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arXiv:0712.2925 · Physical Review B

Coherent adiabatic theory of two-electron quantum dot molecules in external spin baths

Raymond Nepstad, L. Sælen, J. P. Hansen

Published Mar 12, 2008• 9 citations
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Abstract

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.

DOI
10.1103/physrevb.77.125315

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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 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 investigate the utilization of external magnetic field for the manipulation of the quantum states in a two-electron double quantum dot. The singlet and triplet states are coupled through the hyperfine interaction between the electrons and surrounding nuclei. When the magnetic field is changed as a function of time, the singlet-triplet transition is possible for certain values of magnetic field, when the singlet state becomes degenerate with the triplet state. The transition probability depends on the sweeping speed of the magnetic field through the averaged Landau-Zener formula. We evaluate proper time scales for efficient control of the quantum dot, evaluate the singlet probabilities for different time-dependent magnetic fields, and study the average of the final singlet probability, averaged over the orientations of the nuclear spins surrounding the quantum dot.
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.