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arXiv:1408.6700 · Physical Review B

Interplay of spin-orbit and hyperfine interactions in dynamical nuclear polarization in semiconductor quantum dots

Marko J. Rančić, Guido Burkard

Published Dec 22, 2014• 14 citations
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Abstract

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 ${T}_{2}^{*}$ 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 ${T}_{2}^{*}$, we determine the singlet return probability ${P}_{s}$, 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 ${T}_{2}^{*}$.

DOI
10.1103/physrevb.90.245305

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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+S\ensuremath{-}{T}_{+}S\ensuremath−T+​) anticrossing. The goal of the scheme under study is to extend the singlet-triplet (S\ensuremath−T0S\ensuremath{-}{T}_{0}S\ensuremath−T0​) 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+S\ensuremath{-}{T}_{+}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−T0S\ensuremath{-}{T}_{0}S\ensuremath−T0​ qubit decoherence time T2∗{T}_{2}^{*}T2∗​.
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.
We have evaluated hyperfine-induced electron spin dynamics for two electrons confined to a double quantum dot. Our quantum solution accounts for decay of a singlet-triplet correlator even in the presence of a fully static nuclear spin system, with no ensemble averaging over initial conditions. In contrast to an earlier semiclassical calculation, which neglects the exchange interaction, we find that the singlet-triplet correlator shows a long-time saturation value that differs from 12\frac{1}{2}21​, even in the presence of a strong magnetic field. Furthermore, we find that the form of the long-time decay undergoes a transition from a rapid Gaussian to a slow power law $(\ensuremath{\sim}1∕{t}^{3∕2})$ when the exchange interaction becomes nonzero and the singlet-triplet correlator acquires a phase shift given by a universal (parameter independent) value of $3\ensuremath{\pi}∕4$ at long times. The oscillation frequency and time-dependent phase shift of the singlet-triplet correlator can be used to perform a precision measurement of the exchange interaction and Overhauser field fluctuations in an experimentally accessible system. We also address the effect of orbital dephasing on singlet-triplet decoherence and find that there is an optimal operating point where orbital dephasing becomes negligible.
We simulate the control of the spin states in a two-electron double quantum dot when an external detuning potential is used to pass the system through an anticrossing. The hyperfine coupling of the electron spins with the surrounding nuclei causes not only anticrossing of the spin states but also decoherence of the spin states. We calculate numerically the singlet–triplet decoherence for different detuning values and find good agreement with the experimental measurement results for a similar setup. We predict an interference effect due to the coupling of the T 0 and T + states.
The hyperfine coupling of the electronic spins in quantum dots to nuclear spins in the semiconductor host material poses a major challenge, as it can lead to decoherence of the electron spins. In this work, the authors revert the typical approach in which the nuclear spins are considered as an environment for the electronic spin, but rather rather view the nuclear spins as the quantum system coupled to an electronic environment with an exceptional degree of tunability. They show that nuclear spin bath could be turned from the dominant source of decoherence into a useful resource for manipulating an electron spin qubit.
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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.