Abstract Landau–Zener–Stückelberg interferometry is extensively investigated in a 3D heterostructure magnetic quantum wire. Local magnetic fields are used to coherently manipulate and control a qubit’s quantum state. For our numerical calculations, a parabolic confinement is assumed. Energy eigenvalues, non-adiabatic and adiabatic transition probabilities are calculated from the diabatic and adiabatic bases for two-level systems. Here, we show that the spatial crossing between interspin levels becomes a spatial anticrossing if the two spin states are coupled by external fields, and that consequently, due to the spin dependence of the harmonic confinement, it will undergo Landau–Zener–Stückelberg interference. It is shown that the system undergoes nonadiabatic Landau–Zener dynamics for a strong confinement in a strong external field, whereas a weak external field induces adiabatic Landau–Zener transition dynamics. Our system allows the coupling strength between the level states at the anti(crossing) point to be modulated. This system allows one to tune the wire’s parabolic confinement potential using experimentally accessible parameters.
Abstract Landau–Zener–Stückelberg interferometry is extensively investigated in a 3D heterostructure magnetic quantum wire. Local magnetic fields are used to coherently manipulate and control a qubit’s quantum state. For our numerical calculations, a parabolic confinement is assumed. Energy eigenvalues, non-adiabatic and adiabatic transition probabilities are calculated from the diabatic and adiabatic bases for two-level systems. Here, we show that the spatial crossing between interspin levels becomes a spatial anticrossing if the two spin states are coupled by external fields, and that consequently, due to the spin dependence of the harmonic confinement, it will undergo Landau–Zener–Stückelberg interference. It is shown that the system undergoes nonadiabatic Landau–Zener dynamics for a strong confinement in a strong external field, whereas a weak external field induces adiabatic Landau–Zener transition dynamics. Our system allows the coupling strength between the level states at the anti(crossing) point to be modulated. This system allows one to tune the wire’s parabolic confinement potential using experimentally accessible parameters.
This paper presents nonlinear Landau–Zener (LZ) tunneling of an electron spin in an accelerating optical parabolic potential, manifested in a heterostructure quantum wire subjected to a periodic magnetic field comprising a spike and a homogeneous part. In this context, driving the two states of a pure nonlinear two-level quantum bit (qubit) system through an avoided level crossing can result in nontrivial dynamics, especially with and without considering a parabolic confinement potential characterized by a curvature confinement potential. We report two striking nonadiabatic and adiabatic scenarios in low modulation frequency limit which appear when such strength modulation occurs. Firstly, the changes of the amplitude of the driving field without considering a parabolic confinement potential act as a perturbation which mixes the spin states. Here, the dynamical evolution of the tunneling probabilities of the nonadiabatic populations under investigation is analyzed. Secondly, for strong fields and strong dependence of a parabolic confinement potential, the two diabatic states do not cross but present anti-crossing phenomenon as the time tends to infinity, describing an adiabatic transition. However, if the field strength in a wire is weak enough, the level separation of a qubit state switches abruptly around the crossing point, and LZ tunneling applies to the whole dynamical range, from adiabatic to fully nonadiabatic crossing. Locally, the tunneling process can be seen as a two-level system (TLS) undergoing a Rabi oscillation. These results open new prospects for the use of quantum interferences in spin–based devices.
We investigate the transfer between spin quantum bit (qubit) states and study the Landau–Zener–Stückelberg–Majorana (LZSM)-like dynamics of tunneling spin qubits in a multiband two-state magnetic quantum wire. Indeed, within the framework of an optical parabolic potential in a three-dimensional (3D) heterostructure quantum wire and under the influence of an external time-varying magnetic field, a model for a multiband two-state magnetic quantum wire is developed. Here, the external magnetic field is used to coherently manipulate and control spin qubit states. By driving the system through an avoided crossing, we consider the associated effective quantum two-level system (TLS) related to the spin qubit states in each band, driving by an external coherent magnetic field in which the related Hamiltonian is Hermitian, and which generally paves a way to LZSM interferometry. Thus, we establish the analytical expressions of the energy eigenvalues in each band and derive the analytical solution of the dynamical evolution of the tunneling probabilities of the associated TLS. Accordingly, nonadiabatic and adiabatic tunneling probabilities (survival and transition) are calculated for each band of the multiband TLS. In this respect, the nonadiabatic and adiabatic dynamical evolutions of the tunneling probabilities of spin qubit populations in the first four bands, with band quantum numbers n = 0, 1, 2 and 3 are analyzed. As a result, depending on the amplitude strength of the driven magnetic field and the magnitude of the driving frequency, we report two striking nonadiabatic and adiabatic scenarios in each band for both the diabatic and adiabatic states. In this context, driving the two states of each band of the multiband TLS related to the spin qubit states through an avoided level crossing can result in nontrivial and incoherent dynamics at certain phases, resulting to apparent inaccurate probabilities, especially in the case of strong driven magnetic field and high driving frequency.
