Fully Quantum Theory Achieves Tunable Entangled Multi-Photon States in High-Harmonic Generation

High-harmonic generation (HHG) is rapidly becoming a powerful technique for creating intense, multi-photon states of light, but accurately modelling the quantum behaviour of this process has remained a significant challenge. Sebastián de-la-Peña, Heiko Appel, Angel Rubio, and Ofer Neufeld, from the Max Planck Institute for the Structure and Dynamics of Matter and the Technion, Israel Institute of Technology, now present a complete quantum theory of HHG, solving the fundamental light-matter interaction without approximation. This breakthrough achieves the first qualitative agreement between theory and recent experiments, demonstrating that the correlation between emitted photons decreases with increasing laser power, and predicts that this behaviour extends to higher-energy photons. The team’s work reveals how precise control of laser power can enhance specific features of HHG, and establishes a new benchmark for understanding and ultimately engineering complex, non-classical multi-photon states for advanced applications in the XUV and ultrafast regimes.

Quantum Entanglement in High-Harmonic Generation Theory

Scientists have developed a comprehensive theoretical framework to explore entanglement generation in high-harmonic generation (HHG), a process used to create high-frequency light. This work establishes a formally exact approach by solving the light-matter interaction without relying on approximations used in previous studies, addressing a long-standing debate regarding the appropriate theoretical level for describing HHG emission. The study centers on a model atom consisting of a single active electron interacting with quantized photon modes within a photonic cavity, allowing for precise calculations of quantum correlations. Researchers engineered a system where the electron experiences a soft-Coulomb potential, and the overall light-matter interaction incorporates the electron’s momentum, the Coulomb potential, and interaction with the quantized photon modes.

Simulations truncate the computational space by selecting effective modes with frequencies matching multiples of the driving laser frequency, enabling efficient computation of entanglement between emitted harmonics. This approach crucially incorporates focal averaging of the laser beam, a factor previously neglected in quantum HHG theories, and demonstrates its essential role in recovering experimentally observed behavior. The study predicts both the magnitude and trend of entanglement between the third and fifth harmonics to be consistent with recent experimental observations in semiconductors, validating the theoretical framework. Furthermore, simulations reveal strong oscillations in the correlation parameter with the driving laser intensity, demonstrating that tuning the irradiated intensity can maximize entanglement and potentially guide emerging experiments. By considering different atomic models, scientists found that long electron trajectories can drastically change entanglement behavior, highlighting the importance of accurately treating the atomic system.

Entanglement Control in High-Harmonic Generation

Scientists have developed a comprehensive quantum theory to explore entanglement in high-harmonic generation (HHG), a process used to create high-frequency light. This work establishes a new understanding of entanglement features in HHG by solving the light-matter interaction exactly, avoiding approximations used in previous approaches. The team’s simulations demonstrate qualitative agreement with recent experiments, specifically showing that a parameter measuring entanglement between emitted photons decreases with increasing laser power for below-threshold harmonics. The research reveals that fine-tuning laser power can significantly enhance HHG entanglement features, which oscillate with the driving power and exhibit local maxima indicative of non-classical behavior.

Importantly, the theory predicts these oscillatory entanglement patterns will appear not only for below-threshold harmonics, but also for both above-threshold harmonics and between above- and below-threshold harmonic pairs. By analyzing different atomic targets, scientists found that the long-range behavior of driven electronic trajectories can qualitatively change the resulting entanglement, suggesting that the specific atomic system strongly influences quantum correlations in HHG. Measurements confirm that focal averaging plays a crucial role in entanglement measures, a factor previously neglected in quantum HHG theories, and can even change the qualitative behavior of observables.

Quantum Light Correlations in High-Harmonic Generation

This research presents a significant advancement in understanding high-harmonic generation (HHG), a process with potential applications in creating intense states of light. Scientists have developed a comprehensive theoretical framework that accurately describes the quantum properties of light emitted during HHG, moving beyond previous approximations. The team’s calculations demonstrate that the correlations between different harmonics, specifically the third and fifth, exhibit non-classical behaviour, violating established inequalities and confirming the generation of uniquely quantum light. Notably, the study reveals that these correlations oscillate with the intensity of the driving laser, a phenomenon linked to the closing of specific electronic channels. Crucially, the researchers found that averaging over the spatial distribution of the laser beam plays a vital role in determining these quantum properties and can even alter the observed behaviour, suggesting that careful control of the laser’s spatial profile could be used to enhance and tailor the characteristics of the emitted light.