A team of researchers and OPTOlogic team members theoretically prove that the emitted light after a high harmonic generation (HHG) process is not classical, but quantum and squeezed. The study unveils the potential of HHG as a new source of bright entangled and squeezed light, two inherent quantum features with several cutting-edge applications within quantum technologies.
High Harmonic Generation: A Non-linear Phenomenon
High harmonic generation is a highly non-linear phenomenon where a system (for example, an atom) absorbs many photons of an incoming laser and emits a single photon of much higher energy.
The Significance of HHG in Attoscience
This process is crucial for attoscience (the science of the ultrafast processes), since it generates attosecond pulses of ultraviolet light, an essential ingredient for many applications within the field.
Challenges in Understanding HHG
In this regime, HHG experiments can be explained by means of semi-classical theory with great success: matter (the electrons of the atoms) is treated quantum-mechanically, while the incoming light is treated classically. According to this approach, unsurprisingly the emitted light turns out to be classical, something which was in agreement with all previous observations.
However, physicists tend to feel uncomfortable when using two different theories (quantum and classical) to describe the same phenomenon. During the last years, the efforts to understand HHG from a full quantum optical perspective have kept growing, but a more general description to show different aspects of the quantum nature of the outgoing radiation remained an elusive milestone.
A Quantum Perspective on HHG
Now, ICFO researchers Philipp Stammer, Javier Rivera, Dr. Javier Argüello led by Prof. ICREA Maciej Lewenstein, together with researchers from other institutions (the Aarhus University, University of Crete, ELI-ALPS, Guadong Technion-Israel Institute of Technology) have theoretically described high-harmonic generation using just quantum physics and, for the first time, they have found squeezing and entanglement features simultaneously in the emitted light. The study, published in Physical Review Letter, explains why previous classical descriptions were not in disagreement with the observations and, at the same time, unveils a new method to generate quantum optical resources with squeezing and massive entanglement in a new bright frequency regime, two features of current technological interest.
A new method to generate entanglement and squeezing in light
Entanglement stands as a cornerstone of quantum physics, representing one of its defining characteristics. Simply put, when two particles become entangled, measuring one of them affects the outcomes obtained from measuring the other, even when these particles are arbitrarily separated, leading to what is known as “non-local correlations”. Nowadays, the scientific community recognizes entanglement not merely as a curious phenomenon, but as playing a pivotal role within quantum technologies. Hence, the quantum community actively seeks methods to generate entanglement, not only between pairs of particles, but also among a greater number of them (referred to as “multipartite entanglement”).
Quantum Nature of Squeezed States
Another defining quantum feature is the unavoidable noise when one measures some specific pairs of properties of a physical system (for example, the position and the momentum). For quasi-classical states, also called “coherent states”, the amount of uncertainty is equal for both quantities and its product is minimal. However, with squeezed states one can decrease the noise of one property (for instance, the position) at the expense of increasing the other one (the momentum), while its product is still kept at its lowest value. This feature, which is a direct manifestation of the quantum nature of squeezed states, makes them desirable for several quantum technology applications.
Insights from Traditional Quantum Optical Models
Traditional theoretical quantum optical models of HHG described the modes of the resulting light beam (that is, the different frequencies at which the electromagnetic field oscillates) as coherent states without entanglement, independent from each other. In this context, the recently published paper has brought two valuable insights.
Neglected States and Quantum Features
In the first place, it points out that previous studies neglected the states the electron can occupy during HHG process and that the final state of light was not showing any quantum features because of that. Even though this assumption was reasonable in most experiments, it was not providing the most general explanation of the phenomenon.
Quantum Final State of Light
Secondly, researchers improved the whole calculation by explicitly taking into account the different states the electron can occupy. The resulting final state of light revealed that the modes are squeezed, contrasting with coherence, and demonstrating multipartite entanglement instead of independence. ICFO researchers indicate how this situation, although not standard for attosecond experiments, could be relatively easy to engineer in the laboratory.
Potential of HHG for Quantum Technologies
All in all, the team has demonstrated that, under specific – but achievable – experimental conditions, one can utilize HHG as a source of squeezed light with multipartite entanglement. Philipp Stammer, the first author of the paper, explains that “massive entangled states are crucial for optical quantum technologies, opening up a new research frontier aimed at generating extreme light fields with quantum properties.” Potential applications include quantum spectroscopy, nonlinear optics, or quantum metrology, where entanglement and squeezing offer advantages over classical lasers. Now, the experimental realization of their discovery is necessary to fully harness this new source of quantum light.
Reference article
Stammer, P., Rivera-Dean, J., Maxwell, A. S., Lamprou, T., Argüello-Luengo, J., Tzallas, P., Ciappina, M. F., Lewenstein, M. (2024). Entanglement and Squeezing of the Optical Field Modes in High Harmonic Generation.Physical Review Letters, 132(14), 143603. https://doi.org/10.1103/PhysRevLett.132.143603
