CaF+CaF interactions in the ground and excited electronic states: implications for collisional losses

TL;DR

This work addresses loss mechanisms in ultracold CaF+CaF collisions by computing excited-state Ca2F2 potential energy surfaces using multireference CI with a large active space, including spin-orbit and spin-spin interactions and transition dipole moments. The authors generate 1D and 2D PESs for 12 electronic states arising from three dissociation channels up to ~19000 $cm^{-1}$, finding strongly bound excited surfaces with numerous avoided crossings and conical intersections. They show that the lowest triplet 1A' surface can be shifted by 1064 nm light to intersect excited states, implying a feasible photoexcitation-induced loss pathway during collisions, while spin-orbit coupling between 1A' and 1A' is weak due to large energy gaps, though not entirely negligible. The study identifies two plausible mechanisms for observed collisional losses on the spin-polarized CaF+CaF surface and highlights the need for full dynamical scattering calculations to quantify these effects and guide future experiments.

Abstract

Accurate \textit{ab initio} potential energy surfaces are essential to understand and predict collisional outcomes in ultracold molecular systems. In this study, we explore the intermolecular interactions between two laser-cooled CaF molecules, both in their ground and excited electronic states, aiming to understand the mechanisms behind the observed collisional losses on the non-reactive, spin-polarized surface of the CaF+CaF system. Using state-of-the-art \textit{ab initio} methods, we compute twelve electronic states of the Ca$_2$F$_2$ complex within the rigid rotor approximation applied to CaF. Calculating the potential energy surfaces for the excited electronic states of Ca$_2$F$_2$ is challenging and computationally expensive. Our approach employs the multireference configuration interaction method, restricted to single and double excitations, along with a reasonably large active space to ensure the convergence in the excited states. We also compute the spin-orbit coupling between the ground state and the lowest spin-polarized triplet state, as well as the spin-spin coupling within the lowest triplet state (1) $^3\mathrm{A}'$. Additionally, we determine the electric transition dipole moments for the (1) $^3\mathrm{A}'$-(2) $^3\mathrm{A}'$ and (1) $^3\mathrm{A}'$-(1) $^3\mathrm{A}''$ transitions. Notably, we find that the lowest spin-polarized state (1) $^3\mathrm{A}'$, shifted by 1064 nm of laser light from the optical dipole trap, intersects several electronically excited states. Finally, by analyzing the potential energy surfaces, we discuss two plausible pathways that may account for the observed collisional losses on the spin-polarized surface of the CaF+CaF system.

Figures (7)

• Figure 1: Schematic diagram for the molecular orientations of CaF+CaF in the Jacobi coordinates.
• Figure 2: One-dimensional cuts of potential energy surfaces as a function of $R$ for six orientations of CaF+CaF: two linear configurations in panels (a) and (b), two T-shaped configurations in panels (c) and (d), and two parallel configurations in panels (e) and (f), where the former includes a global minimum geometry. The solid black and red dashed curves represent the $^1\mathrm{A}'$ and $^3\mathrm{A}'$ states, respectively. The $^1\mathrm{A}"$ and $^3\mathrm{A}"$ states are shown as green dash-dotted and orange dash-double-dotted curves, respectively. The blue dashed curve represents the PES of the (1) $^3\mathrm{A}'$ state shifted by the energy of the photon of 1064 nm wavelength. The circle in panel (b) presents a conical intersection, which is further discussed and analyzed in the context of the validity of the rigid rotor approximation in PES calculations for CaF+CaF.
• Figure 3: Variation of interaction energy under rigid and nonrigid rotor approximations of CaF, evaluated for a specific CaF+CaF configuration ($\theta_1 = 0^\circ$, $\theta_2 = 180^\circ$). The solid black and red curves represent the lowest $^3\Sigma$ and $^3\Pi$ states, respectively, under the C$_{\mathrm{2v}}$ point group. Panel (b) shows the potential energy surfaces at the equilibrium bond length of CaF, while panels (a) and (c) depict PESs for bond compression and elongation, respectively. Panel (d) shows an additional elongation case. The interaction energy is calculated with respect to the ground state asymptote, CaF$(\mathrm{X}~ ^2\Sigma^+)$+CaF$(\mathrm{X}~ ^2\Sigma^+)$. Note different vertical scales in different panels.
• Figure 4: Upper panel: variation of the spin-orbit matrix element between the two lowest electronic states, (1) $^1\mathrm{A}'$ and (1) $^3\mathrm{A}'$, as a function of $R$ for different configurations of CaF+CaF under the rigid rotor approximation. The effect of nonrigidity in SOC is also investigated and is presented by the green dashed and blue dashed-dotted curves. Lower panel: energy difference between these two states for the corresponding geometries.
• Figure 5: The red solid curve represents the variation of the spin-spin coupling as a function of $R$ for a linear configuration, ($\theta_1=0^\circ, \theta_2=0^\circ$) under the rigid rotor approximation, whereas the blue dashed curve present the same for the second linear configuration, ($\theta_1=0^\circ, \theta_2=180^\circ$). For the latter, it is difficult to get a smooth curve at a very short range regime due to the issue of convergence.