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

TL;DR

This paper introduces universal protocols to measure quantum geometric properties in non-Abelian systems using Rabi oscillations and Landau-Zener transitions, overcoming experimental access challenges.

Contribution

It proposes novel methods to determine the quantum geometric tensor in non-Abelian systems via resonant driving and transition probabilities.

Findings

Rabi oscillations relate to the quantum geometric tensor.

Transition probabilities are proportional to geometric tensor elements.

Protocols enable eigenstate preparation of the quantum metric.

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.