Two electron spins form the spin singlet or triplet state if these spins have the same g-factor value, or a mix state consisting of both the singlet and triplet states if these spins have different g-factor values. It is considered that two energy levels of electrons are formed in a double quantum dot device for use in quantum information processing; however, the g-factors of the electrons have not been treated as an important factor because they cannot be changed easily in experiments. We introduce a numerical calculation method for the singlet–triplet mix state due to the g-factor mismatch in double quantum dots. It is found that this mismatch changes the energy levels of the original singlet and triplet states; thus, it affects the intersecting points of the energy levels of the singlet and triplet states where a dynamic nuclear polarization appears via hyperfine interaction.Two electron spins form the spin singlet or triplet state if these spins have the same g-factor value, or a mix state consisting of both the singlet and triplet states if these spins have different g-factor values. It is considered that two energy levels of electrons are formed in a double quantum dot device for use in quantum information processing; however, the g-factors of the electrons have not been treated as an important factor because they cannot be changed easily in experiments. We introduce a numerical calculation method for the singlet–triplet mix state due to the g-factor mismatch in double quantum dots. It is found that this mismatch changes the energy levels of the original singlet and triplet states; thus, it affects the intersecting points of the energy levels of the singlet and triplet states where a dynamic nuclear polarization appears via hyperfine interaction.

Japanese Journal of Applied PhysicsApr 1, 20112 citations

Spin dynamics at the singlet–triplet crossings in a double quantum dot

J Särkkä, Ari Harju

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.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.

arXiv:1007.0080New Journal of PhysicsApr 8, 201113 citations

Singlet-triplet decoherence due to nuclear spins in a double quantum dot

W. A. Coish, Daniel Loss

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 $\frac{1}{2}$ , 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 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 $\frac{1}{2}$, 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.

arXiv:cond-mat/0506090Physical Review BSep 21, 2005195 citations

Decoherence of coupled electron spins via nuclear spin dynamics in quantum dots

Wen Yang, Ren‐Bao Liu

In double quantum dots, the exchange interaction between two electron spins renormalizes the excitation energy of pair flips in the nuclear spin bath, which in turn modifies the non-Markovian bath dynamics. As the energy renormalization varies with the static Overhauser field mismatch between the quantum dots, the electron singlet-triplet decoherence resulting from the bath dynamics depends on sampling of nuclear spin states from an ensemble, leading to the transition from superexponential decoherence in single-sample dynamics to power-law decay under ensemble averaging. In contrast, the decoherence of a single electron spin in one dot is essentially the same for different choices of the nuclear spin configuration.In double quantum dots, the exchange interaction between two electron spins renormalizes the excitation energy of pair flips in the nuclear spin bath, which in turn modifies the non-Markovian bath dynamics. As the energy renormalization varies with the static Overhauser field mismatch between the quantum dots, the electron singlet-triplet decoherence resulting from the bath dynamics depends on sampling of nuclear spin states from an ensemble, leading to the transition from superexponential decoherence in single-sample dynamics to power-law decay under ensemble averaging. In contrast, the decoherence of a single electron spin in one dot is essentially the same for different choices of the nuclear spin configuration.

arXiv:0707.2529Physical Review BFeb 5, 200817 citations

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

Marko J. Rančić, Guido Burkard

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 ${T}_{2}^{*}$ .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 ${T}_{2}^{*}$.

arXiv:1408.6700Physical Review BDec 22, 201414 citations

Nonequilibrium electron spin polarization in a double quantum dot: Lande mechanism

Yuri A. Serebrennikov

In moderately strong magnetic fields, the difference in Land\'e $g$ factors in each of the dots of a two-electron double quantum dot (DQD) may induce oscillations between singlet and triplet states of an entangled pair and lead to a nonequilibrium electron spin polarization in the system. The calculated bipolar polarization reflects the strong spin correlation in the spatially separated pair of electrons that occupy almost degenerate states in a coupled DQD. We will show that this polarization may partially survive the rapid inhomogeneous decoherence caused by random nuclear magnetic fields.In moderately strong magnetic fields, the difference in Land\'e $g$ factors in each of the dots of a two-electron double quantum dot (DQD) may induce oscillations between singlet and triplet states of an entangled pair and lead to a nonequilibrium electron spin polarization in the system. The calculated bipolar polarization reflects the strong spin correlation in the spatially separated pair of electrons that occupy almost degenerate states in a coupled DQD. We will show that this polarization may partially survive the rapid inhomogeneous decoherence caused by random nuclear magnetic fields.

arXiv:cond-mat/0508566Physical Review BJul 20, 20063 citations

\frac{1}{2}

, 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.

{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}^{*}

In moderately strong magnetic fields, the difference in Land\'e

g

factors in each of the dots of a two-electron double quantum dot (DQD) may induce oscillations between singlet and triplet states of an entangled pair and lead to a nonequilibrium electron spin polarization in the system. The calculated bipolar polarization reflects the strong spin correlation in the spatially separated pair of electrons that occupy almost degenerate states in a coupled DQD. We will show that this polarization may partially survive the rapid inhomogeneous decoherence caused by random nuclear magnetic fields.