I am still alive, and there are big news for the project – news that are over one month overdue, but I was so focused on writing grant proposals that I couldn’t find time to write about it. Long story short: we finished the preprint of our spin liquid paper (https://arxiv.org/pdf/2512.05630). This work originated much before I came to Darrick Chang’s group, thus I am only a third author, but I did my part within the QUINTO project.
What is it about? Basically, atoms can make photons interacting with each other. In general, the interaction of many simple objects can lead to unusual, counterintuitive behavior. For example, many interacting electrons can form fractional quantum Hall states, and many interacting spins can form spin liquids – both being complicated quantum states, whose unusual properties manifest themselves with emergence of “quasiparticles” – objects that behave like individual particles, although in reality they are collective states of many particles. These quasiparticles can behave unlike any elementary particle found in nature – for example, they can have a fraction of single electron charge, and be neither bosons nor fermions but “anyons”. In the paper, we ask: can we observe similar effects with atoms and light?
We just came back from the "Light-Matter Interactions and Collective Effects" workshop in Paris. We heard some interesting talks on how quantum emitters (not only atoms, but also e.g. molecules and quantum dots) interact with each other and how people try to arrange them into arrays (like, putting chains of molecules inside a carbon nanotube). Darrick (my boss and supervisor of the project) gave a talk on spin liquids, while I presented a poster on fractional quantum Hall states in atom arrays.
Our second approach to create a topological order in atom arrays is to focus on a different kind of topological order: fractional quantum Hall (FQH) states. These were first discovered in condensed matter. It is possible to confine electrons to move in two-dimensions only (such as in the 2D material graphene or in so-called metal-oxide-semiconductor transistors) and then put them in a strong perpendicular magnetic fields. The electrons then move in circles (so-called “cyclotron motion”), but since they are quantum objects, only some values of radius are allowed. Thus, the energy can only take certain fixed values (we call them “Landau levels”). There are however different possibilities of an electron having the same energy, because the center of the orbit can be located in different places – we say that Landau levels are “degenerate”. And when there is degeneracy, the interaction between electrons becomes very important. Without interactions, there are many possible ways of arranging electrons within a Landau level, all with the same energy. In the presence of interactions, some arrangements become preferred – and it turns out those correspond to topological orders known as the FQH states. Such systems host anyons which look like fractions of an electron – like somehow the electron split into several parts.
On the left: a hexagonal array of atoms (red balls with small arrows arranged in the xy plane) in a magnetic field (big arrow in the z direction). On the right: the energy levels of each atom: black bar on the bottom denoting the ground state, dashed black line denoting the frequency of atomic transition, and two bars denoting excited states: red bar below the dashed line and blue bar above the dashed line. The distance between the dashed line and each of the bar is mu*B. Each of the excited states is connected with the ground state with double-sided arrow in respective colour, denoting the fact that it can absorb and emit circularly polarized light (red and blue correspond to opposite circular polarizations).The figure comes from the following paper: https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.119.023603