Evidence of the Quantum Optical Nature of High-Harmonic Generation

High-harmonic generation is a light up-conversion process occurring in a strong laser field, leading to coherent bursts of extreme ultrashort broadband radiation [Lewenstein et al., Phys. Rev. A 49 , 2117 (1994)]. As a new perspective, we propose that ultrafast strong-field electronic or photonic processes such as high-harmonic generation can potentially generate nonclassical states of light well before the decoherence of the system occurs [Gorlach et al., Nat. Commun. 11 , 4598 (2020); Stammer et al ., Phys. Rev. Lett. 128, 123603 (2022)]. This could address fundamental challenges in quantum technology such as scalability, decoherence, or the generation of massively entangled states [Lewenstein et al., Luca Argenti Michael Chini, 27 (2024)]. Here, we report experimental evidence of the nonclassical nature of the harmonic emission in several semiconductors excited by a femtosecond infrared laser. By investigating single- and double-beam intensity cross-correlation [Loudon, Rep. Prog. Phys. 43 , 913 (1980)], we measure characteristic nonclassical features in the single-photon statistics. We observe two-mode squeezing in the generated harmonic radiation, which depends on the laser intensity that governs the transition from super-Poissonian to Poissonian photon statistics. The measured violation of the Cauchy-Schwarz inequality realizes a direct test of multipartite entanglement in high-harmonic generation [Wasak, Phys. Rev. A 90 , 033616 (2014)]. This result is supported by the theory of multimodal detection and the Hamiltonian from which the effective squeezing modes of the harmonics can be derived [Gonoskov et al., Phys. Rev. B 109, 125110 (2024); Christ et al. New J. Phys. 13 , 033027 (2011)]. With this work, we show experimentally that high-harmonic generation is a new quantum bosonic platform that intrinsically produces nonclassical states of light with unique features such as multipartite broadband entanglement or multimode squeezing. The source operates at room temperature, using standard semiconductors and a standard commercial fiber laser, opening up new routes for the quantum industry, such as optical quantum computing, communication, and imaging.