Colloquium: Quantum optics of intense light--matter interaction

TL;DR

This Colloquium surveys a growing framework where quantum optics and strong-field physics converge into Extreme Quantum Optics, enabling fully quantized light–matter interactions in HHG and ATI. It develops a quantum-state, Heisenberg-picture, and phase-space approach to show that intense-field processes can generate nonclassical light (squeezing, entanglement, optical cat states) and light–matter entanglement across harmonics and continua. Key contributions include predictions of squeezing and entanglement in HHG, conditioning protocols for optical cat states, and the extension to nonclassical driving fields and many-body systems, alongside analog quantum simulations of attosecond dynamics. The work highlights potential quantum technologies, such as metrology with HHG cat states and quantum-information pathways, while identifying challenges in state verification, propagation decoherence, and scalable quantum platforms for attosecond science.

Abstract

Intense light-matter interaction largely relies on the use of high-power light sources, creating fields comparable to, or even stronger than, the field keeping the electrons bound in atoms. Under such conditions, the interaction induces highly nonlinear processes such as high harmonic generation, in which the low-frequency photons of a driving laser field are upconverted into higher-frequency photons. These processes have enabled numerous groundbreaking advances in atomic, molecular, and optical physics, and they form the foundation of attosecond science. Until recently, however, such processes were typically described using semi-classical approximations, since the quantum properties of the light field were not required to explain the observables. This has changed in the recent past. Ongoing theoretical and experimental advances show that fully quantized descriptions of intense light-matter interactions, which explicitly incorporate the quantum nature of the light field, open new avenues for both fundamental research and technological applications at the fully quantized level. These advances emerge from the convergence of quantum optics with strong-field physics and ultrafast science. Together, they have given rise to the field of quantum optics and quantum electrodynamics of strong-field processes.

Figures (15)

• Figure 1: With the advent of the laser and the theory of quantum optics and optical coherence, two important but distinct fields have emerged. On one side lies the low-photon-number regime, where quantum optical descriptions of photons have led to remarkable applications in quantum information science; on the other side is the high-photon-number regime of strong laser-field physics, with applications in ultrafast science. Recent progress has demonstrated how these previously separate fields can now be integrated.
• Figure 2: A schematic of the semiclassical approach to the interaction of an atom with an intense infrared (IR) laser pulse of femtosecond (fs) duration. The light field is treated classically and the atom quantum mechanically. (a) Electron recollision picture. (b) Intensity of high harmonics (showing the plateau and cut-off regions) generated by the interaction of an intense linearly polarized laser pulse with Argon atoms. (c) Photoelectron spectrum generated by the interaction of Argon atoms with an intense linearly polarized laser pulse. Figs. (b) and (c) reproduced from Huillier_Nobel_2024 and Paulus1994PRL, respectively.
• Figure 3: A schematic of the fully quantized description of intense laser--matter interaction. Here, as an example, we show the interaction of matter (which can be atoms, molecules or solids) with intense driving light fields of a coherent (laser), squeezed and an optical "cat" state of frequency $\omega$. In the driving fields we emphasize on the quantum noise of the different driving field distributions. $H_{I}$ is the interaction part of the Hamiltonian. The interaction products are electrons and photons including high harmonics of frequencies $\omega_{q}=q \omega$. $\rho_{in}=\ket{\Psi_{in}} \bra{\Psi_{in}}$ is the density operator describing the field state before the interaction, $\rho_{out}$ is the density operator describing the state of the system after the interaction and $\ket{ \{0_q\}}$ is the vacuum state of the harmonic modes $q$ before the interaction.
• Figure 4: Depletion of the driving laser amplitude $\abs{\alpha + \delta \alpha (t)}$ from the initial amplitude $\alpha$ due to the strong field interaction and photon upconversion of the driving field into harmonic photons. The pulse of the driving laser field is shown (green, dashed) and the depletion (blue, solid) follows the ionization events of the electron. The inset shows how the amplitude's phase evolves over time. The figure has been reproduced from rivera2022strong.
• Figure 5: (a) Squeezing parameter of the fundamental field mode after HHG interaction as a function of the relative phase (CEP) between the carrier wave and the envelope (shown in the upper panels for specific CEP values indicated by arrows). The color coding indicates the squeezing angle. (b) Squeezing parameter of the harmonic spectrum for a driven Mott insulator. At the resonance frequency of the exciton, the squeezing shows dominant features in the non-classical response. The figures have been reproduced from (a) stammer2024entanglement, and (b) lange_excitonic_2025.