Electron spin evolution induced by interaction with nuclei in a quantum dot

TL;DR

This paper investigates how hyperfine interactions with nuclei cause non-exponential decoherence of a single electron spin in a quantum dot, revealing a power-law decay and tunable precession behavior influenced by magnetic fields.

Contribution

It provides an exact solution for electron spin decoherence in quantum dots considering non-Markovian nuclear interactions, highlighting differences between single-dot decoherence and ensemble dephasing.

Findings

Decoherence follows a power-law decay rather than exponential.

Decay time is proportional to  N/A, with N as the number of nuclei.

Magnetic field can tune precession amplitude and decay behavior.

Abstract

We study the decoherence of a single electron spin in an isolated quantum dot induced by hyperfine interaction with nuclei for times smaller than the nuclear spin relaxation time. The decay is caused by the spatial variation of the electron envelope wave function within the dot, leading to a non-uniform hyperfine coupling $A$. We show that the usual treatment of the problem based on the Markovian approximation is impossible because the correlation time for the nuclear magnetic field seen by the electron spin is itself determined by the flip-flop processes. The decay of the electron spin correlation function is not exponential but rather power (inverse logarithm) law-like. For polarized nuclei we find an exact solution and show that the precession amplitude and the decay behavior can be tuned by the magnetic field. The decay time is given by $\hbar N/A$, where $N$ is the number of nuclei inside the dot. The amplitude of precession, reached as a result of the decay, is finite. We show that there is a striking difference between the decoherence time for a single dot and the dephasing time for an ensemble of dots.