Franck-Condon Tuning of Optical Cycling Centers by Organic Functionalization

Photoswitching Molecules Functionalized with Optical Cycling Centers Provide a Novel Platform for Studying Chemical Transformations in Ultracold Molecules

A novel molecular structure that bridges the fields of molecular optical cycling and molecular photoswitching is presented. It is based on a photoswitching molecule azobenzene functionalized with one and two CaO- groups, which can act as optical cycling centers (OCCs). This paper characterizes the electronic structure of the resulting model systems, focusing on three questions: (1) how the electronic states of the photoswitch are impacted by a functionalization with an OCC; (2) how the states of the OCC are impacted by the scaffold of the photoswitch; and (3) whether the OCC can serve as a spectroscopic probe of isomerization. The experimental feasibility of the proposed design and the advantages that organic synthesis can offer in the further functionalization of this molecular scaffold are also discussed. This work brings into the field of molecular optical cycling a new dimension of chemical complexity intrinsic to only polyatomic molecules.

Clock-Line-Mediated Sisyphus Cooling

We demonstrate subrecoil Sisyphus cooling using the long-lived ^{3}P_{0} clock state in alkaline-earth-like ytterbium. A 1388-nm optical standing wave nearly resonant with the ^{3}P_{0}→^{3}D_{1} transition creates a spatially periodic light shift of the ^{3}P_{0} clock state. Following excitation on the ultranarrow clock transition, we observe Sisyphus cooling in this potential, as the light shift is correlated with excitation to ^{3}D_{1} and subsequent spontaneous decay to the ^{1}S_{0} ground state. We observe that cooling enhances the loading efficiency of atoms into a 759-nm magic-wavelength one-dimensional (1D) optical lattice, as compared to standard Doppler cooling on the ^{1}S_{0}→^{3}P_{1} transition. Sisyphus cooling yields temperatures below 200 nK in the weakly confined, transverse dimensions of the 1D optical lattice. These lower temperatures improve optical lattice clocks by facilitating the use of shallow lattices with reduced light shifts while retaining large atom numbers to reduce the quantum projection noise. This Sisyphus cooling can be pulsed or continuous and is applicable to a range of quantum metrology applications.

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.

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.

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.

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.

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.

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.

Tuning and Enhancing Quantum Coherence Time Scales in Molecules via Light-Matter Hybridization

Protecting quantum coherences in matter from the detrimental effects introduced by its environment is essential to employ molecules and materials in quantum technologies and develop enhanced spectroscopies. Here, we show how dressing molecular chromophores with quantum light in the context of optical cavities can be used to generate quantum superposition states with tunable coherence time scales that are longer than those of the bare molecule, even at room temperature and for molecules immersed in solvent. For this, we develop a theory of decoherence rates for molecular polaritonic states and demonstrate that quantum superpositions that involve such hybrid light-matter states can survive for times that are orders of magnitude longer than those of the bare molecule while remaining optically controllable. Further, by studying these tunable coherence enhancements in the presence of lossy cavities, we demonstrate that they can be enacted using present-day optical cavities. The analysis offers a viable strategy to engineer and increase quantum coherence lifetimes in 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.

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.

Magneto-optical trapping and sub-Doppler cooling of a polyatomic molecule

Laser cooling and trapping^1,2, and magneto-optical trapping methods in particular², have enabled groundbreaking advances in science, including Bose-Einstein condensation^3-5, quantum computation with neutral atoms^6,7 and high-precision optical clocks⁸. Recently, magneto-optical traps (MOTs) of diatomic molecules have been demonstrated^9-12, providing access to research in quantum simulation¹³ and searches for physics beyond the standard model¹⁴. Compared with diatomic molecules, polyatomic molecules have distinct rotational and vibrational degrees of freedom that promise a variety of transformational possibilities. For example, ultracold polyatomic molecules would be uniquely suited to applications in quantum computation and simulation^15-17, ultracold collisions¹⁸, quantum chemistry¹⁹ and beyond-the-standard-model searches^20,21. However, the complexity of these molecules has so far precluded the realization of MOTs for polyatomic species. Here we demonstrate magneto-optical trapping of a polyatomic molecule, calcium monohydroxide (CaOH). After trapping, the molecules are laser cooled in a blue-detuned optical molasses to a temperature of 110 μK, which is below the Doppler cooling limit. The temperatures and densities achieved here make CaOH a viable candidate for a wide variety of quantum science applications, including quantum simulation and computation using optical tweezer arrays^15,17,22,23. This work also suggests that laser cooling and magneto-optical trapping of many other polyatomic species^24-27 will be both feasible and practical.

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.

Zeeman-Sisyphus Deceleration of Molecular Beams

We present a robust, continuous molecular decelerator that employs high magnetic fields and few optical pumping steps. CaOH molecules are slowed, accumulating at low velocities in a range sufficient for loading both magnetic and magneto-optical traps. During the slowing, the molecules scatter only seven photons, removing around 8 K of energy. Because large energies can be removed with only a few spontaneous radiative decays, this method can in principle be applied to nearly any paramagnetic atomic or molecular species, opening a general path to trapping of complex 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.

Accurate prediction and measurement of vibronic branching ratios for laser cooling linear polyatomic molecules

We report a generally applicable computational and experimental approach to determine vibronic branching ratios in linear polyatomic molecules to the 10^-5 level, including for nominally symmetry-forbidden transitions. These methods are demonstrated in CaOH and YbOH, showing approximately two orders of magnitude improved sensitivity compared with the previous state of the art. Knowledge of branching ratios at this level is needed for the successful deep laser cooling of a broad range of molecular species.

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.