The Quantum Polariton Hamiltonian that Reproduces the Same High-Harmonic Generation Spectra as the Classical Hamiltonian in Strong Laser Fields

Research Overview

This paper establishes a formal equivalence between the high-harmonic generation (HHG) spectra predicted by classical Floquet theory and a newly defined quantum polariton Hamiltonian within a quantum electrodynamics (QED) framework. While Floquet theory is the standard tool for modeling atoms in strong, classical laser fields, the author demonstrates that a fully quantum treatment—where the laser field is quantized—yields identical results under specific physical conditions.

Theoretical Approach

The author constructs a polariton Hamiltonian that describes an atom interacting with a quantized infrared (IR) field and a single ultraviolet (UV) mode. By employing complex-scaling Floquet theory and degenerate perturbation theory, the study shows that the matrix representations of the Floquet Hamiltonian and the QED Hamiltonian become effectively indistinguishable when the average number of photons in the laser mode is sufficiently large. The author validates this by comparing the eigenvalues and eigenvectors of both models using a one-dimensional model potential for a Xenon atom.

High-harmonic generation is a cornerstone of attosecond science, typically modeled using classical electromagnetic fields. This work provides a rigorous bridge between semi-classical Floquet approaches and a full QED description. By proving that the quantum polariton Hamiltonian reproduces classical results, the paper justifies the continued use of computationally efficient Floquet methods while providing a theoretical foundation for exploring quantum-optical effects in strong-field physics where the semi-classical approximation might eventually fail.