Electron spin dynamics in quantum dots and related nanostructures due to hyperfine interaction with nuclei

TL;DR

This paper reviews recent theoretical and experimental studies on how hyperfine interactions between electron spins and nuclear spins affect electron spin dynamics in quantum dots, which is crucial for quantum computing applications.

Contribution

It provides a comprehensive summary of exact and approximate solutions for electron spin dynamics influenced by hyperfine interactions in quantum dots.

Findings

Exact analytical solutions for fully polarized nuclei

Numerical results for partially polarized nuclei

Comparison of approximation methods with exact results

Abstract

We review and summarize recent theoretical and experimental work on electron spin dynamics in quantum dots and related nanostructures due to hyperfine interaction with surrounding nuclear spins. This topic is of particular interest with respect to several proposals for quantum information processing in solid state systems. Specifically, we investigate the hyperfine interaction of an electron spin confined in a quantum dot in an s-type conduction band with the nuclear spins in the dot. This interaction is proportional to the square modulus of the electron wave function at the location of each nucleus leading to an inhomogeneous coupling, i.e. nuclei in different locations are coupled with different strength. In the case of an initially fully polarized nuclear spin system an exact analytical solution for the spin dynamics can be found. For not completely polarized nuclei, approximation-free results can only be obtained numerically in sufficiently small systems. We compare these exact results with findings from several approximation strategies.