Low-frequency failure of the G\"oppert-Mayer gauge transformation and consequences for the Strong-Field Approximation

TL;DR

This paper investigates the failure of the G"oppert-Mayer gauge transformation at low frequencies and its impact on the gauge invariance of the Strong-Field Approximation, explaining the preference for the length gauge in certain regimes.

Contribution

It reveals the unphysical nature of the GM gauge transformation at low frequencies and clarifies its implications for the gauge invariance issues in the Strong-Field Approximation.

Findings

G"oppert-Mayer gauge transformation becomes unphysical as frequency approaches zero.

Failure of gauge invariance in the dipole-approximation SFA is linked to this low-frequency behavior.

Length gauge is favored in analytical methods for static or low-frequency fields.

Abstract

The G\"oppert-Mayer (GM) gauge transformation, of central importance in atomic, molecular, and optical physics since it connects the length gauge and the velocity gauge, becomes unphysical as the field frequency declines towards zero. This is not consequential for theories of transverse fields, but it is the underlying reason for the failure of gauge invariance in the dipole-approximation version of the Strong-Field Approximation (SFA). This failure of the GM gauge transformation explains why the length gauge is preferred in analytical approximation methods for fields that possess a constant electric field as a zero-frequency limit.