We collaborate with our good friends in Mike Zaletel’s group to explore topological order: An intrinsically quantum mechanical phenomenon, that has time-and-again stirred excitement and intrigue in the realm of condensed matter physics. A distinct departure from the traditional Landau-Ginzburg paradigm, topological order extends beyond symmetry breaking, introducing a new paradigm of order without symmetry, rooted in global and not local properties of a system.

Topological ordered states are characterized by ground-state degeneracy and excitations that obey anyonic statistics, far removed from the bosonic or fermionic particles that we encounter in our everyday world. This exotic ordering is immune to local perturbations, rendering topologically ordered states incredibly robust. The most famed example of topological order is perhaps the fractional quantum Hall effect, where seemingly conventional electrons coalesce to form emergent fractional particles with braiding statistics.

Diving deeper into the topic, several key subtopics underpin the field of topological order. They range from the study of quantum spin liquids, a class of disordered states where topological order can emerge, to topological insulators, materials that are insulating in the bulk but possess conducting edge states due to their topological nature.

One of the significant avenues of research undertaken by our group is the study of the Dirac Spin Liquid (DSL). This enigmatic phase, which resides at the brink of quantum criticality, is described by a theory known as conformal field theory (CFT). Exhibiting a range of captivating properties, DSLs offer a fertile ground for the exploration of topological order. Through fruitful collaborations with experimental groups, we are harnessing the power of Rydberg tweezer array platforms to engineer such tantalizing phases of matter.

Simultaneously, our focus also extends to Chiral Spin Liquids (CSLs). Through our research, we have identified a CSL phase in a Heisenberg-type model on a breathing Kagome lattice. Intriguingly, this CSL phase emerges within a specific range of breathing strength, a parameter that can delicately tune between different phases.

Leveraging the novel phenomenon known as the 3-spin Rashba effect, we are able to construct systems that exhibit robust topological order. This effect allows us to design topologically ordered phases by integrating spin-orbit coupling, expanding the possibilities for the exploration of topological states.

Furthermore, our group has pioneered a novel protocol for dynamically generating topological order known as Floquet flux attachment (FFA). We apply this protocol to a bosonic hopping model defined on a hexagonal lattice, and our findings have been astounding. We’ve observed a bosonic analogue of the integer quantum Hall effect, a significant step forward in our understanding of topological phases.

To conclude, the journey into the realm of topological order unveils an extraordinary world where quantum mechanics takes center stage, bringing forth a novel understanding of order in quantum systems. The work of our research group, from the study of Dirac Spin Liquids to the exploration of dynamic topological order generation, contributes to the ever-expanding knowledge frontier of this captivating topic. Our continued pursuit promises to push the boundaries of current scientific understanding and pave the way for new technological applications.