Landau-Zener transitions in a qubit periodically driven in both longitudinal and transverse directions

TL;DR

This paper models the dynamics of a spin-qubit driven by both RF and microwave fields in longitudinal and transverse directions, aiming to optimize qubit control and coherence in quantum devices.

Contribution

It introduces a theoretical model combining RF and microwave drives in both directions, analyzing qubit dynamics to enhance control and coherence in quantum computing.

Findings

Analytical expressions for qubit populations match numerical simulations.

Identifies conditions for minimizing decoherence effects.

Provides insights into controlling qubit transitions under combined drives.

Abstract

We theoretically investigate the dynamics of a spin-qubit periodically driven in both longitudinal and transverse directions by two classical fields respectively a radio-frequency (RF) and a microwave (MW) field operating at phase difference $\phi$. The qubit is simultaneously locally subject to a linearly polarized magnetic field which changes its sign at a degeneracy point in the longitudinal direction and remains constant in the transverse direction. We superimpose the RF and MW signals respectively to the longitudinal and transverse components of the magnetic field. The proposed model may be used to optimize the control of a qubit in quantum devices. The various fields applied are relevant to {\it nearly-decouple} the spin-qubit from its environment, minimize decoherence effects and improve on the coherence time. The study is carried out in the Schr\"odinger and Bloch pictures. We consider the limits of weak and strong longitudinal drives set up by comparing the characteristic time of non-adiabatic transitions with the coherence time of the longitudinal drive. Expressions for populations are compared with numerics and remarkable agreements are observed as both solutions are barely discernible.