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 Λ± related to the integrals of the products of the singlet and triplet amplitudes c̃∗Sc̃T+ along the sweep. The real part P of Λ± 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 PLZ=1−e−2πγ, where γ is the Landau-Zener parameter. The imaginary part Q of Λ+ 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 than ℏ 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.