# Ultracold atoms dressed in light simulate gauge theories

**Our modern understanding of the physical world is based on gauge theories: mathematical models from theoretical physics that describe the interactions between elementary particles (such as electrons or quarks) and explain quantum mechanically three of the fundamental forces of nature: the electromagnetic, weak and strong forces. The fourth fundamental force, gravity, is described by Einstein’s theory of general relativity, which, although not yet understood in the quantum regime, is also a gauge theory. Gauge theories can also be used to explain the exotic quantum behavior of electrons in certain materials or the error-correcting codes that future quantum computers will need to operate reliably, and are the workhorse of modern physics. .**

In order to better understand these theories, one possibility is to realize them using artificial and highly controllable quantum systems. This strategy is called quantum simulation and is a special kind of quantum computing. It was first proposed by physicist Richard Feynman in the 80 years, more than fifteen years after he was awarded the Nobel Prize in Physics for his pioneering theoretical work on gauge theories. Quantum simulation can be seen as a quantum LEGO game where experimental physicists give reality to abstract theoretical models. They build them in the laboratory “quantum brick by quantum brick”, using very well-controlled quantum systems such as ultracold atoms or ions. After assembling a quantum LEGO prototype for a specific model, researchers can measure its properties very precisely in the lab and use their results to better understand the theory it mimics. Over the past decade, quantum simulation has been extensively exploited to study quantum materials. However, playing the quantum LEGO game with gauge theories is fundamentally more difficult. Until now, only electromagnetic drive could be studied in this way.

In a recent study published in Character, ICFO experimental researchers Anika Frölian, Craig Chisholm, Ramón Ramos, Elettra Neri and Cesar Cabrera, led by ICFO Professor ICREA Leticia Tarruell, in collaboration with Alessio Celi, theoretical researcher of the Talent program at the Autonomous University of Barcelona, were able to simulate for the first time a theory of gauge other than electromagnetism, using ultracold atoms.

The team set out to achieve in the laboratory a gauge theory belonging to the class of topological gauge theories , different from the class of dynamical gauge theories to which electromagnetism belongs.

In the language of gauge theory,: a particle of light which can propagate even in the absence of matter. However, in two-dimensional quantum materials subjected to very strong magnetic fields. As a result, electrons have very particular properties: they can only cross the edges of the material, in a way determined by the orientation of the magnetic field, and their cost becomes apparently fractional. This behavior is known as the Fractional Quantum Corridor effect and is described by the Chern-Simons gauge theory (named after the mathematicians who developed one of its key elements). The behavior of electrons restricted to a single edge of the material should also be described by a gauge theory, in this case called chiral BF, which was proposed in the years 90 but not performed in the lab until researchers at ICFO and UAB pulled it out. from the freezer.

To bring this topological gauge theory to life and simulate it in their experiment, the team used a cloud of atoms cooled to temperatures of around one billionth of a degree above absolute zero. As an atomic species they chose potassium because one of its isotopes has two states that interact with different forces and can be used as quantum bricks to build the BF chiral gauge theory. They then shined laser light to combine the two states into a single new one. This system, called “dressing the atoms with light”, made them acquire particular interactions whose strength and sign depended on the speed of the cloud. Finally, they created an optical waveguide that would restrict the movement of atoms to a line, and used additional lasers to kick the cloud around and make it move at different speeds along it.

Under normal conditions, letting the atoms evolve freely in the wave information would have caused the cloud to expand. However, with the dressing light on. As Ramon Ramos explains, “In our system, when atoms move to the right, their interactions are attractive and cancel out the behavior of atoms trying to expand. So what you actually see is that the shape of the cloud stays the same. In tactical terms, we made a soliton. But, if the atoms move to the left, those atoms expand like a normal gas. Observing atoms that behave differently when moving in opposite directions demonstrates that the system is chiral, that is, different from its mirror print. “When we first observed the effect of chiral interactions in our atomic cloud, we were not trying to simulate a gauge theory. But the data was so beautiful and intriguing that we felt we really needed to understand its meaning better. made me completely change the research plans of the team”, explains Leticia Tarruell.

The team quickly realized that their observations were linked to a short theoretical paper published ten years earlier, which proposed using an almost identical setup to study a modified kind of electromagnetism. However, the results of the experiment never seemed to meet their expectations. As Craig Chisholm recalls, initially, “the results we were getting didn’t seem to line up with theory at all. The challenge was to understand what regime you had to be in to really see the correct effect coming from the right place and to eliminate the effect coming from the wrong place.”

For the experimental team, the meaning of modified electromagnetism mentioned in the article was also very unclear. He was citing mathematical physics papers from the years 90, which made the connection to the gauge theories used to describe the Fractional Quantum Corridor effect. However, as Tarruell says, “For experimental atomic physicists like us, the content of this work was very difficult to grasp, because it was written in a language of mathematical physics completely different from ours. It was really frustrating to know that the answer to our questions was there, but we weren’t able to figure it out! It was then that we decided that we had to involve a theoretician.

## A very fruitful experimentation-theory collaboration

For theoretical physicist Alessio Celi, who had worked for many years in high energy physics and gravity before moving on to quantum simulation, reading the original content on gauge theory was easy. At the same time, he could understand the regime in which experiments could be performed and their challenges. He sat down with the experimental team and, after several discussions, came up with a model that could explain the experimental results correctly. As he explains, “the main problem we had was getting into the right frame. Once you knew where to look, it became an easy problem to solve.” Remarkably, there was a parameter regime where this model was exactly the topological gauge theory proposed years earlier to describe the behavior of electrons at the edges of Corridor materials fractional quantums.

“I think this project shows us the strength of interdisciplinary collaborations. The combination of experimental tools from ultra-low temperature physics and theoretical tools from high energy physics has made us all better physicists and resulted in the first quantum simulation of a topological gauge theory.” concludes Tarruell.

The team is already ready to explore the new avenues of research opened up by this project. Their goal now is to try to extend the experiments and theory from a line to a plane, which would allow them to observe the fractional quantum Hall effect without the need for quantum material. This would provide access to exotic quasi-particles, called anyons, which could in the future be used for more robust forms of quantum computing.