# SU(3) Landau-Zener interferometry with a transverse periodic drive

## TL;DR

This paper investigates how periodic transverse drives influence Landau-Zener interferometry in SU(3) quantum triangles, revealing complex beat and step patterns dependent on frequency, size, and static components, with both semi-classical and quantum explanations.

## Contribution

It introduces a detailed analysis of frequency-dependent interference patterns in SU(3) quantum triangles under periodic drives, expanding understanding of non-adiabatic dynamics and tunneling phenomena.

## Key findings

- Coexistence of beats and steps at specific frequencies for large triangles
- Maximum of four steps observed at high frequencies in large triangles
- Unexpected two-step patterns in small triangles at high frequencies

## Abstract

Quantum triangles can work as interferometers. Depending on their geometric size and interactions between paths, "beats" {\it and/or} "steps" patterns are observed. We show that when inter-level distances between level positions in quantum triangles periodically change with time, formation of beats {\it and/or} steps no longer depends only on the geometric size of the triangles but also on the characteristic frequency of the transverse signal. For large-size triangles, we observe the coexistence of beats {\it and} steps when the frequency of the signal matches that of non-adiabatic oscillations and for large frequencies, a maximum of four steps instead of two as in the case with constant interactions is observed. Small-size triangles also revealed counter-intuitive interesting dynamics for large frequencies of the field: unexpected two-step patterns are observed. When the frequency is large and tuned such that it matches the uniaxial anisotropy, three-step patterns are observed. We have equally observed that when the transverse signal possesses a static part, steps maximize to six. These effects are semi-classically explained in terms of Fresnel integrals and quantum mechanically in terms of quantized fields with a photon-induced tunneling process. Our expressions for populations are in excellent agreement with the gross temporal profiles of exact numerical solutions. We compare the semi-classical and quantum dynamics in the triangle and establish the conditions for their equivalence.