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Journal of Physics A Mathematical and Theoretical

Using perturbed general solutions to transparently control robust spin–orbit qubits

Kuo Hai, Qiong Chen, Yunrong Luo, Wenhua Hai

Published Jul 10, 2026• 0 citations
Publisher

Abstract

Abstract We use quantum perturbation theory with the exact general solutions of the perturbed equations to investigate a single electron confined in a gated nanowire quantum dot (NQD) with arbitrarily strong spin–orbit coupling (SOC) and weak static magnetic field. Treating the weak field as a perturbation, we obtain the maximal spin-motion entangled kitten states. From the double-boundedness and self-consistence conditions of the general bound-state solutions we uncovered two corrected energies and the explicit dependence of the spin–orbit state phase on the orientation of the applied magnetic field and the SOC parameters. The two-level states correspond to a spin–orbit qubit with the level splitting being much less than the unperturbed level-difference. We demonstrate the higher stability of the ground states and the SOC strength-related decoherence-averse effect, meaning the robustness of the qubit against external fluctuations (or decoherence). We suggest an alternative scheme to perform the qubit manipulation, simply by adjusting the orientation angle of magnetic field to produce the quantized phase jumps. Such an adjustment can lead to the SOC phase-related spin flipping of the state vectors and the position exchanging of the probability-density wavepackets, which can be explained as the quantized change of the qubit spin axis. The results can be applied to a weakly coupled array of NQDs for coherently encoding the robust spin–orbit qubits, and could be extended to a cold-atomic system with the laser-induced SOC.

