Single-spin state evolution induced by the Landau-Zener-St\"uckelberg-Majorana (LZSM) interference in a Zeeman-spit four-level system in a periodically driven double quantum dot is studied theoretically by the Floquet stroboscopic method. An interplay between spin-conserving and spin-flip tunneling processes with the electric dipole spin resonance (EDSR) that is induced in an individual dot and enhanced by the LZSM multiple level crossings with the neighboring quantum dot is investigated as a function of the microwave (MW) frequency, driving amplitude, interdot detuning, and magnetic field. A number of special points in the parameter space are identified, out of which all three features are merged. Under this triple-crossing resonance condition, the interdot tunneling is combined with a fast spin evolution in each dot at the EDSR frequency. Harmonics of the EDSR are revealed in the spin-dependent tunneling maps versus variable magnetic field and MW frequency. The results are applicable for both electron and hole systems with strong spin-orbit interaction and may be useful for developing new time-efficient schemes of the spin control and readout in qubit devices.
Single-spin state evolution induced by the Landau-Zener-St"uckelberg-Majorana (LZSM) interference in a Zeeman-spit four-level system in a periodically driven double quantum dot is studied theoretically by the Floquet stroboscopic method. An interplay between spin-conserving and spin-flip tunneling processes with the electric dipole spin resonance (EDSR) that is induced in an individual dot and enhanced by the LZSM multiple level crossings with the neighboring quantum dot is investigated as a function of the microwave (MW) frequency, driving amplitude, interdot detuning, and magnetic field. A number of special points in the parameter space are identified, out of which all three features are merged. Under this triple-crossing resonance condition, the interdot tunneling is combined with a fast spin evolution in each dot at the EDSR frequency. Harmonics of the EDSR are revealed in the spin-dependent tunneling maps versus variable magnetic field and MW frequency. The results are applicable for both electron and hole systems with strong spin-orbit interaction and may be useful for developing new time-efficient schemes of the spin control and readout in qubit devices.
Landau-Zener-Stuckelberg-Majorana (LZSM) physics has been exploited to coherently manipulate two-electron spin states in a GaAs double quantum dot (DQD) at a singlet (S)-triplet (T+) anti-crossing. The anti-crossing results from the hyperfine interaction with the nuclear spins of the host material [1,2]. However, the fluctuations of the nuclear spin bath result in spin dephasing within T ∗ 2 ∼ 10− 20 ns. As a consequence, the sweep through the anti-crossing would have to be performed on a timescale comparable to T ∗ 2 to achieve LZSM oscillations with 100% visibility. Moreover, the S-T+ anti-crossing is located near the (1, 1)− (2, 0) interdot charge transition, where (nl, nr) denotes the number of electrons in the left and right quantum dot. As a result the singlet state involved in the dynamics is a superpostion of (1, 1) and (2, 0) singlet states. Here we show that it is possible to increase the oscillation visibility while keeping sweep times less than T ∗ 2 using a tailored pulse with a detuning dependent level velocity. The pulse includes a slow level velocity portion that is chosen to coincide with the passage through the S-T+ anti-crossing and two fast level velocity portions. The latter minimize the time spent in regions where spin and charge degrees of freedom are entangled, which renders the qubit susceptible to charge noise. The slow level velocity portion of the pulse results in a stronger effective coupling between the spins states, which increases the oscillations visibility [3,4]. In particular, we were able to obtain a visibility of ∼ 0.5 for LZSM oscillations. This constitutes an important step towards the implementation of a Hadamard gate.
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.
