Quantum Optical Aspects of High-Harmonic Generation

TL;DR

This paper develops a quantum electrodynamics framework to analyze high-harmonic generation, incorporating atomic binding and photon quantization effects, offering a new perspective on strong-field phenomena.

Contribution

It introduces an analytic nonperturbative method in quantum electrodynamics for high-harmonic generation, accounting for atomic and photon quantum effects simultaneously.

Findings

Derived a quantum optical generalization of the Kramers-Heisenberg formula.

Framework allows analysis of photon statistics effects on high-harmonic generation.

Provides a basis for exploring quantal effects in strong-field physics.

Abstract

The interaction of electrons with strong laser fields is usually treated with semiclassical theory, where the laser is represented by an external field. There are analytic solutions for the free electron wave functions, which incorporate the interaction with the laser field exactly, but the joint effect of the atomic binding potential presents an obstacle for the analysis. Moreover, the radiation is a dynamical system, the number of photons changes during the interactions. Thus, it is legitimate to ask how can one treat the high order processes nonperturbatively, in such a way that the electron-atom interaction and the quantized nature of radiation be simultaneously taken into account? An analytic method is proposed to answer this question in the framework of nonrelativistic quantum electrodynamics. As an application, a quantum optical generalization of the strong-field Kramers-Heisenberg formula is derived for describing high-harmonic generation. Our formalism is suitable to analyse, among various quantal effects, the possible role of arbitrary photon statistics of the incoming field. The present paper is dedicated to the memory of Prof. Dr. Fritz Ehlotzky, who had significantly contributed to the theory of strong-field phenomena over many decades.