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

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.

Optical Trapping of a Polyatomic Molecule in an ℓ-Type Parity Doublet State

We report optical trapping of a polyatomic molecule, calcium monohydroxide (CaOH). CaOH molecules from a magneto-optical trap are sub-Doppler laser cooled to 20(3)  μK in free space and loaded into an optical dipole trap. We attain an in-trap molecule number density of 3(1)×10^{9}  cm^{-3} at a temperature of 57(8)  μK. Trapped CaOH molecules are optically pumped into an excited vibrational bending mode, whose ℓ-type parity doublet structure is a potential resource for a wide range of proposed quantum science applications with polyatomic molecules. We measure the spontaneous, radiative lifetime of this bending mode state to be ∼0.7  s.

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.

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.

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.

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.

Direct laser cooling of a symmetric top molecule

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

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

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

Long-Range N-N Bonding by Rydberg Electrons

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

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

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