AN OPTICAL PLAQUETTE: MINIMUM EXPRESSIONS OF TOPOLOGICAL MATTER

Abstract

Topological matter is an unconventional form of matter: it exhibits a global hidden order which is not associated with the spontaneous breaking of any symmetry. The defects of this exotic type of order are anyons, quasiparticles with fractional statistics. Moreover, when living on a surface with non-trivial topology, like a plane with a hole or a torus, this type of matter develops a number of degenerate states which are locally indistinguishable and could be used to build a quantum memory naturally resistant to errors. Except for the fractional quantum Hall effect there is no experimental evidence as to the existence of topologically ordered phases, and it remains a huge challenge to develop theoretical techniques to look for them in realistic models and find them in the laboratory. Here we show how to use ultracold atoms in optical lattices to create and detect different instances of topological order in the minimum nontrivial system: four spins in a plaquette. By combining different techniques we show how to prepare these spins in mimimum versions of topical topological liquids like resonant valence bond or Laughlin states, probe their fractional quasiparticle excitations, and exploit them to build a mini-topological quantum memory.