Analytical Solution of Electron Spin Decoherence Through Hyperfine Interaction in a Quantum Dot

TL;DR

This paper provides an analytical solution for electron spin decoherence in quantum dots caused by hyperfine interactions, revealing the significant role of virtual nuclear spin flip-flops and the impact of nuclear polarization on spin coherence times.

Contribution

It introduces an analytical approach to model non-Markovian electron spin dynamics considering hyperfine interactions, including effects of nuclear polarization.

Findings

Virtual nuclear spin flip-flops significantly contribute to decoherence.

Nuclear polarization can increase electron spin $T_2$ time by nearly 100 times.

Electron spin correlation decays as 1/t^2 at long times.

Abstract

We analytically solve the {\it 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 transverse electron spin correlation function. Our results show that a 90% nuclear polarization can enhance the electron spin $T_2$ time by almost two orders of magnitude. In the long time limit, the electron spin correlation function has a non-exponential $1/t^2$ decay in the presence of both polarized and unpolarized nuclei.