When light interacts with matter, for example, when a laser beam hits a
two-dimensional material like graphene, it can substantially change the
behavior of the material. Depending on the form of interaction between light
and matter, some chemical reactions appear differently, substances turn
magnetic or ferroelectric or begin to conduct electricity without any
losses. In particularly thrilling cases, an actual light source may not even
be necessary because the mere possibility for light to exist, i.e., its
quantum equivalent, the photons, can change the behavior of matter.
Theoretical scientists try to describe and predict these fascinating
phenomena because they could be crucial in the development of new quantum
technologies.

However, calculating quantum light-matter interactions not only eats up
enormous amounts of time and computing power—it also becomes very
cumbersome. Describing the strong interaction between a realistic material
with photons easily consumes thousands of Euros. Now scientists from the
Theory Department of the Max Planck Institute for the Structure and Dynamics
of Matter (MPSD) in Hamburg have found a way to simplify some of these
calculations. Their work, now published in PNAS, provides a significant step
towards integrating the quantum nature of light into modern-day devices.

"Imagine you are given a set of construction bricks to build a model of the
famous Berlin Gate," says Christian Schäfer, lead author of the study.
"Intuitively, we start placing the stones on top of each other to resemble
the shape of the gate, but with each stone, the construction becomes more
unstable and expensive. Similarly, because we sometimes have to consider
many hundreds of photons, our calculations can become overwhelmingly complex
and the cost of our theoretical predictions spirals very quickly. In fact,
this cost is so prohibitive that predicting the full interplay between many
photons and realistic molecules is de facto impossible to compute, even on
the fastest and biggest existing super-computers."

Now, the MPSD team, based at the Centre for Free-Electron Laser Science
(CFEL) in Hamburg, has found a simple but brilliant way to circumvent this
problem. By reshaping the equation so that the material part itself accounts
for the quantum mechanical uncertainty of the light, far fewer additional
photons are needed to describe the combined system of quantum light and
matter.

"In effect, we built the Berlin Gate by carving it from the first stone to
arrive at approximately the same result," explains Schäfer. "This allows us
to describe the quantum interaction between light and matter with very
little additional cost compared to just considering the material."

To take an example, when the interaction between light and matter becomes so
strong that both systems become truly interlacing, each possible
configuration of the light-field can demand the consideration of hundreds of
photons. The new approach can capture most features of this extreme limit
without the need to consider any photon at all. Adding just a few photons is
then enough to provide the full picture.

The method yields considerable savings in computing time and provides a
framework for scientists to predict the interplay between quantum light and
matter for realistic systems in situations that were prohibitive to
simulate. "Our approach can serve as a solid foundation for future
developments, providing a path to integrate quantum light more strongly into
chemistry, material design and quantum technology," Schäfer says. "Within
the general formalism many novel effects might still await discovery," adds
MPSD Theory director Angel Rubio. "The engineering of materials and
molecular complexes through light is becoming a reality. We are embarking on
a long and exciting journey to explore its full potential implications in
novel quantum technologies and the team's work provides an important step
along this path."

## Reference:

Christian Schäfer et al, Making ab initio QED functional(s): Nonperturbative
and photon-free effective frameworks for strong light–matter coupling,
Proceedings of the National Academy of Sciences (2021).
DOI: 10.1073/pnas.2110464118

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