Quantum Scattering of Fullerene 12C60 with Rare Gas Atoms and its selection rules for rotational quenching

Abstract

The discovery of the C60 fullerene opened new horizons to design carbon nanostructures with targeted electronic structure as well as transport and optical properties. For example, endohedral 12C60 molecules were proposed as candidates for functional quantum architectures to store and manipulate encased atomic and molecular qubits. Recent advances in cryogenic buffer-gas cooling and frequency-comb spectroscopy have enabled rovibrational quantum-state-resolved measurements of gas-phase 12C60, revealing rotational fine structure reflecting its high icosahedral symmetry. Here, we present a perturbative quantum description of the 12C60 molecule interacting with a buffer gas of 40Ar atoms at temperatures of order 100 K, including a detailed analysis of their electronic structure, their interaction anisotropies, and the collision-induced rotational quenching of 12C60 in its vibrational and electronic ground state. The role of the icosahedral symmetry on the collisional dynamics is emphasized leading to unusual selection rules. Finally, we compute the isotropic and anisotropic static and dynamic dipole polarizability of 12C60 in its absolute ground state in order to evaluate the long-range, van der Waals interaction between 12C60 and 40Ar.

Figures (8)

• Figure 1: Schematic of depopulation (quenching) and repopulation of rotational states (black and blue horizontal lines) of the energetically lowest vibrational state of $^{12}$C$_{60}$ in collisions with argon atoms.
• Figure 2: Surface plot of the ground-state C$_{60}$-Ar potential as a function of Jacobi angles $(\theta, \phi)$ for the equilibrium separation $R=13.6 a_0$ between the centers of masses of $^{12}$C$_{60}$ and $^{40}$Ar.
• Figure 3: Dominant non-zero radial expansion coefficients $V_{l,m}(R)$ of C$_{60}$-Ar as functions of the separation between the centers of masses of C$_{60}$ and Ar. Reproduced with permission from Ref. Liu2022.
• Figure 4: Population or probability distributions of rotational levels $J$ of the ground vibrational state of the $^{12}$C$_{60}$ fullerene at temperatures of $T=100$ K (cyan curve), 150 K (blue curve) and 300 K (red curve). The smooth solid lines going through the center of jagged curves are rotational distributions that treat the $^{12}$C$_{60}$ as a rigid spherical top, for which the degeneracy factor is $(2J+1)^2$ for each $J$.
• Figure 5: Collision-induced quenching and repopulation rate coefficients of rotational levels $J_{\rm ini}$ of $^{12}$C$_{60}$ between 60 and 67 (panels (a) through (h)) with $^{40}$Ar as functions of the final rotational state $J_{\rm out}$ at collisional energy $E = k\times 150$ K. The vertical axes are the same for all panels except that for panel (f).