Topology in out of equilibrium strongly correlated systems

Topologically protected states of matter have sparked tremendous interest in the recent decades.

They require new ways to classify quantum phases and bring abstract concepts defined in mathematics of topology to daylight in the form of integer or fractionally quantized response.

Being based on nonlocal quantities, they are extremely robust and constitute promising candidates for the fault-tolerant quantum computation.

Fractional quantum Hall (FQH) states –an intrinsically strongly correlated phenomena– prove to be even more exotic with the possibility of harboring nonabelian anyons.

Although the initial studies on topology have focused on equilibrium properties, life is a dynamical system and our technology relies on non-equilibrium physics.

Meanwhile following Feynman’s revolutionary idea of quantum simulations, ultracold quantum gases have been firmly established as clean and controllable platforms to investigate condensed matter models.

Not only several topological systems like the Nobel-cited Haldane model have been observed for the first time in cold atoms, their success has extended beyond equilibrium.

Even though the recent studies on out-of-equilibrium topological dynamics reveals new classification schemes and new connections between topological invariants, so far they remain restricted to single-particle physics.

At this milestone highlighting the timeliness of this project, we will pioneer theoretical investigations into the uncharted territory of the out-of-equilibrium response of strongly correlated topological systems.

Equipped with our expertise in non-equilibrium phenomena in single-particle topology, we will conduct analytical calculations supported by numerics to uncover the many-body analogues.

This will include classification of out-of-equilibrium topological invariants and introduction of novel quench techniques into the study of FQH states, all the while bridging the gap with experiments by identifying system specific protocols to observe them.