Analytical solution of electron spin decoherence through hyperfine interaction in a quantum dot

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.