How to generate high harmonics with quantum light despite decoherence

The shortest light pulses to date are just a few attoseconds long. They are so much shorter than the blink of an eye that our brains have a difficult time trying to imagine them. But that is precisely what allows them to investigate extremely fast electronic processes ubiquitous to life on Earth; processes that occur when chemical reactions unfold or when biological molecules transfer energy from one to another.

High-harmonic generation (HHG) –the generation of high-order harmonics of a given light pulse when it is absorbed by an atom– is the physical precursor of the shortest light pulses to date. While HHG has been extensively studied when driven by a classical light source, quantum light has recently been shown to have this capacity as well. But does the quantumness remain after harmonic generation? That is one of the most important questions currently under investigation. 

There are many different types of quantum light, however, each with distinct properties. Bright squeezed vacuum (BSV) is an especially interesting one because, as the name suggests, it exhibits squeezing – a purely quantum feature that reduces noise in one observable (for instance, position) at the expense of increasing noise in its conjugate (momentum) – and, at the same time, carries a high number of photons. BSV is therefore suitable for inducing strong light-matter interactions, like those needed to produce high-harmonic generation.

So far, theoretical investigations of BSV-driven HHG have only considered the interaction with a single atom. But for assessing the real-world applicability of BSV light sources, the much more realistic situation of a medium full of atoms must be considered. This is precisely the scenario that ICFO researchers, Dr. Javier Rivera-Dean and Dr. Philipp Stammer, led by Prof. Dr. Maciej Lewenstein, have theoretically investigated, in collaboration with the Institute of Electronic Structure & Laser in Crete, the Technische Universität Wien, the Max-Born-Institut für Nichtlineare Optik und Kurzzeitspektroskopie, ELI ALPS, and the Center for Quantum Science and Technologies (FORTH-QuTech).

Published in Nature Communications, the study reveals that high-harmonic generation driven by BSV may be obscured by atomic ionization and photon losses –collateral effects of BSV propagation through the medium. This degrades the quantum features of the radiation, limits its maximum propagation length, and decreases the number of emitted harmonics.

Fortunately, these decoherence effects are not an insurmountable obstacle. “We demonstrate that, under the appropriate conditions, BSV can preserve its quantumness and efficiently generate harmonics with quantum properties,” says Prof. at ICFO Maciej Lewenstein, long-time expert in HHG who was involved in the study. The conditions include significantly reducing photon losses from atomic ionization and carefully controlling BSV intensity, so that decoherence is minimized while preserving BSV’s ability to generate high harmonics.

The researchers are now planning to determine the precise conditions for experimental realization. Implementing the proposed theoretical framework would further deepen our understanding of BSV propagation through media, which in turn would bring the fields of ultrafast and quantum physics closer together.

Reference:

Rivera-Dean, J., Kanti, D., Stammer, P., Carlström, S., Tsatrafyllis, N., Ivanov, M. Yu, Lewenstein, M., & Tzallas P., Propagation effects in high harmonic generation media driven by bright squeezed vacuum light. Nat Commun 17, 8457 (2026).

DOI: https://doi.org/10.1038/s41467-026-75173-8

Acknowledgements:

The group of P.T. at FORTH acknowledges the Hellenic Foundation for Research and Innovation (HFRI) and the General Secretariat for Research and Technology (GSRT) under grant agreement CO2toO2 Nr.:015922, the European Union’s HORIZON-MSCA-2023-DN-01 project QU-ATTO under the Marie Skłodowska-Curie grant agreement No 101168628 and ELI–ALPS. The ELI ALPS project (GINOP-2.3.6-15-2015-00001) is supported by the European Union and co financed by the European Regional Development Fund. H2020-EU research and innovation program under the Marie Skłodowska-Curie (No. 847517). ICFO-QOT group acknowledges support from: European Research Council AdG NOQIA; MCIN/AEI (PGC2018-0910.13039/501100011033, CEX2019-000910 - S/10.13039/501100011033, Plan National STAMEENA PID2022-139099NB, project funded by MCIN/AEI/10.13039/501100011033 and by the “European Union NextGenerationEU/PRTR" (PRTR - C17.I1), FPI); project funded by the EU Horizon 2020 FET-OPEN OPTOlogic, Grant No 899794, QU-ATTO, 101168628), Fundació Cellex; Fundació Mir-Puig; Generalitat de Catalunya (European Social Fund FEDER and CERCA program. P.S. acknowledges funding from the European Union’s Horizon 2020 research and innovation program under the Marie Skłodowska-Curie grant agreement No 847517. M.I. and S.C. acknowledge support of the Project No. 545591821 "GENIOUS" and Project No. 560535838 "Qu-NOIR". J. R.-D. acknowledges funding from UK Engineering and Physical Sciences Research Council (EPSRC) Funding, Grant UKRI2300 - Attosecond Photoelectron Imaging with Quantum Light (APIQuL).