Time-Fractional Schr\"odinger Evolution in Coupled Double Quantum Dots: Memory Effects on Quantum Resources

TL;DR

This study investigates how memory effects modeled by a time-fractional Schrödinger equation influence the dynamics of quantum resources like entanglement and coherence in coupled double quantum dots.

Contribution

It introduces a fractional Schrödinger equation approach to analyze non-Markovian quantum dynamics and explores how key parameters affect quantum resource behavior over time.

Findings

Lower fractional parameter $ au$ rapidly generates maximal entanglement.

Higher $ au$ values slow entanglement but prolong quantum resource significance.

Increased interaction frequency $ ext{V}$ stabilizes coherence and accelerates correlations.

Abstract

Our work explore the time evolution of entanglement, local quantum uncertainty, and correlated coherence, within a system modeled by two double quantum dots. The dynamics is represented using a time-fractional Schr\"odinger equation, which includes memory effects in a non-Markovian regime. We vary the fractional parameter $\tau$, the tunneling amplitudes $\delta_A$ and $\delta_B$, as well as the inter-dot interaction strength $\mathcal{V}$, to investigate how these key parameters govern the generation, stabilization, and decay of quantum resources within the system. The obtained results reveal that, for both initial states, fractional dynamics with a low $\tau$ rapidly generates entanglement expecting maximal values $\mathcal{LN}\approx 1$ and non-classical correlations quantified by local quantum uncertainty. Conversely, higher values of $\tau$ lead to slower entanglement but memory effects allow quantum resources to remain significant for a longer time, with the negativity remaining above ($\approx 0.6$). We also find that higher interaction frequencies $\mathcal{V}$ accelerate correlations and stabilize coherence, while a strong tunneling asymmetry degrades entanglement and coherence despite the initial benefits of increasing quantum resources.