Confinement-Induced Floquet Engineering and Non-Abelian Geometric Phases in Driven Quantum Wire Qubits

TL;DR

The study addresses robust, topologically protected qubit control in quantum-wire spin qubits under a biharmonic drive. By formulating a driven two-level system with a confinement-tunable parameter $Ω$ and applying Floquet theory plus a rotating-wave approximation, it reveals a confinement-induced synthetic gauge field and non-Abelian geometric structure that enable holonomic quantum computation. Key contributions include a confinement-triggered topological LZ transition with chiral LZS interference, non-Abelian geometric phases in cyclic $(Ω/ω, θ)$ evolution, and Floquet-Bloch oscillations and fractal-like spectra signaling coherent transport in a synthetic dimension. These findings suggest quantum-wire materials as a versatile platform for Floquet engineering, topological quantum control, and fault-tolerant quantum information processing, with feasible experimental implementation using current nano-fabrication and microwave-control technologies.

Abstract

This work theoretically demonstrates that a spin qubit in a parabolic quantum wire driven by a bichromatic field exhibits a confinement-tunable synthetic gauge field, leading to novel Floquet topological phenomena. The study presents the underlying mechanism for topological protection of qubit states against time-periodic perturbations. The analysis reveals a confinement-induced topological Landau-Zener transition, marked by a shift from preserved symmetries to chiral interference patterns in Landau-Zener-St$\ddot{u}$ckelberg-Majorana interferometry. Notably, the emergence of non-Abelian geometric phases under cyclic evolution in curved confinement and phase-parameter space is identified, enabling holonomic quantum computation. Additionally, the prediction of unconventional Floquet-Bloch oscillations in the quasi-energy and resonance transition probability spectra as a function of the biharmonic phase indicates exotic properties, including fractal spectra and fractional Floquet tunneling. These phenomena provide direct evidence of coherent transport in the synthetic dimension. Collectively, these findings position quantum wire materials has a versatile platform for Floquet engineering, topological quantum control, and fault-tolerant quantum information processing.

Figures (4)

• Figure 1: (Color online) Drive waveform for different values of a curved confinement (a) $\Omega$= 1, (b) $\Omega$ = 1.5, and (c) $\Omega$ =3.5 when the drive asymmetry parameter is fitted at $\theta$ =0 and $\theta = \pi$. We have observed that the waveform becomes asymmetric in time when $\theta \neq 0$. However, as the curved confinement increases, consecutive phases of the drive signal will lead to a buildup of excited-state population. The system parameters used here are $\omega$ = 1 rad/s, $\alpha$= 0.5 and $\beta$ = 1.2
• Figure 2: (Color online) Quasi-energy levels waveform for different values of the a curved confinement $\Omega/\omega =0.5$, (b) $\Omega/\omega =5$ when the drive asymmetry parameter is fitted respectively at (a), (b) $\theta = 0$ and (c), (d) $\theta = \pi$ (by a set of $n = m =2k$, with $k \in \mathbb{N}^*$). Other parameters utilized in this study are $\omega =1rad/s$ and $\Delta =0.47$.
• Figure 3: (Color online) The probability $P_{|\downarrow\rangle \rightarrow |\uparrow\rangle}$ is shown as functions of $\theta$, the driving amplitude ($\alpha/\omega$, $\beta/\omega$) plan for $\Omega/\omega = 0.5$ in (a, c, e and g) and $\Omega/\omega = 5$ in (b, d, f and h). The system parameters utilized in this study are $\Delta = 0.47$ and $\alpha/\omega = 4.4$.
• Figure 4: (Color online) The probability $P_{|\downarrow\rangle \rightarrow |\uparrow\rangle}$ of the excited state $|\uparrow\rangle$ and the quasi-energy versus the different phase $\theta$ and the driving amplitude $\beta/\omega$ plan: $\Omega/\omega$ = 0.5 (a, c) and $\Omega/\omega$ = 5 in (b, d). The system parameters utilized here are: $\Delta$ = 0.47 and $\alpha/\omega$ = 4.4