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Nature Communications

Propagation effects in high harmonic generation media driven by bright squeezed vacuum light

Javier Rivera-Dean, Deeksha Kanti, Philipp Stammer, Stefanos Carlström, Nikolaos Tsatrafyllis, Misha Ivanov, Maciej Lewenstein, P. Tzallas

Published Jul 9, 2026• 0 citations
Publisher

Abstract

Recent developments in quantum light engineering have enabled the use of infrared bright squeezed vacuum (BSV) femtosecond pulses in nonlinear optics, including strong-field physics and high-harmonic generation. However, theory has focused on single-atom interactions, neglecting the crucial macroscopic aspect of light propagation through media. This raises a key question: How does BSV propagate in nonlinear media, and how this affects the nonlinear signals and the radiation’s quantumness? We address this with a fully quantized framework for propagation in gas media undergoing high-harmonic generation. We find that ionization and the associated photon losses cause decoherence, which limits the propagation length, degrades radiation’s quantumness, and reduces the emitted harmonics. However, these effects are not detrimental. We identify conditions that minimize propagation-induced decoherence while preserving detectable harmonics with super-Poissonian photon statistics. Our results establish fully quantized basis for exploring BSV in nonlinear optics, strong-field-quantum optics, and ultrafast science in all states of matter. Recent developments in strong-field quantum optics are usually modelled with approaches neglecting the propagation dynamics inside the medium. Here, the authors introduce a fully quantized framework for bright squeezed vacuum states propagating inside atomic media undergoing high-harmonic generation, unveiling the role of decoherence effects.

DOI
10.1038/s41467-026-75173-8

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Recent developments in quantum light engineering have enabled the use of infrared bright squeezed vacuum (BSV) femtosecond pulses in nonlinear optics, including strong-field physics and high-harmonic generation. However, theory has focused on single-atom interactions, neglecting the crucial macroscopic aspect of light propagation through media. This raises a key question: How does BSV propagate in nonlinear media, and how this affects the nonlinear signals and the radiation’s quantumness? We address this with a fully quantized framework for propagation in gas media undergoing high-harmonic generation. We find that ionization and the associated photon losses cause decoherence, which limits the propagation length, degrades radiation’s quantumness, and reduces the emitted harmonics. However, these effects are not detrimental. We identify conditions that minimize propagation-induced decoherence while preserving detectable harmonics with super-Poissonian photon statistics. Our results establish fully quantized basis for exploring BSV in nonlinear optics, strong-field-quantum optics, and ultrafast science in all states of matter. Recent developments in strong-field quantum optics are usually modelled with approaches neglecting the propagation dynamics inside the medium. Here, the authors introduce a fully quantized framework for bright squeezed vacuum states propagating inside atomic media undergoing high-harmonic generation, unveiling the role of decoherence effects.
Attosecond quantum light, formed by the superposition of high-order harmonics driven by intense quantum light, opens new routes to probe quantum-mechanical correlations in matter. In this study, we have investigated the macroscopic propagation effects of quantum high-order harmonics generated by the combination of strong coherent and weak bright squeezed vacuum (BSV) lasers interacting with atomic gas. Our results reveal that the pressure-dependent intensity of harmonics arising from absorbing or emitting BSV photons differs from that of harmonics generated using only strong coherent pulses. Macroscopic propagation simulations indicate that the action phase of harmonics is perturbed by the weak BSV pulses. This perturbation modulates the phase mismatch of sub-cycle attosecond bursts and affects their quantum properties when the gas pressure varies. The ability to generate bright quantum high-order harmonics lays a foundation for the establishment and application of attosecond quantum spectroscopy.
Abstract Attosecond quantum light, formed by the superposition of high-order harmonics driven by intense quantum light, opens new routes to probe quantum-mechanical correlations in matter. In this study, we have investigated the macroscopic propagation effects of quantum high-order harmonics generated by the combination of strong coherent and weak bright squeezed vacuum (BSV) lasers interacting with atomic gas. Our results reveal that the pressure-dependent intensity of harmonics arising from absorbing or emitting BSV photons differs from that of harmonics generated using only strong coherent pulses. Macroscopic propagation simulations indicate that the action phase of harmonics is perturbed by the weak BSV pulses. This perturbation modulates the phase mismatch of sub-cycle attosecond bursts and affects their quantum properties when the gas pressure varies. The ability to generate bright quantum high-order harmonics lays a foundation for the establishment and application of attosecond quantum spectroscopy.
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High-harmonic generation (HHG) driven by intense quantum light has recently emerged as a new frontier in strong-field physics. Yet, the mechanism underlying HHG with nonclassical fields such as bright squeezed vacuum (BSV) light—characterized by a vanishing mean electric field—remains elusive. In this work, we develop a fully quantum theory for HHG under arbitrary quantum driving fields. We show that the fluctuation component of the dipole correlation operator plays a central role in HHG with quantum light and is essential for BSV-driven HHG. Furthermore, our framework reveals the photon statistics distribution within individual harmonics and across different harmonics, demonstrating that the statistics inherit the statistical properties of the driving field. This theory overcomes key limitations of existing approaches and uncovers new quantum features of HHG in the presence of nonclassical light.
High-harmonic generation (HHG) is a prototypical strong-field process in which intense light drives matter to emit radiation at integer multiples of the driving frequency. Extending HHG into the quantum-optical regime offers new opportunities to probe and control strongly nonlinear light-matter interactions using nonclassical states of light. Yet describing this regime requires a fully quantum treatment of the correlated electron-photon dynamics, which becomes computationally challenging for broadband, strongly squeezed fields. Here we solve the quantum-electrodynamical dynamics of a two-level system driven by bright squeezed vacuum in a converged multimode Hilbert space. Both the driving field and emitted harmonics are fully quantized, with the light-matter interaction treated nonperturbatively. This enables direct access to the multimode quantum state and its higher-order correlations beyond semiclassical sampling or perturbative descriptions. We show that squeezed-vacuum driving produces harmonic emission with qualitatively distinct second- and third-order photon correlations compared with coherent excitation. Moreover, back-action from the driven emitter strongly reshapes the incident squeezed field, generating pronounced Wigner-function negativities that evolve on attosecond timescales. Our results establish a fully quantum framework for broadband strong-field dynamics with squeezed light and provide a route to predicting and interpreting quantum-HHG experiments and their extension to more complex emitters.
High harmonic generation (HHG) is a highly nonlinear optical process in which radiation from a strong driving field is up-converted into its high-order harmonics. In atomic systems, this nonlinearity manifests itself through the intensity scaling of the emitted harmonics with the driving field strength. Despite the highly nonlinear nature of HHG, when the driving field is prepared in a classical Gaussian state and atomic depletion remains negligible, the quantum statistical properties of the generated harmonics retains classical Gaussian quantum statistics. Driving HHG with bright squeezed vacuum (BSV) light challenges this paradigm, as its enhanced field fluctuations can modify the statistical properties of the generated harmonics. In this work, we investigate the conditions under which BSV-driven HHG gives rise to non-classical Gaussian states, and identify the regimes where this Gaussian description breaks down. For bichromatic driving by a strong coherent field at frequency ωωω and a perturbative BSV field at 2ω2ω2ω, the even-harmonic response is approximately linear in the BSV quadrature, leading to non-classical multimode Gaussian entanglement in the harmonic field. We show that this state can be described as a distributed collective squeezed mode over the even-harmonic manifold, and characterize its covariance matrix, entanglement structure, and quantum teleportation fidelity as an operational benchmark. Our results highlight the potential of non-classically driven HHG as a platform for engineering Gaussian and non-Gaussian states of light in the extreme ultraviolet regime.