Nuclear spin state narrowing via gate--controlled Rabi oscillations in a double quantum dot

Abstract

We study spin dynamics for two electrons confined to a double quantum dot under the influence of an oscillating exchange interaction. This leads to driven Rabi oscillations between the $|\uparrow \downarrow ⟩$--state and the $|\downarrow \uparrow ⟩$--state of the two--electron system. The width of the Rabi resonance is proportional to the amplitude of the oscillating exchange. A measurement of the Rabi resonance allows one to narrow the distribution of nuclear spin states and thereby to prolong the spin decoherence time. Further, we study decoherence of the two-electron states due to the hyperfine interaction and give requirements on the parameters of the system in order to initialize in the $|\uparrow \downarrow ⟩$--state and to perform a $\sqrt{\mathrm{SWAP}}$ operation with unit fidelity.

v1:9 pages, 1 figure; v2: 13 pages, 2 figures, added section on measurement, to appear in Phys. Rev. B

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