Rotational excitation in sympathetic cooling of diatomic molecular ions by laser-cooled atomic ions

TL;DR

This work investigates whether rotational excitations induced by Coulomb coupling during sympathetic cooling degrade internal-state purity of diatomic molecular ions. It develops a framework separating translational and rotational dynamics, modeling translational cooling for two setups—a single atomic ion and a Coulomb crystal—via classical 1/r scattering and impact-parameter averaging, to estimate energy transfer per collision and cooling times. For rotational dynamics, apolar and polar diatomic ions are treated with perturbative and adiabatic approaches, respectively, yielding closed-form estimates for apolar accumulated excitation and adiabatic bounds for polar cases; in many practical scenarios, apolar ions experience only modest rotation, whereas polar ions require careful handling depending on dipole moment and collision energy. The results offer actionable guidance for trap-depth and ion selection to preserve rotational state during cooling and point to broader applicability to polyatomic species, where rotational structure may pose greater challenges.

Abstract

Sympathetic cooling of molecular ions through the Coulomb interaction with laser-cooled atomic ions is an efficient tool to prepare translationally cold molecules without, ideally, affecting the internal state of the molecular ions. However, the electric field due to the Coulomb interaction may induce rotational transitions that change the purity of initially quantum state prepared molecules. Here, we use estimates of rotational state changes in single collisions of diatomic ions with atomic ions [arXiv:1905.02130] to determine the overall rotational excitation accumulated over the sympathetic cooling. Considering two different experimental scenarios, that of a molecular ion co-trapped with a single atomic ion and a molecular ion immersed in a Coulomb crystal of atomic ions, we also estimate the cooling time.

Figures (4)

• Figure 1: Sympathetic cooling of a molecular ion via collisions with laser-cooled atomic ions: The considered cooling scenarios with either a single trapped atom (a) or many atomic ions forming a Coulomb crystal (b).
• Figure 2: CM-frame translational energy transfer, relative to the collision energy, as a function of the impact parameter $b$ for two collision energies $E = 2$eV (solid lines) and $E = 1$ eV (dashed dotted lines) and various pairings of molecular and atomic ions.
• Figure 3: Accumulated excitation for apolar molecular ions after a complete cooling cycle as function of the initial scattering energy, comparing numerical calculations taking both the quadrupole and polarizability interactions into account BerglundPRA1 (dashed lines) to PT (solid lines, $d \approx 5.3$$\mu$m).
• Figure 4: Accumulated excitation probability, Eq. \ref{['eq:Sigma']}, for polar molecular ions after a complete cooling cycle, as a function of the initial scattering energy with $E_{final} = 0.1\,$eV, comparing the estimate (solid lines) based on approximation \ref{['eq:cAdiabatic']} (with $\delta E = 0.05\,$eV) to full numerical simulations (dashed lines, $\delta E = 0.1$ eV). Within each interval $\delta E$, the excitation occurring in a single collision, $\tilde{\epsilon}$, can be evaluated at the highest and lowest energy, $E_i$ and $E_i -\delta E$, defining the shaded region, or taken to be the arithmetic mean, indicated by the dashed lines. The horizontal gray line marks an excitation level of 5%.