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

Dual Optical Cycling Centers Mounted on an Organic Scaffold: New Insights from Quantum Chemistry Calculations and Symmetry Analysis

Molecules cooled to ultracold temperatures are desirable for applications in fundamental physics and quantum information science. However, cooling polyatomic molecules with more than six atoms has not yet been achieved. Building on the idea of an optical cycling center (OCC), a moiety supporting a set of localized and isolated electronic states within a polyatomic molecule, molecules with two OCCs (bi-OCCs) may afford better cooling efficiency by doubling the photon scattering rate. By using quantum chemistry calculations, we assess the extent of the coupling of the two OCCs with each other and the molecular scaffold. We show that promising coolable bi-OCC molecules can be proposed by following chemical design principles.

Extending the Large Molecule Limit: The Role of Fermi Resonance in Developing a Quantum Functional Group

Polyatomic molecules equipped with optical cycling centers (OCCs), enabling continuous photon scattering during optical excitation, are exciting candidates for advancing quantum information science. However, as these molecules grow in size and complexity, the interplay of complex vibronic couplings on optical cycling becomes a critical but relatively unexplored consideration. Here, we present an extensive exploration of Fermi resonances in large-scale OCC-containing molecules using high-resolution dispersed laser-induced fluorescence and excitation spectroscopy. These resonances manifest as vibrational coupling leading to intensity borrowing by combination bands near optically active harmonic bands, which require additional repumping lasers for effective optical cycling. To mitigate these effects, we explore altering the vibrational energy level spacing through substitutions on the phenyl ring or changes in the OCC itself. While the complete elimination of vibrational coupling in complex molecules remains challenging, our findings highlight significant mitigation possibilities, opening new avenues for optimizing optical cycling in large polyatomic molecules.

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.

Zwitterions Functionalized by Optical Cycling Centers: Toward Laser-Coolable Polyatomic Molecular Cations

Functionalization of large aromatic compounds and biomolecules with optical cycling centers (OCC) is of considerable interest for the design and engineering of molecules with a highly selective optical photoresponse. Both internal and external dynamics in such molecules can be precisely controlled by lasers, enabling their efficient cooling and opening up broad prospects for high-precision spectroscopy, ultracold chemistry, enantiomer separation, and various other fields. The way the OCC is bonded to a molecular ligand is crucial to the optical properties of the OCC, first of all, for the degree of closure of the optical cycling loop. Here we introduce a novel type of functionalized molecular cation where a positively charged OCC is bonded to various organic zwitterions with a particularly high permanent dipole moment. We consider strontium(I) complexes with betaine and other zwitterionic ligands and show the possibility of creating efficient and highly closed population cycling for dipole-allowed optical transitions in such complexes.

Long-range interactions of aromatic molecules with alkali-metal and alkaline-earth-metal atoms

The isotropic and anisotropic coefficients C_n ^l,m of the long-range spherical expansion ∼1/Rⁿ (R-the intermolecular distance) of the dispersion and induction intermolecular energies are calculated using the first principles for the complexes containing an aromatic molecule (benzene, pyridine, furan, and pyrrole) and alkali-metal (Li, Na, K, Rb, and Cs) or alkaline-earth-metal (Be, Mg, Ca, Sr, and Ba) atoms in their electronic ground states. The values of the first- and second-order properties of the aromatic molecules are calculated using the response theory with the asymptotically corrected LPBE0 functional. The second-order properties of the closed-shell alkaline-earth-metal atoms are obtained using the expectation-value coupled cluster theory and of the open-shell alkali-metal atoms using analytical wavefunctions. These properties are used for the calculation of the dispersion C_n,disp ^l,m and induction C_n,ind ^l,m coefficients (C_n ^l,m=C_n,disp ^l,m+C_n,ind ^l,m) with n up to 12 using the available implemented analytical formulas. It is shown that the inclusion of the coefficients with n > 6 is important for reproducing the interaction energy in the van der Waals region at R ≈ 6 Å. The reported long-range potentials should be useful for constructing the analytical potentials valid for the whole intermolecular interaction range, which are needed for spectroscopic and scattering studies.

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.

Laser Spectroscopy of Aromatic Molecules with Optical Cycling Centers: Strontium(I) Phenoxides

We report the production and spectroscopic characterization of strontium(I) phenoxide (SrOC₆H₅ or SrOPh) and variants featuring electron-withdrawing groups designed to suppress vibrational excitation during spontaneous emission from the electronically excited state. Optical cycling closure of these species, which is the decoupling of the vibrational state changes from spontaneous optical decay, is found by dispersed laser-induced fluorescence spectroscopy to be high, in accordance with theoretical predictions. A high-resolution, rotationally resolved laser excitation spectrum is recorded for SrOPh, allowing the estimation of spectroscopic constants and identification of candidate optical cycling transitions for future work. The results confirm the promise of strontium phenoxides for laser cooling and quantum state detection at the single-molecule level.

High-Resolution Laser Spectroscopy of a Functionalized Aromatic Molecule

We present a high-resolution laser spectroscopic study of the òB₂-X̃²A₁ and B̃²B₁-X̃²A₁ transitions of calcium(I) phenoxide, CaOPh (CaOC₆H₅). The rotationally resolved band systems are analyzed using an effective Hamiltonian model and are accurately modeled as independent perpendicular (b- or c-type) transitions. The structure of calcium monophenoxide is compared to previously observed Ca-containing radicals, and implications for direct laser cooling are discussed. This work demonstrates that functionalization of aromatic molecules with optical cycling centers can preserve many of the properties needed for laser-based control.

