In the last years, topology has emerged as a central notion in condensed matter physiscs, allowing to classify and discover phases with novel properties, with applications ranging from material design to quantum technologies. Although non-interacting topological phases have been extensively explored using cold-atom quantum simulators, the more interesting but also challenging interacting cases have been less studied experimentally. Our goal here is two-fold. On the one hand, we are interested in extending the capabilities of cold-atom systems to control and measure strongly-correlated topological states beyond the possibilities offered by traditional solid-state experiments. For example, we proposed how to implement phonon-matter interactions in static optical lattices using a second atomic species, allowing to directly observe topological Peierls transitions and fractionalized topological defects. We also expanded the cold-atom quantum simulation toolbox by showing how long-range interactions mediated by light fermionic atoms can be easily tuned experimentally, allowing to prepare topological phases induced by magnetic frustration.
On the other hand, we have investigated how atomic systems allow us to design novel topological phenomena without a counterpart in natural materials, arising, for instance, from the interplay between symmetry breaking and symmetry protection. In a similar spirit, we have explored novel topological phases driven by dipolar atomic interactions, including higher-order topological quantum paramagnets and topological critical points. Finally, we have shown how higher-order topological phases can also appear in atom-cavity systems, where we uncovered for the first time a 2D bosonic Peierls transition. At the moment, we are investigating how long-range Rydberg interactions give rise to deconfined quantum criticality, and how this phenomenon could be observe in tweezer-array experiments.
Lattice Gauge Theories (LGTs), invariant under local transformations, form the mathematical framework behind the Standard Model of Particle Physics, as well as serving as effective descriptions of topologically-ordered states in condensed matter. Many open questions, such as the thermalization of a quark-gluon plasma, remain unsolved due to the limitations to simulate these theories in certain regimes using classical computers. These include non-equilibrium dynamics as well as finite fermionic densities, regimes where quantum simulators could show an advantage. In our group, we are exploring how state-of-the-art cold-atom quantum simulators could be harnessed to investigate particle physics phenomenology in low-dimensional systems.
In this direction, we showed how ultracold atomic mixtures can be used to probe confinement-deconfinement phase transitions between fractionally-charged quasi-particles, akin to quarks in quantum chromodynamics. We also employed tools from quantum information to investigate fermionic LGTs, using entanglement properties and tensor networks to uncover their topological structure, as well as their unconventional non-equilibrium dynamics. Finally, in a recent collaboration with Quera Computing and the Lukin group at Harvard, we used a quantum simulator based on Rydberg atom arrays to experimentally observe dynamical string breaking on a (2+1)D U(1) LGT. Currently, we are exploring how to simulate phenomena driven by multi-body plaquette interactions, such as topological spin liquids or non-equilibrium radiation dynamics, by investigating efficient encodings in various geometries, as well as with dual-species arrays.