Researchers theoretically unveil high harmonic generation as a new source of squeezed quantum light

A team of researchers, some of them Dynamite 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.

Quantum Entanglement in High-Harmonic Generation

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.

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. 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.

Now, ICFO researchers Philipp Stammer, Javier Rivera, Dr. Javier Argüello led by Prof. ICREA Maciej Lewenstein (Dynamite project coordinator), 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 lies at the heart of quantum physics as one of its defining features. Simply put, when two particles entangle, measuring one influences the results of measuring the other. Surprisingly, this holds true even when the particles separate significantly, causing “non-local correlations”. Today, entanglement isn’t just a curious phenomenon; the quantum community widely recognizes its crucial role in quantum technologies. As a result, researchers actively seek ways to generate entanglement not only between two particles but among many (“multipartite entanglement”).

Quantum physics also features unavoidable noise when measuring specific pairs of properties in a physical system (e.g., position and momentum). Quasi-classical states, or “coherent states,” have equal uncertainty for both quantities, and their product is minimal. However, squeezed states allow us to decrease the noise of one property (e.g., position) by increasing the noise of the other (e.g., momentum), while their product remains minimal. This direct manifestation of the quantum nature of squeezed states makes them attractive for various quantum technology applications.

Quantum Insights in High-Harmonic Generation

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.

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.

Secondly, researchers improved the whole calculation by explicitly taking into account the different states the electron can occupy. The resulting final state of light turned out to be quantum in the sense that the modes are squeezed, as opposed to coherent; and that they are no longer independent, but show multipartite entanglement instead. ICFO researchers indicate how this situation, although not standard for attosecond experiments, could be relatively easy to engineer in the laboratory.

All in all, the team has proved that, under specific -but feasible- experimental conditions, one can use HHG as a source of squeezed light with multipartite entanglement. The first author of the paper, Philipp Stammer, explains that “massive entangled states are important for optical quantum technologies, and open a new field of research, which is generating extreme light fields with quantum properties”. The applications could include quantum spectroscopy, non-linear optics or quantum metrology, where entanglement and squeezing can provide an advantage over classical lasers. Now, an experimental realization of their discovery is needed to be able to exploit this new source of quantum light in all its potential.

Original 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