Geometrical Rabi oscillations in non-Abelian systems

Topological phases of matter became a new standard to classify quantum systems in many cases, yet key quantities like the quantum geometric tensor providing local information about topological properties are still experimentally hard to access, especially in non-Abelian systems when states are degenerate and the quantum geometric tensor has a non-Abelian form. We propose protocols to determine the quantum geometric tensor in non-Abelian quantum systems. We show theoretically that for a weak resonant driving of the local parameters the coherent Rabi oscillations and their frequencies are related to the non-Abelian quantum geometric tensor. Our schemes suggest also a way to prepare eigenstates of the quantum metric, a task that is difficult otherwise in a degenerate subspace.