We characterize numerically and analytically the signatures of the spin-orbit interaction in a two-electron GaAs double quantum dot in the presence of an external magnetic field. In particular, we obtain the return probability of the singlet state by simulating Landau-Zener voltage detuning sweeps which traverse the singlet-triplet ($S\ensuremath{-}{T}_{+}$) resonance. Our results indicate that non-spin-conserving interdot tunneling processes arising from the spin-orbit interaction have well defined signatures. These allow direct access to the spin-orbit interaction scales and are characterized by a frequency shift and Fourier amplitude modulation of the Rabi flopping dynamics of the singlet-triplet qubits $S\ensuremath{-}{T}_{0}$ and $S\ensuremath{-}{T}_{+}$. By applying the Bloch-Feshbach projection formalism, we demonstrate analytically that the aforementioned effects originate from the interplay between spin-orbit interaction and processes driven by the hyperfine interaction between the electron spins and those of the GaAs nuclei.
The spin dynamics in two electron double quantum dots embedded in a two-dimensional electron gas at the interface between SrTiO3 and LaAlO3 is studied by an exact numerical solution of the time-dependent Schr\"odinger equation in the context of the electric-dipole-spin-resonance experiment. On the basis of the three-band model of 3d electrons localized at Ti ions on the square lattice, we analyze in detail the singlet-triplet transition induced by the ac electric field, in the magnetic field range close to the avoided crossing that appears as a result of the spin-orbit coupling. For symmetric double quantum dots the single-photon spin-flip transition is prohibited due to the parity symmetry, and the transition can occur only by the higher-order two-photon processes. For a weakly asymmetric system, when the first-order singlet-triplet transitions are released due to the parity symmetry breaking, the spin-flip transition has a character of the Rabi oscillations for a low electric field amplitude. As the amplitude is increased, the frequency of the transition is blueshifted (redshifted) for the magnetic field below (above) the single-triplet avoided crossing. For a sufficiently high magnetic field and high ac-field amplitude, the electric field drives the system across the avoided crossing, inducing the spin flip by the Landau-Zener-Stueckelberg-Majorana effect. Finally, the optimization of the geometrical parameters of the system with respect to the time of spin flip of its fidelity is also presented.
Electrical spin manipulation in double SrTiO3/LaAlO3 quantum dots
The spin dynamics in two electron double quantum dots embedded in two dimensional electron gas at the interface between SrTiO3 and LaAlO3 is studied by an exact numerical solution of the time-dependent Schrödinger equation, in the context of the electric dipole spin resonance experiment. Based on the three band model of 3d-electrons localized at Ti ions on the square lattice we analyze in details the singlet-triplet transition induced by the AC electric field, in the magnetic field range close to the avoided crossing which appears as a result of the spin-orbit coupling. Our calculations show that for symmetric double quantum dots the single photon spin-flip transitions is prohibited due to the parity symmetry and the transition can occur only by the higher order two-photon processes. For a weakly asymmetric system, when the first order singlet-triplet transitions are released due to the parity symmetry breaking, the spin-flip transition has a character of the Rabi oscillations for a low electric field amplitude. As the amplitude is increased the frequency of the transition is blueshifted (redshifted) for the magnetic field below (above) the single-triplet avoided crossing. Interestingly, for a sufficiently high magnetic field and high AC field amplitude the electric field drives the system across the avoided crossing inducing the spin-flip by the Landau-Zener-Stueckelberg-Majorana transitions with 100\% spin flip probability for a slow sweep. Finally, the optimization of the geometrical parameters of the system with respect to the time of spin-flip of its fidelity is also presented.
Abstract We investigate the effect of spin–orbit interaction on the intra- and interdot particle dynamics of a double quantum dot (QD) under ac electric fields. The former is modeled as an effective ac magnetic field that produces electric-dipole spin resonance transitions, while the latter is introduced via spin-flip tunneling amplitudes. We observe the appearance of non-trivial spin-polarized dark states (DSs), arising from an ac-induced interference between photo-assisted spin-conserving and spin-flip tunneling processes. These DSs can be employed to precisely measure the spin–orbit coupling in QD systems. Furthermore, we show that the interplay between photo-assisted transitions and spin-flip tunneling enables the system to operate as a highly tunable spin filter. Finally, we investigate the operation of the system as a resonant flopping-mode qubit for arbitrary ac voltage amplitudes, allowing for high tunability and enhanced qubit control possibilities.