Production of ultracold polyatomic molecules with strong polarity by laser cooling: A detailed theoretical study on CaNC and SrNC

Laser cooling molecules to the ultracold regime is the prerequisite for many novel science and technologies. It is desirable to take advantage of theoretical approaches to explore polyatomic molecular candidates, which are capable of being cooled to the ultracold regime. In this work, we explore two polyatomic candidates, CaNC and SrNC, which are suitable for laser cooling. These molecules possess impressively large permanent dipole moments (∼6 Debye), which is preferred for applications using an external electric field. High-level ab initio calculations are carried out to reveal electronic structures of these molecules, and the calculated spectroscopic constants agree very well with the available experimental data. For each molecule, the Franck-Condon factor matrix is calculated and shows a diagonal distribution. The radiative lifetimes for CaNC and SrNC are estimated to be 15.5 and 15.8 ns, respectively. Based upon the features of various electronic states and by choosing suitable spin-orbit states, we construct two feasible laser cooling schemes for the two molecules, each of which allows scattering nearly 10000 photons for direct laser cooling. These indicate that CaNC and SrNC are excellent ultracold polyatomic candidates with strong polarity.

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.

Functionalizing aromatic compounds with optical cycling centres

Molecular design principles provide guidelines for augmenting a molecule with a smaller group of atoms to realize a desired property or function. We demonstrate that these concepts can be used to create an optical cycling centre, the Ca(I)-O unit, that can be attached to a number of aromatic ligands, enabling the scattering of many photons from the resulting molecules without changing the molecular vibrational state. Such capability plays a central role in quantum state preparation and measurement, as well as laser cooling and trapping, and is therefore a prerequisite for many quantum science and technology applications. We provide further molecular design principles that indicate the ability to optimize and expand this work to an even broader class of molecules. This represents a great step towards a quantum functional group, which may serve as a generic qubit moiety that can be attached to a wide range of molecular structures and surfaces.

A combined experimental and computational study on the transition of the calcium isopropoxide radical as a candidate for direct laser cooling

Vibronically resolved laser-induced fluorescence/dispersed fluorescence (LIF/DF) and cavity ring-down (CRD) spectra of the electronic transition of the calcium isopropoxide [CaOCH(CH₃)₂] radical have been obtained under jet-cooled conditions. An essentially constant energy separation of 68 cm^-1 has been observed for the vibrational ground levels and all fundamental vibrational levels accessed in the LIF measurement. To simulate the experimental spectra and assign the recorded vibronic bands, Franck-Condon (FC) factors and vibrational branching ratios (VBRs) are predicted from vibrational modes and their frequencies calculated using the complete-active-space self-consistent field (CASSCF) and equation-of-motion coupled-cluster singles and doubles (EOM-CCSD) methods. Combined with the calculated electronic transition energy, the computational results, especially those from the EOM-CCSD calculations, reproduced the experimental spectra with considerable accuracy. The experimental and computational results suggest that the FC matrix for the studied electronic transition is largely diagonal, but transitions from the vibrationless levels of the à state to the X̃-state levels of the CCC bending (ν₁₄ and ν₁₅), CaO stretch (ν₁₃), and CaOC asymmetric stretch (ν₉ and ν₁₁) modes also have considerable intensities. Transitions to low-frequency in-plane [ν₁₇(a')] and out-of-plane [ν₃₀(a'')] CaOC bending modes were observed in the experimental LIF/DF spectra, the latter being FC-forbidden but induced by the pseudo-Jahn-Teller (pJT) effect. Both bending modes are coupled to the CaOC asymmetric stretch mode via the Duschinsky rotation, as demonstrated in the DF spectra obtained by pumping non-origin vibronic transitions. The pJT interaction also induces transitions to the ground-state vibrational level of the ν₁₀(a') mode, which has the CaOC bending character. Our combined experimental and computational results provide critical information for future direct laser cooling of the target molecule and other alkaline earth monoalkoxide radicals.

Production of ultracold CaCCH and SrCCH molecules by direct laser cooling: A theoretical study based on accurate ab initio calculations

Laser cooling of polyatomic molecules to the ultracold regime may enable some new science and technology applications; however, the related study is still at its very early stage. Here, by means of accurate ab initio and dynamical calculations, we identify two new candidate tetratomic molecules that are suitable for laser cooling and demonstrate the feasibility and advantage of two laser cooling schemes that are able to produce ultracold CaCCH and SrCCH molecules. The internally contracted multiconfiguration reference configuration interaction method is applied, and excellent agreement is achieved between the computed and experimental spectroscopic data. We find that the X²Σ_1/2 ⁺→A²Π_1/2 transitions for both candidates feature diagonal Franck-Condon factors, short radiative lifetimes, and no interference from intermediate electronic states. In addition, the crossings with higher electronic states do not interfere. We further construct feasible laser cooling schemes for CaCCH and SrCCH, each of which allows scattering 10⁴ photons for direct laser cooling. The estimated Doppler temperatures for both CaCCH and SrCCH are on the order of μK.

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.

Equation-of-motion coupled-cluster method with double electron-attaching operators: Theory, implementation, and benchmarks

We report a production-level implementation of the equation-of-motion (EOM) coupled-cluster (CC) method with double electron-attaching (DEA) EOM operators of 2p and 3p1h types, EOM-DEA-CCSD. This ansatz, suitable for treating electronic structure patterns that can be described as two-electrons-in-many orbitals, represents a useful addition to the EOM-CC family of methods. We analyze the performance of EOM-DEA-CCSD for energy differences and molecular properties. By considering reduced quantities, such as state and transition one-particle density matrices, we compare EOM-DEA-CCSD wave functions with wave functions computed by other EOM-CCSD methods. The benchmarks illustrate that EOM-DEA-CCSD is capable of treating diradicals, bond-breaking, and some types of conical intersections.

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.