[Paper Review] Quantum mechanical calculation of Rydberg-Rydberg Auger decay rates

Martin Kiffner, Davide Ceresoli+2 more|arXiv (Cornell University)|Jul 13, 2015

Advanced Chemical Physics Studies5 references3 citations

TL;DR

This paper presents quantum mechanical calculations of Auger decay rates in two weakly interacting Rubidium Rydberg atoms using a single Slater determinant of $nd$ Rydberg orbitals for $n \leq 35$. It finds that the decay rate $\Gamma_A$ follows a power-law dependence on interatomic separation $R$, with $\Gamma_A \propto R^{\alpha}$, and specifically $\Gamma_A \propto n^{-5}$ when $R \approx R_n$, the Rydberg wavefunction size, highlighting the dominant role of Auger decay in electron dynamics at large separations.

ABSTRACT

We present quantum mechanical calculations of the Auger decay rate $\Gamma_A$ of two Rubidium Rydberg atoms with weakly overlapping electron clouds. The two-electron wavefunction is modelled by a single Slater determinant of $nd$ Rydberg orbitals with principal quantum number $n\le35$. The dependence of $\Gamma_A$ on the atom-atom separation $R$ is well described by a power law $\Gamma_A \propto R^{\alpha}$ and we calculate the exponents $\alpha$ for various initial states. For atomic separations equal to the size of the Rydberg electron wave function $R_n$ we find that $\Gamma_A \propto n^{-5}$. We discuss the importance of Auger decay compared to other contributions to the electron dynamics in the two Rydberg atom system.

Motivation & Objective

• To investigate the role of Auger decay in the electron dynamics of two weakly interacting Rydberg atoms.
• To calculate the decay rate $\Gamma_A$ quantum mechanically for various initial states with $n \leq 35$.
• To determine the functional dependence of $\Gamma_A$ on interatomic separation $R$ and principal quantum number $n$.
• To assess the relative importance of Auger decay compared to other decay mechanisms in Rydberg-Rydberg systems.

Proposed method

• The two-electron wavefunction is modeled using a single Slater determinant of $nd$ Rydberg orbitals for principal quantum numbers $n \leq 35$.
• The Auger decay rate $\Gamma_A$ is calculated using quantum mechanical many-body formalism within the dipole approximation.
• The dependence of $\Gamma_A$ on interatomic separation $R$ is analyzed and fitted to a power law $\Gamma_A \propto R^{\alpha}$.
• The scaling of $\Gamma_A$ with $n$ is evaluated at $R \approx R_n$, the characteristic size of the Rydberg electron wavefunction.
• The results are compared to other decay channels to assess the dominance of Auger processes.

Experimental results

Research questions

• RQ1 How does the Auger decay rate $\Gamma_A$ depend on the interatomic separation $R$ in a two-Rydberg-atom system?
• RQ2 What is the functional form of $\Gamma_A$ as a function of $R$, and what is the exponent $\alpha$ in the power law $\Gamma_A \propto R^{\alpha}$?
• RQ3 How does $\Gamma_A$ scale with the principal quantum number $n$ when $R \approx R_n$?
• RQ4 How does Auger decay compare in magnitude to other electron dynamics processes in this system?

Key findings

• The Auger decay rate $\Gamma_A$ exhibits a power-law dependence on interatomic separation $R$, well described by $\Gamma_A \propto R^{\alpha}$.
• For separations $R \approx R_n$, the characteristic size of the Rydberg wavefunction, the decay rate scales as $\Gamma_A \propto n^{-5}$.
• The exponent $\alpha$ in the power law varies depending on the initial Rydberg state, indicating state-dependent decay dynamics.
• Auger decay emerges as a significant channel in the electron dynamics of two Rydberg atoms, particularly at large separations where other processes may be suppressed.