Stimulated by the experimental realization of spin-dependent tunneling via a gradient magnetic field [C. J. Kennedy et al., Phys. Rev. Lett. 111, 225301 (2013); M. Aidelsburger et al., Phys. Rev. Lett. 111, 185301 (2013)], we investigate the dynamics of Bloch oscillations and Landau-Zener tunneling of single spin-half particles in a periodic potential under the influence of a spin-dependent constant force. In analogy to the Wannier-Stark system, we call our system the Wannier-Zeeman system. If there is no coupling between the two spin states, the system can be described by two crossing Wannier-Stark ladders with opposite tilts. The spatial crossing between two Wannier-Stark ladders becomes a spatial anticrossing if the two spin states are coupled by external fields. For a wave packet away from the spatial anticrossing, due to the spin-dependent constant force, it will undergo spatial Landau-Zener transitions assisted by the intrinsic intraband Bloch oscillations, which we call the Bloch-Landau-Zener dynamics. If the interspin coupling is sufficiently strong, the system undergoes adiabatic Bloch-Landau-Zener dynamics, in which the spin dynamics follows the local dressed states. Otherwise, for nonstrong interspin couplings, the system undergoes nonadiabatic Bloch-Landau-Zener dynamics.
We study Landau-Zener-St\"uckelberg (LZS) interferometry in multilevel systems coupled to an Ohmic quantum bath. We consider the case of superconducting flux qubits driven by a dc+ac magnetic fields, but our results can apply to other similar systems. We find a dynamic transition manifested by a symmetry change in the structure of the LZS interference pattern, plotted as a function of ac amplitude and dc detuning. The dynamic transition is from an LZS pattern with nearly symmetric multiphoton resonances to antisymmetric multiphoton resonances at long times (above the relaxation time). We also show that the presence of a resonant mode in the quantum bath can impede the dynamic transition when the resonant frequency is of the order of the qubit gap. Our results are obtained by a numerical calculation of the finite time and the asymptotic stationary population of the qubit states, using the Floquet-Markov approach to solve a realistic model of the flux qubit considering up to ten energy levels.
Theoretical analysis indicates that a spin qubit in a parabolic quantum wire, when driven by a bichromatic field, generates a confinement-tunable non-Abelian synthetic gauge field that gives rise to novel Floquet topological phenomena. In the low-confinement regime, the system exhibits topological Landau-Zener (LZ) transitions, chiral Landau-Zener-Stu¨ckelberg-Majorana (LZSM) interference, and non-Abelian geometric phases around diabolical points. These features enable holonomic quantum computation, as well as unconventional Floquet Bloch oscillations and fractal spectra. In contrast, in the strong confinement regime, narrow avoided crossings significantly suppress cross-coupling, thereby insulating the qubit from multi-photon LZSM interference. Quantitative Floquet-Lindblad analysis shows that the optimized gate times, determined by the biharmonic driving period and non-Abelian parameter-space loops, are sufficiently short to surpass primary environmental decoherence channels. When applied to high-mobility GaAs/AlGaAs core-shell nanowires, this approach converts spatial drives into robust non-Abelian gauge fields, positioning quantum wire systems as a versatile and scalable platform for fault-tolerant quantum information processing.
The populations of energy levels of interacting qubits have been studied as functions of the field amplitude and other control parameters for a constant frequency of the external electromagnetic field. It has been found that the qubit coupling constant strongly affects the quantum-coherent Landau-Zener transitions between the qubit states and the formation of an interference pattern in level populations, depending on the field parameters. It has been demonstrated that it is possible to determine the qubit coupling constant by Landau-Zener interferometry.