Gauge invariance and wave packet simulations in the presence of dipole fields

TL;DR

This paper introduces a gauge transformation-based method for wave packet simulations in dipole fields, explicitly incorporating the dipole interaction into the vector potential, and applies it to model Rabi oscillation-based switching devices.

Contribution

It develops a generalized scheme for wave packet evolution in dipole fields using gauge transformations and the Caley form, enabling explicit calculation of the evolution operator.

Findings

Probability to tunnel shows plateau structure after Rabi oscillations.

Wave function emission occurs in bursts corresponding to Rabi cycles.

Method effectively models switching devices based on Rabi oscillations.

Abstract

A method for performing wave packet simulations in dipole fields is presented. Starting from a Hamiltonian with non commuting terms, a gauge transformation leads to a new Hamiltonian which allows to calculate explicitly the evolution operator. In this new gauge, the dipole field is fully included in the {\it vector} potential. The method of Goldberg, Schwartz and Schey based on the Caley form of the evolution operator is then generalized, and the resulting scheme is applied to describe a switching device based on Rabi oscillations. The probability to tunnel in the free region exhibits a plateaux structure as the wave function is emitted by ``bursts'' after each Rabi oscillation has been completed.