About the role of short and long trajectories on the quantum optical state after high-harmonic generation

TL;DR

This paper investigates how short and long electron trajectories in high-harmonic generation influence the quantum optical state, revealing entanglement and enabling heralded creation of optical Schrödinger cat states.

Contribution

It demonstrates the signatures of different trajectories on the quantum state and shows how propagation effects impact non-classical light properties in HHG.

Findings

Short and long trajectories leave distinct signatures on the quantum optical state.

Entanglement between driving field and harmonics enables heralded Schrödinger cat state generation.

Propagation effects influence the non-classical features of emitted light.

Abstract

High-harmonic generation (HHG) involves the up-conversion of a high-intensity driving field into its harmonic orders. This process is intrinsically non-classical, requiring from quantum mechanics for a complete explanation as, under suitable conditions, involves phenomena such as particle tunneling through a potential barrier. When exposed to a high-intensity, low-frequency laser field, bound electrons ionize via tunneling, accelerate under the driving field, and recombine with the parent ion, emitting high-harmonic radiation. However, electrons can follow two distinct pathways -- short and long trajectories -- during these steps. In this work, we evaluate the signatures left by these trajectories on the quantum optical state after HHG, and observe that they lead to entanglement between the driving field and the generated harmonics. By leveraging these correlations, we use harmonic generation to herald the creation of optical Schr\"odinger cat-like states in the driving field. Additionally, using an ab-initio approach, we examine how propagation effects, which spatially separate the harmonic contributions from short and long trajectories, influence the non-classical characteristics of the emitted light.