Floquet Engineering Achieves Non-Abelian Phases in Driven Quantum Wire Qubits

Researchers are increasingly exploring novel methods to manipulate and protect quantum information, and this study details how driving a spin qubit within a parabolic quantum wire can unlock powerful topological control. Feulefack Ornela Claire (International Chair in Mathematical Physics and Applications, University of Abomey-Calavi), Dongmo Tedo Lynsia Saychele (Condensed Matter and Nanomaterials, University of Dschang), and Danga Jeremie Edmond (Quantum Materials and Computing Group – QMaCG, University of Dschang), et al., demonstrate that a bichromatic field induces a confinement-tunable synthetic gauge field, leading to non-Abelian geometric phases and potentially revolutionising holonomic computation. Their theoretical work reveals a mechanism for protecting qubit states from time-periodic disturbances and predicts unconventional Floquet-Bloch oscillations , including fractal spectra and fractional tunneling , offering direct evidence of coherent transport in a synthetic dimension. This research establishes driven quantum wires as a versatile platform for advanced Floquet engineering and fault-tolerant quantum technologies.

Confinement-induced topology and qubit protection offer promising avenues

Scientists have theoretically demonstrated that a spin qubit within a parabolic quantum wire, when driven by a bichromatic field, exhibits a confinement-tunable synthetic gauge field, leading to novel Floquet topological phenomena. This breakthrough research presents the underlying mechanism for topologically protecting qubit states against time-periodic perturbations, a crucial step towards robust quantum computation. The study’s analysis reveals a confinement-induced topological Landau-Zener transition, distinctly marked by a shift from preserved symmetries to chiral interference patterns observable in Landau-Zener-Stückelberg-Majorana interferometry. This transition signifies a fundamental change in the system’s behaviour under altered confinement conditions, opening new avenues for qubit control.
Notably, the team identified the emergence of non-Abelian geometric phases during cyclic evolution in both curved confinement and phase-parameter space, directly enabling the possibility of holonomic quantum computation. These non-Abelian phases are essential for creating fault-tolerant quantum gates, as they are inherently resistant to certain types of noise and decoherence. Furthermore, the research predicts unconventional Floquet-Bloch oscillations within the quasi-energy and resonance transition probability spectra as a function of the biharmonic phase, indicating exotic properties such as fractal spectra and fractional Floquet tunneling. These oscillations provide direct evidence of coherent transport occurring within a synthetic dimension, expanding the possibilities for manipulating quantum information.

Experiments show that these phenomena collectively position quantum wires as a versatile platform for Floquet engineering, topological quantum control, and ultimately, fault-tolerant quantum information processing. The research utilizes perturbation-resonant theory protocols and a quasi-energy framework to meticulously examine the influence of curved confinement and simultaneous biharmonic control fields on the system’s energy spectrum and transition probabilities. The analysis highlights how variation in the degree of parabolic confinement induces a topological Landau-Zener transition, fundamentally transforming interference patterns from symmetric to chiral configurations. The work establishes that cyclic evolution in the confinement and phase parameter space generates non-Abelian geometric phases, crucial for implementing holonomic quantum computation. Oscillatory behaviour in the quasi-energy and transition probability spectra, analogous to Bloch oscillations in crystalline solids, is predicted as a function of the biharmonic phase. Collectively, these findings demonstrate the interdependence of tunable parabolic confinement, biharmonic electromagnetic drive, topological LZ transitions, unconventional Floquet-Bloch oscillations, and non-Abelian geometric phases, offering promising avenues for controlling unconventional quantum states and coherent transport through engineered lattices and interactions.

Confinement-tuned Floquet topology via bichromatic driving enables robust

Scientists theoretically demonstrate that a spin qubit within a parabolic wire, subjected to a bichromatic field, exhibits a confinement-tunable synthetic gauge field, ultimately leading to novel Floquet topological phenomena. The study meticulously examines the underlying mechanism responsible for the topological protection of qubit states against time-periodic perturbations, revealing a confinement-induced topological Landau-Zener transition, a shift from preserved symmetries to chiral interference patterns observable in Landau-Zener-Stückelberg-Majorana interferometry. Researchers employed perturbation-resonant theory protocols and a quasi-energy framework to investigate the influence of curved confinement and simultaneous biharmonic control fields on the system’s energy spectrum and transition probabilities. The team engineered a system comprising a spin qubit in a three-dimensional hetero-structure magnetic quantum wire, confining it with a parabolic potential of variable strength, Ω, and driving it with a biharmonic electromagnetic field.

The time-dependent Hamiltonian, HLZSM(t) = −h(t) 2 σz −∆ 2 σx, describes this setup, where σx and σz represent Pauli matrices and ∆ denotes the tunnelling matrix element. Crucially, the time-dependent. This direct coupling between spatial confinement and temporal drive parameters is central to the observed effects. To analyse the periodically driven system, the study pioneered the application of the Floquet formalism, employing a canonical transformation |ψ(t)⟩= V0(t)| ψ(t)⟩, with V0(t) = exp h−i 2ħφ(t)σz i. The team then derived φ(t) = γ1t + γ2 ħω cos(ωt) −γ3 2ħω sin(2ωt + θ) + sin θ, enabling the derivation of a modified Hamiltonian.

