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.
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.
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.
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.
Landau-Zener (LZ) transition has received renewed interest as an alternative approach to control single-qubit states. An LZ transition occurs when a system passes through an avoided crossing that arises from quantum mechanical coupling of two levels, taking the system to a coherent superposition of the two states. Then, multiple LZ transitions induce interference known as Landau-Zener-Stückelberg (LZS) interference whose amplitude strongly depends on the velocity or adiabaticity of the passage. Here, we study the roles of LZ transitions and LZS interference in coherent charge oscillations of a one-electron semiconductor double quantum dot by time-domain experiments using standard rectangular voltage pulses. By employing density matrix simulations, we show that, in the standard setup using rectangular pulses, even a small distortion of the pulse can give rise to LZ transitions and hence LZS interference, which significantly enhances the measured oscillation amplitude. We further show experimentally that the nature of the coherent charge oscillations changes from Rabi-type to LZS oscillations with increasing pulse distortion. Our results thus demonstrate that it is essential to take into account LZS interference for both precise control of charge qubits and correct interpretation of measurement results.
The application of nonresonant electromagnetic fields, a technique known as 'dressing', provides critical control over the properties of fundamental quantum systems. We investigate the time evolution of a dressed-atom coherent spin ensemble, effectively representing a qubit, driven by a non-resonant electromagnetic field with two components, one along the quantisation static magnetic field and the other one orthogonal to it. While this second component produces a Larmor precession of the spin, the longitudinal dressing modifies the instantaneous field value, leading to a frequency modulated temporal evolution of the spin. This dual-dressing configuration represents an extension of the Landau-Zener multipassage interferometry in the presence of an additional dressing field controlling the tunneling process by its amplitude and phase. Our measurement of the qubit coherence introduces additional features to the transition probability readout of standard interferometry. The coherence time evolution is characterized by oscillations at several frequencies, each of them produced by a different quantum contribution. Such frequency description introduces a new picture of the qubit multipassage evolution. Our tuning-dressed configuration expands the toolbox for quantum state manipulation and quantum control applications. The experiments are performed in rubidium and caesium atomic magnetometers, confined in a magneto-optical trap and in a vapour cell, respectively. Static fields in the μT range and kHz oscillating fields with large Rabi frequencies are applied. Because the present low-frequency dressing operation does not fall within the standard Floquet engineering paradigm based on the high-frequency expansion, we develop an ad-hoc dressing perturbation treatment. Numerical simulations support the adiabatic and non-adiabatic qubit evolution.
Landau–Zener (LZ) tunneling, i.e., the nonadiabatic level transition under strong parameter driving, is a fundamental concept in modern quantum mechanics. With the advent of non-Hermitian physics, research interest has been paid to the LZ tunneling involving level dissipations. However, experimental demonstrations of such an interesting non-Hermitian LZ problem remain yet elusive. By harnessing a synthetic temporal lattice using a fiber-loop circuit, we report on the first real-time measurement of non-Hermitian LZ tunneling in a dissipative two-band lattice model. An innovative approach based on mode interference is developed to measure the transient band occupancies, providing a powerful tool to explore the non-Hermitian LZ tunneling dynamics in non-orthogonal eigenmodes. We find that the loss does not change the final LZ tunneling probability but can highly affect the tunneling process by modifying the typical band occupancies oscillation behaviors. We initiate exploring intriguing LZ physics and measurements beyond the standard Hermitian paradigm, with potential applications in coherent quantum control and quantum technologies.