DOI
10.1088/1751-8121/ae895c

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arXiv:cond-mat/0510411•Physical Review Letters•Jan 30, 2006•283 citations
Abstract We use quantum perturbation theory with the exact general solutions of the perturbed equations to investigate a single electron confined in a gated nanowire quantum dot (NQD) with arbitrarily strong spin–orbit coupling (SOC) and weak static magnetic field. Treating the weak field as a perturbation, we obtain the maximal spin-motion entangled kitten states. From the double-boundedness and self-consistence conditions of the general bound-state solutions we uncovered two corrected energies and the explicit dependence of the spin–orbit state phase on the orientation of the applied magnetic field and the SOC parameters. The two-level states correspond to a spin–orbit qubit with the level splitting being much less than the unperturbed level-difference. We demonstrate the higher stability of the ground states and the SOC strength-related decoherence-averse effect, meaning the robustness of the qubit against external fluctuations (or decoherence). We suggest an alternative scheme to perform the qubit manipulation, simply by adjusting the orientation angle of magnetic field to produce the quantized phase jumps. Such an adjustment can lead to the SOC phase-related spin flipping of the state vectors and the position exchanging of the probability-density wavepackets, which can be explained as the quantized change of the qubit spin axis. The results can be applied to a weakly coupled array of NQDs for coherently encoding the robust spin–orbit qubits, and could be extended to a cold-atomic system with the laser-induced SOC.
We consider an electron confined in a gated nanowire quantum dot (NQD) with arbitrarily strong spin-orbit coupling (SOC) and weak static magnetic field, and treat the latter as a perturbation to seek the maximal spin-motion entangled states with the exact general solutions of the perturbed equations. From the boundedness and self-consistent conditions of the general solutions we find two corrected energies to any n level of the unperturbed system with ground state n = 0, which are much less than the unperturbed level-difference and corresponds to a spin-orbit qubit. We demonstrate the metastability of the two-level states and the decoherence-averse effect of SOC, and suggest an alternative scheme to perform the qubit control, simply by adjusting the orientation of magnetic field for any fixed SOC. Such a adjustment can lead to the spin flipping of the state vector and the position exchanging of the probability-density wavepackets which can be proposed as the non-Abelian quasiparticles. The results could be directly extended to a weakly coupled array of NQDs for coherently encoding the robust spin-orbit qubits.
We report on the first set of exact orthonormalized states to an ac driven one-dimensional (1D) two-electron nanowire quantum dot with the Rashba-Dresselhaus coexisted spin-orbit coupling (SOC) and the controlled magnetic field orientation and trapping frequency. In the ground state case, it is shown that the spatiotemporal evolutions of probability densities occupying internal spin states and the transfer rates between different spin states can be adjusted by the ac electric field and the intensities of SOC and magnetic field. Effects of the system parameters and initial-state-dependent constants on the mean entanglement are revealed, where the approximately maximal entanglement associated with the stronger SOC and its insensitivity to the initial and parametric perturbations are demonstrated numerically. A novel resonance transition mechanism is found, in which the ladder-like time-evolution process of expected energy and the transition time between two arbitrary exact states are controlled by the ac field strength. Using such maximally entangled exact states to encode qubits can render the qubit control more transparent and robust. The results could be extended to 2D case and to an array of two-electron quantum dots with weak neighboring coupling for quantum information processing.
By investigating a harmonically confined and periodically driven particle system with spin–orbit coupling (SOC) and a specific controlled parameter, we demonstrate an exactly solvable two-level model with a complete set of spin-motion entangled Schrödinger kitten (or cat) states. In the undriven case, application of a modulation resonance results in the exact stationary states. We show a decoherence-averse effect of SOC and implement a transparent coherent control by exchanging positions of the probability-density wavepackets to create transitions between the different degenerate ground states. The expected energy consisting of quantum and continuous parts is derived, and the energy deviations caused by the exchange operations are much less than the quantum gap. The results could be directly extended to a weakly coupled single-particle chain for transparently encoding spin–orbit qubits via the robust spin-motion entangled degenerate ground states.
A spin-orbit qubit is a hybrid qubit that contains both orbital and spin degrees of freedom of an electron in a quantum dot. Here we study the exchange coupling between two spin-orbit qubits in a nanowire double quantum dot (DQD) with strong spin-orbit coupling (SOC). We find that while the total tunneling in the DQD is irrelevant to the SOC, both the spin-conserved and spin-flipped tunnelings are SOC dependent and can compete with each other in the strong SOC regime. Moreover, the Coulomb repulsion between electrons can combine with the SOC-dependent tunnelings to yield an anisotropic exchange coupling between the two spin-orbit qubits. Also, we give an explicit physical mechanism for this anisotropic exchange coupling.
Solid state based quantum information processing is focused on physical implementation of all necessary elements of quantum computation and quantum information in solid state systems, mainly due to their scalability compared to e.g. optical systems. Among many proposals to realize these types of devices, such as quantum dots as charge qubits or Josephson junction circuits, we study here one of the most promising candidates, i.e., the spin of an electron confined to a quantum dot as a qubit. Experimentally, it has been shown that the relaxation rate of this two level system can be pushed above few seconds in low magnetic fields. Moreover, using spin echo techniques, \nthe spin dephasing time can be maximized up to milliseconds with the current technology. This long spin decay time is one of the main reasons that make this system desirable for quantum computation and quantum information purposes. \nWe reexamined the recent measurement based proposal called one-way quantum computation which exploits entanglement and local measurements as tools to perform quantum computation on N qubits. Although it was suggested in the original work to entangle the qubits via the nearest neighbor Ising interaction, we investigated how one can generate the so-called cluster states with the Heisenberg interaction. We extended our method to include more general forms of Heisenberg interaction such as asymmetric coupling of adjacent qubits. These forms of couplings, rather than Ising interaction, are more encountered in solid state devices, and therefore make it possible to perform one-way quantum computation with electron spins in quantum dots coupled via exchange interaction to their adjacent spins. \n \nChapters II, III, and IV of my thesis are devoted to the study of the spin-orbit interaction in heterostructure quantum dots and its effect on the spin dynamics. We observed that one can actually use spin-orbit interaction to manipulate the spin state of an electron on time scales much smaller than the spin dephasing time. Specifically, in chapter II, we studied the effect of a nearby functioning quantum point contact (QPC) on the relaxation of the electron spin and show that the charge fluctuations in QPC lead to spin relaxation of the confined electron in the presence of spin-orbit interactiom and an applied magnetic field. We also addressed the relation of this rate to the microscopic parameters of the system and found some geometrical dependence of the spin relaxation time on the orientation of the QPC on the substrate. Moreover, we showed in chapters III and IV that the spin-orbit interaction can play a positive role, in order to rotate the spin around the Bloch sphere. We considered different mechanisms, particularly, Electron Dipole Spin Resonance (EDSR) and holonomic unitary gates in quantum dots. We verified that these mechanisms of spin manipulation can be realized in solid state systems with the state of the art semiconductor technologies. \n \nChapter V of the thesis covers a slightly different topic and focuses on the role of the Coulomb interaction in electronic transport. There, we reviewed the non-analytic corrections to the Fermi liquid behavior and their consequences on the momentum occupation number of the electrons in a two dimensional electron gas (2DEG). As an example, we calculated the tunneling rate from an interacting electron reservoir onto a quantum dot and compared our result to the corresponding case for electron tunneling between bilayer 2DEGs. Moreover, within RPA approximation, we found that the electron-plasmon coupling leads to a quadratic frequency dependence of the electron self-energy at low frequencies at the Fermi surface. This correction suppresses the same order corrections due to the particle-hole bubble. \n \n \n
We consider a single electron in a 1D quantum dot with a static slanting Zeeman field. By combining the spin and orbital degrees of freedom of the electron, an effective quantum two-level (qubit) system is defined. This pseudospin can be coherently manipulated by the voltage applied to the gate electrodes, without the need for an external time-dependent magnetic field or spin-orbit coupling. Single-qubit rotations and the controlled-NOT operation can be realized. We estimated the relaxation (T1) and coherence (T2) times and the (tunable) quality factor. This scheme implies important experimental advantages for single electron spin control.