Topology in time-evolving quantum systems*

Topology in time-evolving quantum systems

Topological invariants robustly classify gapped quantum systems in equilibrium, and phenomena such as the quantized Hall effect---the progenitor of the von Klitzing constant---are macroscopic refections of these invariants.

In addition to dimensionality, the presence or absence of symmetries determines the possible topological invariants. Thus, these invariants remain constant provided that no gaps close and no symmetries are added or removed. For this reason, one might expect the topology of a dynamical quantum system to be similarly robust; this expectation is untrue. Instead as a system undergoes far from equilibrium evolution symmetries come and go, allowing the topology to change as well. We experimentally study these dynamics with an ultracold atomic BEC in a 1D bipartite lattice.