Semiclassical model for the absorption or emission of a photon by a charged particle in an intense static electric field

Abstract

Quantum simulations made using Floquet methods show that a charged particle can exchange energy with an oscillating potential barrier in discrete quanta ħω, where ω is the frequency of oscillation. However, this exchange is classically forbidden because no other mass is included in the model, so that energy and momentum could not both be conserved in the absorption or emission of a photon. We define a semiclassical mechanism for these inelastic processes in which a photon may be absorbed by a charged particle moving against an intense static electric field, or emitted when the particle moves with this field. In this model, the particle has an energy loss Q in photon absorption, and an energy gain Q in photon emission. Then the particle travels a short distance at constant momentum until the energy increment Q is made up by the interaction with the static electric field, after which the particle resumes classical motion with the initial energy plus or minus exactly one quantum. We use the energy–time uncertainty relation to determine the minimum value for the static electric field that is required for this process, and this value is typical of the experimental conditions for laser-assisted scanning tunneling microscopy and laser-assisted field emission where the exchange of quanta is found to occur.