High-harmonic generation driven by temporal-mode quantum states of light

TL;DR

This paper presents a theoretical framework for high-harmonic generation driven by quantum states of light, showing that quantum effects are negligible in free-space HHG due to large photon numbers, but could be observable in nanophotonic environments.

Contribution

The authors extend HHG modeling to realistic pulse configurations using a temporal-mode expansion, establishing the negligible role of quantum effects in free-space HHG at typical intensities.

Findings

Correction factor for single-mode approximation remains below 10^{-4} at typical HHG intensities.

Free-space HHG driven by quantum states is well-described by semi-classical averaging, with no genuine quantum effects.

Potential for observing quantum signatures in nanophotonic environments with ultrasmall mode volumes.

Abstract

We develop a theoretical framework for high-harmonic generation (HHG) driven by quantum states of light based on a temporal-mode expansion of the electromagnetic field. This approach extends previous single plane-wave mode treatments to realistic pulse configurations, resolving conceptual inconsistencies arising from non-normalizable infinite plane waves and establishing consistency between analytical and numerical methods. We derive a correction factor that quantifies deviations from the single-mode approximation and show that it remains below $10^{-4}$ for intensities typical of HHG ($\sim 10^{14}~$W/cm$^2$). This result confirms that free-space HHG driven by any quantum state of light is accurately described by averaging semi-classical calculations over the Husimi distribution, with no observable genuine quantum effects. The absence of such effects is attributed to the large photon numbers ($\sim 10^{11}$) required to reach HHG intensities in free space, which render quantum fluctuations negligible. We discuss nanophotonic environments with ultrasmall mode volumes as potential platforms where few-photon strong-field processes could exhibit genuine quantum signatures.