenic cylindrical ion trap velocity map imaging spectrometer. The quartet 14Σu,3/2− state of 79Br2+ is employed as an intermediate state to initiate resonance enhanced two-photon excitation to high-lying dissociative states in the 4.0–5.0 eV energy region above the ground rovibronic state. Total kinetic energy release (TKER) and the two-dimensional recoiling velocity distributions of fragmented 79Br+ ions are measured using the technique of DC-slice velocity map imaging. Branching ratios for individual state-resolved product channels are determined from the TKER spectra. The measured photofragment angular distributions indicate that the dissociation of 79Br2+ occurs in dissociative Ω=3/2 state via ΔΩ=0 parallel transition from the 14Σu,3/2− intermediate state. Due to the considerable spin-orbit coupling effects in the excited states of 79Br2+, higher-lying dissociative quartet states are likely responsible for the observed photodissociation processes.

ExoMol molecular line lists XXXVI: X 2Π – X 2Π and A 2Σ+ – X 2Π transitions of SH

ABSTRACT The GYT line list covering rotational, rovibrational, and rovibronic transitions of the mercapto radical SH is presented. This work extends and replaces the SNaSH line list, which covers the ground (electronic) X 2Π state only. This extension is prompted by the tentative identification of the ultraviolet features of SH as being of importance in the transmission spectrum of the ultrahot Jupiter exoplanet WASP-121b. This GYT line list model is generated by fitting empirical potential energy, spin–orbit, and electronic angular momenta functions to experimentally measured wavelengths within the X 2Π and A 2Σ+ states and to the A 2Σ+–X 2Π band system using ab initio curves as a starting reference point. The fits are compatible with the quoted uncertainty of the experimental data used of ∼0.03–0.3 cm−1. The GYT line list covers wavelengths longer than 0.256 $\mu$m and includes 7686 rovibronic states and 572 145 transitions for 32SH. Line lists for the 33SH, 34SH, 36SH, and 32SD isotopologues are generated including a consideration of non-Born–Oppenheimer effects for SD. The line lists are available from the CDS (http://cdsarc.u-strasbg.fr) and ExoMol (www.exomol.com) data bases.

ExoMol line list – XXXIV. A rovibrational line list for phosphinidene (PH) in its $X\, {}^3\Sigma ^-$ and $a\, {}^1\Delta$ electronic states

ABSTRACTA rovibronic line list for the ground (X 3Σ−) and first excited (a 1Δ) states of phosphinidene, 31PH, is computed. The line list is designed for studies of exoplanetary and cool stellar atmospheres with temperatures up to 4000 K. A combination of empirical and ab initio data is used to produce the line list: potential energy curves (PECs) are fitted using experimental transition frequencies; these transitions are reproduced with a root mean square error of 0.01 cm−1. The nuclear Schrödinger equation is solved using these PECs plus Born–Oppenheimer and spin splitting correction terms. Line intensities and Einstein A coefficients are computed using ab initio dipole moment curves for X–X and a–a transitions. The resulting LaTY line list, which contains 65 055 transitions for 2528 rovibronic states up to 24 500 cm −1 and J = 80, is used to simulate spectra in emission and absorption for a range of temperatures. The line list is made available in electronic form at the CDS and ExoMol data bases.