Demonstration of chiral interactions in a tunable quantum system

In modern physics, our understanding of the world is based on gauge theories: mathematical models of theoretical physics that describe the interactions between elementary particles (such as electrons or quarks) and quantumly explain three of the fundamental forces of life. nature: electromagnetic, weak and strong. The fourth fundamental force, gravity, is described by Einstein’s theory of general relativity, which is a classical gauge theory since we do not yet have a theory that unifies quantum mechanics with gravity. Gauge theories can also be used to explain the exotic behavior of electrons in certain quantum materials, or the error-correcting codes that future quantum computers will need to function reliably. For this reason, gauge theories are essential to understand modern physics.

To better understand these theories, one possibility is to test them using other quantum systems. This strategy is called quantum simulation and is a special type of quantum computing. It was first proposed by the American physicist Richard Feynman in the 1980s, more than fifteen years after he received the Nobel Prize in Physics for his theoretical work on gauge theories. Quantum simulation can be understood as a game of quantum LEGO in which experimental physicists bring abstract theoretical models to life. They build them in the laboratory “quantum piece by quantum piece”, using very well controlled quantum systems, such as ultracold atoms or ions. After assembling a quantum LEGO prototype for a particular model, researchers can measure its properties with great precision in the lab and use their results to better understand the theory it mimics. During the last decade, quantum simulation has been intensively exploited to investigate quantum materials. However, “playing” quantum LEGO with gauge theories is fundamentally more difficult, and until now only the electromagnetic force has been investigated in this way.

In a recent study, researchers Anika Frölian, Craig Chisholm, Ramón Ramos, Elettra Neri and César Cabrera, from the Institute of Photonic Sciences (ICFO) in Castelldefels (Barcelona), led by ICFO ICREA professor Leticia Tarruell, in collaboration with Alessio Celi, a researcher in the Talent program at the Autonomous University of Barcelona (UAB), have been able to simulate for the first time a different gauge theory of electromagnetism, using ultracold atoms.

The team set out to reproduce in the laboratory a gauge theory that falls within the class of topological gauge theories, different from the class of dynamic gauge theories to which electromagnetism belongs.

In the language of gauge theory, the electromagnetic force between two electrons arises when they exchange a photon: a particle of light that can propagate even in the absence of matter. However, in two-dimensional quantum materials subjected to strong magnetic fields, the photons exchanged for the electrons behave as if they are extremely heavy and can only move while bound to matter. This gives the electrons very peculiar properties: they can only flow across the edges of the material, in a direction that is fixed by the orientation of the magnetic field, and their charge becomes apparently fractional. Such behavior is known as the fractional quantum Hall effect, and is described by the Chern-Simons gauge theory (named after the mathematicians who developed one of its key elements). The behavior of the electrons at the edge of the material is also described by a gauge theory, which is called chiral BF. This theory was proposed in the 1990s, but nobody had put it into practice in the laboratory until ICFO and UAB researchers took it out of the freezer.

To realize this topological gauge theory and simulate it in their experiment, the team used a cloud of atoms cooled to temperatures a few billionths of a degree above absolute zero. They chose potassium as the atomic species, because one of its isotopes has two states that interact with different strength and can be used as quantum building blocks to build the chiral BF gauge theory. They then applied laser light to combine the two states into a new one. This technique, called “dressing atoms in light,” caused the atoms to acquire peculiar interactions whose strength and sign depended on the speed of the cloud. Finally, they created an optical waveguide that constrained the atoms’ motion to a line, and used additional lasers to hit the cloud so that it moved at different speeds along the waveguide.

Under normal conditions, by allowing the atoms to evolve freely in the optical waveguide, the potassium cloud should have started to expand immediately. However, the “dress light” completely changed the behavior of the atoms, as the researchers saw when imaging the cloud in the lab. As Ramón Ramos explains, “in our system, when the atoms move to the right, their interactions are attractive and cancel out the behavior of the atoms trying to expand. So what you actually see is that the shape of the cloud follows being the same. In technical terms, we make a soliton. But, if the atoms move to the left, these atoms expand like a normal gas.” The fact that the atoms behave differently when moving in opposite directions shows that the system is chiral, that is, different from its mirror image. “When we first looked at the effect of chiral interactions in our atomic cloud, we weren’t trying to simulate a gauge theory. But the data was so beautiful and intriguing that we thought we needed to better understand what was going on. It completely changed the research agenda.” of the team,” says Leticia Tarruell.

The team quickly understood that their observations were related to a theoretical study published ten years earlier, which proposed using a nearly identical set-up to study a modified type of electromagnetism. However, the results of the experiment were different from those expected. As Craig Chisholm recalls, at first “the results we were getting didn’t seem to match the theory at all. The challenge was understanding what regimen you had to be in to actually see the right effect and remove the effects from the wrong places.”

For the experimental team, the meaning of the modified electromagnetism that was mentioned in that study was also not very clear. It cited mathematical physics studies from the 1990s, which explained the model in much more detail and connected it to the gauge theories used to describe the fractional quantum Hall effect. However, as Tarruell says, “For experimental atomic physicists like us, the content of those articles was very difficult to understand, because they were written in a language of mathematical physics completely different from ours. It was really frustrating to know that the answer to our questions it was there, but we weren’t able to understand it! That’s when we decided to ask a theoretical physicist for help.”

For Alessio Celi, who worked for many years in theoretical high-energy physics and gravity before turning to quantum simulation, reading the original articles on gauge theories was relatively easy. At the same time, he was able to discuss with the ICFO team and understand the regime in which the experiments could be carried out and its challenges. After several failed attempts, he proposed a model that adequately explained the results observed in the laboratory. As he explains, “The main problem we had was getting into the right framework. Once we understood where to look, the problem became easy to solve.” Surprisingly, a parameter regime existed in which this model was exactly the topological gauge theory proposed 30 years earlier to describe the edges of fractional quantum Hall materials.

Artist’s rendering of chiral interactions in an ultracold cloud of atoms clad in light, causing it to behave differently from a version definable as its “mirror image.” This gives away the representation of a topological gauge theory. (Image: ICFO/Scixel. CC BY-NC)

“I think this project shows us the interest of interdisciplinary collaborations. Combining experimental methods of ultra-low temperature physics and theoretical ideas of high energy physics has made us all better physicists. And we have achieved the first quantum simulation of a gauge theory topology”, concludes Tarruell.

The new study is titled “Realizing a 1D topological gauge theory in an optically dressed BEC.” And it has been published in the academic journal Nature.

Now, the team is preparing to explore the new lines of research opened up by this project. Their goal is to try to extend experiments and theory from a line to a plane, which would allow them to observe the fractional quantum Hall effect without the need for a quantum material. In this way, they could create exotic quasiparticles, called anions, in a very controlled way, which in the future could be used for more robust forms of quantum computing. (Source: ICFO)