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arXiv:1607.07852 · Physical review. B./Physical review. B

Spin-orbit signatures in the dynamics of singlet-triplet qubits in double quantum dots

Juan E. Rolon, E. Cota, Sergio E. Ulloa

Published May 8, 2017• 4 citations
arXivHTMLPDF

Abstract

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.

DOI
10.1103/physrevb.95.195407

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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+S\ensuremath{-}{T}_{+}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−T0S\ensuremath{-}{T}_{0}S\ensuremath−T0​ and S\ensuremath−T+S\ensuremath{-}{T}_{+}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.
We theoretically study the interplay of spin-orbit and hyperfine interactions in dynamical nuclear polarization in two-electron semiconductor double quantum dots near the singlet-triplet ($S\ensuremath{-}{T}_{+}$) anticrossing. The goal of the scheme under study is to extend the singlet-triplet ($S\ensuremath{-}{T}_{0}$) qubit decoherence time T2∗{T}_{2}^{*}T2∗​ by dynamically transferring the polarization from the electron spins to the nuclear spins. This polarization transfer is achieved by cycling the electron spins over the $S\ensuremath{-}{T}_{+}$ anticrossing. Here, we investigate, both quantitatively and qualitatively, how this hyperfine-mediated dynamical polarization transfer is influenced by the Rashba and Dresselhaus spin-orbit interaction. In addition to T2∗{T}_{2}^{*}T2∗​, we determine the singlet return probability Ps{P}_{s}Ps​, a quantity that can be measured in experiments. Our results suggest that the spin-orbit interaction establishes a mechanism that can polarize the nuclear spins in the direction opposite to that of hyperfine-mediated nuclear spin polarization. In materials with relatively strong spin-orbit coupling, this interplay of spin-orbit and hyperfine-mediated nuclear spin polarizations prevents any notable increase in the $S\ensuremath{-}{T}_{0}$ qubit decoherence time T2∗{T}_{2}^{*}T2∗​.
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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.
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.
We investigate theoretically the hyperfine-induced dephasing of two-electron-spin states in a double quantum dot with a finite singlet-triplet splitting JJJ. In particular, we derive an effective pure dephasing Hamiltonian, which is valid when the hyperfine-induced mixing is suppressed due to the relatively large JJJ and the external magnetic field. Using both a quantum theory based on resummation of ring diagrams and semiclassical methods, we identify the dominant dephasing processes in regimes defined by values of the external magnetic field, the singlet-triplet splitting, and inhomogeneity in the total effective magnetic field. We address both free induction and Hahn echo decay of superposition of singlet and unpolarized triplet states (both cases are relevant for singlet-triplet qubits realized in double quantum dots). We also study hyperfine-induced exchange gate errors for two single-spin qubits. Results for III-V semiconductors as well as silicon-based quantum dots are presented.
We analyze experimentally and theoretically the transport spectra of a gated lateral GaAs double quantum dot containing two holes. The strong spin-orbit interaction present in the hole subband lifts the Pauli spin blockade and allows to map out the complete spectra of the two-hole system. By performing measurements in both source-drain voltage directions, at different detunings and magnetic fields, we carry out quantitative fitting to a Hubbard two-site model accounting for the tunnel coupling to the leads and the spin-flip relaxation process. We extract the singlet-triplet gap and the magnetic field corresponding to the singlet-triplet transition in the double-hole ground state. Additionally, at the singlet-triplet transition we find a resonant enhancement (in the blockaded direction) and suppression of current (in the conduction direction). The current enhancement stems from the multiple resonance of two-hole levels, opening several conduction channels at once. The current suppression arises from the quantum interference of spin-conserving and spin-flipping tunneling processes.