Geometrical Rabi oscillations and Landau-Zener transitions in non-Abelian systems

Year: 2021

Authors: Weisbrich H., Rastelli G., Belzig W.

Autors Affiliation: Univ Konstanz, Fachbereich Phys, D-78457 Constance, Germany; Univ Trento, INO CNR BEC Ctr, I-38123 Povo, Italy; Univ Trento, Dipartimento Fis, I-38123 Povo, Italy

Abstract: 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. In non-Abelian systems this accessibility to geometric properties can be even more restrictive due to the degeneracy of the states. We propose universal protocols to determine quantum geometric properties in non-Abelian systems. First, we show that for a weak resonant driving of the local parameters the coherent Rabi oscillations are related to the quantum geometric tensor. Second, we derive that in a Landau-Zener-like transition the final probability of an avoided energy crossing is proportional to elements of the non-Abelian quantum geometric tensor. Our schemes suggest a way to prepare eigenstates of the quantum metric, a task that is difficult otherwise in a degenerate subspace.


Volume: 3 (3)      Pages from: 033122-1  to: 033122-7

More Information: The authors acknowledge useful discussions with Guido Burkard and funding provided by Deutsche Forschungsgemeinschaft (DFG, German Research Foundation) Grant No. RA 2810/1 and SFB 1432-Project No. 425217212.
KeyWords: quantum topological systems, Landau-Zener transitions
DOI: 10.1103/PhysRevResearch.3.033122