Non-Perturbative Bounds on Hyperfine-Induced Electron Spin Coherence Times

TL;DR

This paper derives rigorous, non-perturbative bounds on electron spin coherence times affected by hyperfine interactions, showing that high magnetic fields can prevent relaxation but not dephasing, with implications for quantum information stability.

Contribution

It introduces a non-perturbative method to establish bounds on T_1 and T_2 coherence times considering hyperfine interactions, including effects of spin echo sequences.

Findings

T_1 becomes infinite above a critical magnetic field B_c.

Dephasing (T_2) persists even at high magnetic fields.

Lower bounds on T_2 account for spin echo effects.

Abstract

We address the decoherence of a localized electron spin in an external magnetic field due to the hyperfine interaction with a lattice of nuclear spins. Using a completely non-perturbative method, rigorous bounds on the T_1 and T_2 coherence times for the electron spin are provided. It is shown that for magnetic fields B greater than some critical field B_c (B_c ~ .001 - 2 Tesla for the systems studied here), the z-polarization of the electron spin cannot relax, and hence T_1 is infinite. However, even at high fields dephasing can still occur. We provide a lower bound on the T_2 coherence time that explicitly takes into account the effects of a spin echo pulse sequence.