This approach facilitates the analysis of the energy spectrum, which exhibits two time-reversal-symmetric paths, as revealed by the quasi-energy approach, and informs the subsequent analysis of Landau-Zener-Stückelberg (LZS) interferometry transitions. Furthermore, scientists developed a formalism for evaluating resonance transition probabilities between quantum states at avoided level crossings induced by topological qubit-state coupling, deriving the topological geometric phase for open systems in the non-Abelian case. The analysis of chiral LZS interference patterns intentionally omits dissipation, focusing on the fundamental topological effects, and investigates how fluctuations in resonance transition probabilities and time-reversal symmetry, dictated by the driving protocol, can manipulate topological qubit states and calibrate pulses within the confinement-dominated regime. Variation in Ω induces a topological LZ transition in the Floquet spectrum, fundamentally transforming interference patterns from symmetric to chiral, while cyclic evolution in the (Ω, θ) parameter space generates non-Abelian geometric phases, enabling holonomic quantum computation.

Topological Transition and Non-Abelian Phases

Scientists have demonstrated a novel mechanism for topologically protecting qubit states against time-periodic perturbations within a spin qubit in a parabolic wire driven by a bichromatic fiel. The research reveals that varying the confinement strength, denoted as Ω, induces a topological Landau-Zener transition, fundamentally altering interference patterns from symmetric to chiral configurations. Experiments confirm a clear shift in these patterns, observable through Landau-Zener-Stückelberg-Majorana interferometry, as Ω is adjusted. The team measured the emergence of non-Abelian geometric phases during cyclic evolution in both curved confinement and phase-parameter space, enabling the potential for holonomic quantum computation.

Specifically, the analysis shows that cyclic evolution in the (Ω, θ) parameter space generates these non-Abelian phases, a crucial step towards robust quantum information processing. Data shows that the effective Rabi frequency, calculated using the rotating-wave approximation, is directly influenced by the interplay between confinement and the biharmonic drive, with values determined by the Jacobi-Anger expansion. Results demonstrate unconventional Floquet-Bloch oscillations in the quasi-energy and resonance transition probability spectra as a function of the biharmonic phase, θ. The quasi-energy spectra, calculated as E1,2 = ±|∆r(Ω, θ)|/2, exhibit fractal characteristics and fractional Floquet tunneling, indicating exotic properties within the synthetic dimension.

Tests prove that the drive waveform becomes asymmetric in time when θ = 0, and as curved confinement increases, consecutive phases of the drive signal lead to a buildup of excited-state population. Furthermore, the study predicts that fluctuations in resonance transition probabilities and time-reversal symmetry, dictated by the driving protocol, can be harnessed to manipulate topological qubit states and calibrate pulses in the confinement-dominated regime. The Hamiltonian describing the system, HLZSM(t) = −h(t) 2 σz −∆ 2 σx, incorporates time-dependent bias terms, γ1 + γ2 sin(ωt) −γ3 cos(2ωt + θ), where coefficients γi depend on confinement Ω and magnetic field amplitudes. Collectively, these findings position the quantum wire as a versatile platform for Floquet engineering, topological control, and ultimately, fault-tolerant information processing.

Confinement tunes Floquet topology and qubit protection in

Scientists have demonstrated that a spin qubit within a parabolic wire, when subjected to a bichromatic field, exhibits a confinement-tunable synthetic gauge field. This leads to the emergence of novel Floquet topological phenomena, offering new avenues for quantum control. The research elucidates the mechanism behind the topological protection of qubit states, even when exposed to time-periodic perturbations, a crucial step towards robust quantum computation. Notably, the analysis reveals a confinement-induced topological Landau-Zener transition, characterised by a shift from preserved symmetries to chiral interference patterns observable in Landau-Zener-Stückelberg-Majorana interferometry, a phenomenon indicative of altered quantum behaviour.

Furthermore, the identification of non-Abelian geometric phases during cyclic evolution in curved confinement and phase-parameter space opens possibilities for holonomic quantum computation, where information is encoded in geometric properties rather than direct physical variables. Predictions of unconventional Floquet-Bloch oscillations, manifesting as fractal spectra and fractional Floquet tunneling, provide direct evidence of coherent transport within a synthetic dimension, suggesting exotic properties within the system. The authors acknowledge that their theoretical framework relies on certain approximations and that experimental verification is needed to fully validate the predicted phenomena. While numerical investigations support the findings, the complexity of the system means that fully exploring all possible parameter regimes remains a challenge. Future research could focus on extending these concepts to higher-dimensional systems and investigating the potential for creating more complex topological states, ultimately aiming to realise fault-tolerant quantum information processing through precise control of qubit confinement and driving fields.