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

H Weisbrich,W Belzig,G Rastelli

doi:10.1103/physrevresearch.3.033122

H Weisbrich, W Belzig + Show 1 more

Open Access

https://doi.org/10.1103/physrevresearch.3.033122

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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.

Highlights

The geometry of quantum states is crucial in many branches of physics
We show that our approach shows that the rates in a Landau-Zener-like transition are directly determined by the elements of the quantum geometric tensor (QGT)
We presented a new method to extract the quantum geometric tensor in non-Abelian systems with the help of geometric Rabi oscillations

Summary

INTRODUCTION

The geometry of quantum states is crucial in many branches of physics. It scopes the field of the Aharonov-Bohm effect [1,2], the Berry phase [3,4], and more recently the concept of topological phases such as topological insulators [5], topological semimetals [6], and topological superconductors [7]. Its real part yields the quantum metric that quantifies the distance between different quantum states [8] This general property can be connected to a wide spectrum of physical phenomena. Several proposals to measure the Abelian geometric properties, for instance, the quantum metric can be extracted by quantum quenches [21], by analyzing the current noise [22], or in photonic systems [23]. Another approach is via periodic driving to extract the Abelian QGT [24,25].

SINGLE PARAMETER MODULATION

TWO-PARAMETER MODULATION

GEOMETRICAL LANDAU-ZENER TRANSITIONS

DISCUSSION