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Physical Review B

Spin dynamics in a double quantum dot: Exact diagonalization study

Jani Särkkä, Ari Harju

Published Jun 13, 2008• 13 citations
Publisher

Abstract

We study spin dynamics and singlet-triplet decoherence due to the hyperfine interaction in a parabolic double quantum dot. We use exact diagonalization and perturbation theory for calculating the time evolution of the wave function. The probabilities for the singlet state exhibit damped oscillations and converge toward a value, which depends only on the strength of the hyperfine field and the exchange energy. We derive expressions for the asymptotic singlet probability and its variance using a $2\ifmmode\times\else\texttimes\fi{}2$ effective Hamiltonian matrix. The asymptotic values and variances for singlet probabilities are in agreement with previous experimental data.

DOI
10.1103/physrevb.77.245315

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We study spin dynamics and singlet-triplet decoherence due to the hyperfine interaction in a parabolic double quantum dot. We use exact diagonalization and perturbation theory for calculating the time evolution of the wave function. The probabilities for the singlet state exhibit damped oscillations and converge toward a value, which depends only on the strength of the hyperfine field and the exchange energy. We derive expressions for the asymptotic singlet probability and its variance using a 2\ifmmode×\else\texttimes\fi22\ifmmode\times\else\texttimes\fi{}22\ifmmode×\else\texttimes\fi2 effective Hamiltonian matrix. The asymptotic values and variances for singlet probabilities are in agreement with previous experimental data.
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.
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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.
We investigate hyperfine induced electron spin and entanglement dynamics in a system of two quantum dot spin qubits. We focus on the situation of zero external magnetic field and concentrate on approximation-free theoretical methods. We give an exact solution of the model for homogeneous hyperfine coupling constants (with all coupling coefficients being equal) and varying exchange coupling, and we derive the dynamics therefrom. After describing and explaining the basic dynamical properties, the decoherence time is calculated from the results of a detailed investigation of the short-time electron-spin dynamics. The result turns out to be in good agreement with experimental data.
We derive an accurate molecular orbital based expression for the coherent time evolution of a two-electron wave function in a quantum dot molecule where the electrons interact with each other, with external time-dependent electromagnetic fields and with a surrounding nuclear spin reservoir. The theory allows for direct numerical modeling of the decoherence in quantum dots due to hyperfine interactions. Calculations result in good agreement with recent singlet-triplet dephasing experiments by Laird et al. [Phys. Rev. Lett. 97, 056801 (2006)], as well as analytical model calculations. Furthermore, it is shown that using a much faster electric switch than applied in these experiments will transfer the initial state to excited states where the hyperfine singlet-triplet mixing is negligible.