Gauge effects in bound-bound Rydberg-transition matrix elements

TL;DR

This paper computes and compares electric-dipole transition matrix elements for Rydberg atoms using different gauges, highlighting gauge differences and providing guidance for accurate calculations in Rydberg-atom research.

Contribution

It provides a comprehensive analysis of gauge effects on Rydberg-atom transition matrix elements and offers a decision framework for selecting the appropriate gauge in calculations.

Findings

Length-gauge EDTMs deviate from velocity-gauge EDTMs by up to 0.1%

Gauge differences depend on transition series and quantum numbers

Guidelines for choosing the correct gauge in Rydberg-atom calculations

Abstract

Accurate data on electric-dipole transition matrix elements (EDTMs) for bound-bound Rydberg-atom transitions become increasingly important in science and technology. Here we compute radial EDTMs of rubidium using the length, velocity and acceleration gauges for electric-dipole-allowed transitions between states with principal and angular-momentum quantum numbers ranging from 15 to 100. Wave-functions are computed based upon model potentials from Marinescu et al., Phys. Rev. A {\bf{49}}, 982 (1994). Length-gauge EDTMs, often used for low-$\ell$ transitions, are found to deviate from the fundamentally more accurate velocity-gauge EDTMs by relative amounts of up to $\sim 10^{-3}$. We discuss the physical reasons for the observed gauge differences, explain the conditions for applicability of the velocity and length gauges for different transition series, and present a decision tree of how to choose EDTMs. Implications for contemporary Rydberg-atom applications are discussed.