Ultracold atoms dressed by 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, while 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 correction codes that future quantum computers will need to work 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 constitutes a special type of quantum computing. It was first proposed by the physicist Richard Feynman in the 80s, more than fifteen years after being 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 one quantum LEGO prototype for a specific model, the researchers can measure its properties very precisely in the lab, and use their results to understand better the theory that it mimics. During the last decade, quantum simulation has been intensively exploited to investigate quantum materials. However, playing the quantum LEGO game with gauge theories is fundamentally more challenging. Until now, only the electromagnetic force could be investigated in this way.
In a recent study published in Nature, ICFO experimental researchers Anika Frölian, Craig Chisholm, Ramón Ramos, Elettra Neri, and Cesar Cabrera, led by ICREA Prof. at ICFO Leticia Tarruell, in collaboration with Alessio Celi, a theoretical researcher from the Talent program at the Autonomous University of Barcelona, were able to simulate a gauge theory other than electromagnetism for the first time, using ultracold atoms.
A gauge theory for very heavy photons
The team set out to realize 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 gauge theory language, the electromagnetic force between two electrons arises when they exchange a photon: a particle of light that can propagate even when matter is absent. However, in two-dimensional quantum materials subjected to very strong magnetic fields, the photons exchanged by the electrons behave as if they were extremely heavy and can only move as long as they are attached to matter. As a result, the electrons have very peculiar properties: they can only flow through the edges of the material, in a direction that is set by the orientation of the magnetic field, and their charge becomes apparently fractional. This behavior is known as the fractional quantum Hall effect, and is described by the Chern-Simons gauge theory (named after the mathematicians that developed one of its key elements). The behavior of the 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 90s but not realized in a laboratory until the ICFO and UAB researchers pulled it out of the freezer. More