Gauge Invariance beyond the Electric Dipole Approximation

TL;DR

This paper investigates the gauge invariance in laser-matter interactions beyond the electric dipole approximation, establishing equivalence between velocity and length gauges with higher-order expansions, aiding in more accurate nonperturbative simulations.

Contribution

It demonstrates the gauge equivalence of velocity and length gauges with higher-order multipole expansions, enabling consistent nonperturbative simulations beyond the electric dipole approximation.

Findings

Velocity and length gauges are mutually gauge-transformed with higher-order expansions.

The length gauge includes electric and magnetic multipole interactions up to specified orders.

This work facilitates the development of more accurate simulation methods beyond the electric dipole approximation.

Abstract

We study the gauge invariance of laser-matter interaction. The velocity gauge where the vector potential is expanded to the $n$-th order with respect to the spatial coordinate, and the length gauge where the electric and magnetic fields are expanded to the $n$-th and $(n-1)$-th orders, respectively, are mutually gauge-transformed, describing the physically equivalent situation. The latter includes up to the electric $2^{n+1}$-pole and magnetic $2^n$-pole interactions as well as two extra terms. The finding serves to develop consistent nonperturbative simulation methods beyond the electric dipole approximation.