Vibronic coupling limits the use of high-lying electronic states in complex molecules for laser cooling

TL;DR

The paper investigates the viability of laser cooling high-lying electronic states in large polyatomic molecules by examining vibronic coupling between the first three excited states in OCC-functionalized CaOPh and SrOPh. It combines DLIF and excitation spectroscopy with a KDC vibronic Hamiltonian framework to quantify nonadiabatic couplings, finding that $\tilde{C}$ mixes with $\tilde{A}/\tilde{B}$ due to dense rovibronic manifolds, yielding additional decay channels with a mean coupling of about $\approx 0.1\ \mathrm{cm}^{-1}$ and challenging optical cycling via the C state. Because of the high vibrational-state density, these NACs are significant even for small couplings, effectively limiting laser cooling to the lowest excited state ($\tilde{A}$) for large molecules. The work generalizes this intrinsic limit to OCC-functionalized polyatomic systems and clarifies why large molecules can still exhibit favorable diagonal Franck–Condon factors for the lowest transition while high-lying-state cooling remains unfeasible.

Abstract

Laser cooling of large, complex molecules is a long-standing goal, instrumental for enabling new quantum technology and precision measurements. A primary consideration for the feasibility of laser cooling, which determines the efficiency and technical requirements of the process, is the number of excited-state decay pathways leading to vibrational excitations. Therefore, the assessment of the laser-cooling potential of a molecule begins with estimate of the vibrational branching ratios of the first few electronic excited states theoretically to find the optimum cooling scheme. Such calculations, typically done within the BO and harmonic approximations, have suggested that one leading candidate for large, polyatomic molecule laser cooling, alkaline earth phenoxides, can most efficiently be laser-cooled via the third electronically excited C state. Here, we report the first detailed spectroscopic characterization of the C state in CaOPh and SrOPh. We find that nonadiabatic couplings between the A, B, and C states lead to substantial mixing, giving rise to vibronic states that enable additional decay pathways. Based on the intensity ratio of these extra decay channels, we estimate a non-adiabatic coupling strength of 0.1 cm-1. While this coupling strength is small, the large density of vibrational states available at photonic energy scales in a polyatomic molecule leads to significant mixing. Thus, this result is expected to be general for large molecules and implies that only the lowest electronic excited state should be considered when judging the suitability of a molecule for laser cooling.

Figures (9)

• Figure 1: (a) Optical cycling -- laser transitions (solid lines) and decay pathways (dashed lines). In laser-coolable molecules, the spontaneous emission must be confined only to a few vibronic branchings with a dominant decay to the ground vibrational level. (b) Molecular orbitals of the ground $\tilde{X}$ and first three excited electronic states $\tilde{A}$, $\tilde{B}$, and $\tilde{C}$ of the MOPh (M = Ca,Sr) molecules. These metal-centered molecular orbitals ensures similar potential energy surface across these states, leading to favorable FCFs between the same vibrational levels. (c) The effect of non-adiabatic couplings (NAC) between BO states. Red and blue colors denote two (adiabatic) electronic states (lines) and respective vibrational states. NAC gives rise to vibronic states that have contributions from both electronic states. (d) Density of MOPh (M = Ca,Sr) vibrational states as a function of excess energy within a single electronic state. For complex molecules, the higher electronic states resides in the dense vibrational levels of the lower electronic states, enhancing the effect of NACs. The two dashed lines indicate the relative energy difference between $\tilde{C}-\tilde{A}$, and $\tilde{A}-\tilde{X}$ electronic states.
• Figure 2: (a,b) The DLIF spectra of CaOPh and SrOPh from the three excited states to the ground state. The spectra are normalized and centered with respected to the 0-0 transition to facilitate the comparison. In the insets we zoom in for branching decays into the first few vibrational modes. Peaks are labeled as $\nu_{i}^{f}$, where $\nu$ denotes the vibrational mode, $i$ and $f$ define the vibrational quantum number in the excited and ground electronic state. The labels "Ex@A/B/C-X" indicate that the molecule is excited from the ground $\tilde{X}$ state into the vibrationless level of the excited $\tilde{A}/\tilde{B}/\tilde{C}$ state respectively, and the subsequent fluorescence spectra are taken. (c) The schematic of fluorescence decays from the coupled $\tilde{C}$ state as in Eq. \ref{['eq:coupling']}. The "A-X" and "B-X" DLIF peaks are the vertical decays from the coupled $\tilde{A}$ and $\tilde{B}$ components.
• Figure 3: (a) Measured excitation spectra (red line) for CaOPh (left) and SrOPh (right) probing at "$\tilde{A}-\tilde{X}$" diagonal relaxations. The DLIF scan (light cyan) from $\ket{\tilde{A},\nu_0}$ state is shown for comparison. Near the $\ket{\tilde{C},\nu_0}$ energy, we observe multiple extra excitation peaks which are absent in the DLIF measurements (circled for clear identification). (b) Calculated excitation spectra including NAC terms. The colors indicates components from $\tilde{A}$ (blue), $\tilde{B}$ (orange) and $\tilde{C}$ (green) states. Because it is not practical to include NACs from all vibronic states, only a few vibrational modes are included in the calculation. The qualitative match of the multiple peak structures near the $\tilde{C}$ state confirms the presence of NACs.
• Figure S1: Schematic illustration of the experimental setup.
• Figure S2: (a) Calculated density of states as a function of excess energy for SrOPh. Two dashed lines indicate the relative energy differences for $\tilde{C}-\tilde{A}$ and $\tilde{A}-\tilde{X}$. (b) A schematics of the model used to calculate the coupling strength. The coupled states are treated as a number of evenly-spaced states with a constant mean coupling strength to $C,\nu_C$. The coupling strength $H_{coupling}$ is calculated by solving the eigenstate of such a coupling system. (c) Comparison between the measured DLIF spectrum for three $\tilde{C}$ state vibrational excitation levels, $\tilde{C},\nu_0$, $\tilde{C},\nu_3$, and $\tilde{C},\nu_6$ of SrOPh. The spectra are normalized to the highest peak in order to facilitate comparison. The intensity of the $\tilde{C}$ state peak drops dramatically as we increase the excitation energy.