Abstract
We analytically solve the non-Markovian single-electron spin dynamics due to hyperfine interaction with surrounding nuclei in a quantum dot. We use the equation-of-motion method assisted with a large field expansion, and find that virtual nuclear spin flip-flops mediated by the electron contribute significantly to a complete decoherence of the transverse electron spin correlation function. Our results show that a 90% nuclear polarization can enhance the electron spin time ${T}_{2}$ by almost two orders of magnitude. In the long time limit, the electron spin correlation function has a nonexponential $1∕{t}^{2}$ decay in the presence of both polarized and unpolarized nuclei.
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