Nuclear dynamics during Landau-Zener singlet-triplet transitions in double quantum dots

Abstract

We consider nuclear-spin dynamics in a two-electron double dot system near the intersection of the electron spin singlet S and the lower energy component T + of the spin triplet. The electron spin interacts with nuclear spins and is influenced by the spin-orbit coupling. Our approach is based on a quantum description of the electron spin in combination with the coherent semiclassical dynamics of nuclear spins. We consider single and double Landau-Zener passages across the S-T + anticrossings. For linear sweeps, the electron dynamics is expressed in terms of parabolic cylinder functions. The dynamical nuclear polarization is described by two complex conjugate functions ± related to the integrals of the products of the singlet and triplet amplitudesc * Sc T+ along the sweep. The real part P of ± is related to the S-T + spin-transition probability, accumulates in the vicinity of the anticrossing, and for long linear passages coincides with the Landau-Zener probability P LZ = 1 − e −2πγ , where γ is the Landau-Zener parameter. The imaginary part Q of + is specific for the nuclear-spin dynamics, accumulates during the whole sweep, and for γ 1 is typically an order of magnitude larger than P . P and Q also show critically different dependences on the shape and the duration of the sweep. Q has a profound effect on the nuclear-spin dynamics, by (i) causing intensive shakeup processes among the nuclear spins and (ii) producing a high nuclear spin generation rate when the hyperfine and spin-orbit interactions are comparable in magnitude. Even in the absence of spin-orbit coupling, when the change in the the total angular momentum of nuclear spins is less thanh per single Landau-Zener passage, the change in the global nuclear configuration might be considerably larger due to the nuclear-spin shakeups. We find analytical expressions for the back action of the nuclear reservoir represented via the change in the Overhauser fields the electron subsystem experiences.

Electron spin-flip correlations due to nuclear dynamics in driven GaAs double dots

“…During the course of 500 sweeps, there may be a change in the z-polarization of the nuclei due to the effects of dynamic nuclear polarization (DNP), but the polarization will still be very small compared to the maximum polarization. If there were no dephasing of the transverse components of the nuclear spins, there could be conditions where the transverse components of the nuclear Overhauser fields could be significantly reduced after a relatively small number of DNP sweeps [31]. In our experiments, however, we find nuclear dephasing times τ λ of the order of 60 µsec, so the spins are completely dephased after a few hundred sweeps, and this effect should be absent.…”

“…The uniform magnetic field splits the triplet states in energy, producing gaps equal to the net Zeeman energy of the electrons between the m s = ±1 triplet states of the electrons T ± , and the m s = 0 triplet T 0 state. At any given positive detuning, the electronic states in the singlet sector are an admixture of (0, 2) and (1, 1) states due to the tunneling [30][31][32]. On the other hand, due to the total S z conservation tunneling has no influence on the triplet sector.…”

“…Eq. (31).] The column F B shows the theoretical predictions and experimental results for the frequencyindependent background count.…”

Self-quenching of nuclear spin dynamics in the central spin problem

“…The detailed patterns depend on the shape on the pulses on the gates and the instantaneous nuclear configuration. In turn, during each Landau-Zener (LZ) sweep the nuclear configuration changes due to the direct transfer of the angular momentum and shake-up processes [29,30]. Between the LZ sweeps, this configuration changes because of the difference in the Larmor precession rates of different nuclear species.…”

“…In particular, the difference (gradient) in the nuclear polarization of the left and right dots can be used for σ x rotations of a S-T 0 singlet-triplet qubit on the Bloch sphere [8]. Efficient control of a vast ensemble of nuclear spins is very challenging, and many analytical and numerical works have been carried out on this subject [23][24][25][26][27][28][29][30][31]. The principal experimental tool for polarizing nuclear spins and building gradients is based on driving a two-electron DQD electrically through the avoided crossing (S-T + anticrossing) of its singlet level S and the T + component of its electronic triplet T = (T + ,T 0 ,T − ).…”