Phonon-induced decay of the electron spin in quantum dots

TL;DR

This paper investigates how phonons and spin-orbit interactions cause spin relaxation and decoherence in GaAs quantum dots, revealing conditions where decoherence times are comparable to relaxation times and identifying ways to suppress spin decay.

Contribution

It derives an effective Hamiltonian linking electron spin to phonons, showing that decoherence time equals relaxation time under realistic conditions and identifying magnetic field orientations that suppress spin decay.

Findings

$T_2$ can be as large as $T_1$ in GaAs quantum dots.

Decoherence is suppressed for certain magnetic field directions.

$T_2=2T_1$ for all spin-orbit mechanisms in leading order.

Abstract

We study spin relaxation and decoherence in a GaAs quantum dot due to spin-orbit interaction. We derive an effective Hamiltonian which couples the electron spin to phonons or any other fluctuation of the dot potential. We show that the spin decoherence time $T_2$ is as large as the spin relaxation time $T_1$, under realistic conditions. For the Dresselhaus and Rashba spin-orbit couplings, we find that, in leading order, the effective magnetic field can have only fluctuations transverse to the applied magnetic field. As a result, $T_2=2T_1$ for arbitrarily large Zeeman splittings, in contrast to the naively expected case $T_2\ll T_1$. We show that the spin decay is drastically suppressed for certain magnetic field directions and values of the Rashba coupling constant. Finally, for the spin coupling to acoustic phonons, we show that $T_2=2T_1$ for all spin-orbit mechanisms in leading order in the electron-phonon interaction.