Wavefunction considerations for the central spin decoherence problem in a nuclear spin bath

Abstract

Decoherence of a localized electron spin in a solid state material (the ``central spin'' problem) at low temperature is believed to be dominated by interactions with nuclear spins in the lattice. This decoherence is partially suppressed through the application of a large magnetic field that splits the energy levels of the electron spin and prevents depolarization. However, the dephasing decoherence resulting from a dynamical nuclear spin bath cannot be removed in this way. Fluctuations of the nuclear field lead to an uncertainty of the electron's precessional frequency in a process known as spectral diffusion. This paper considers the effect of the electron's wavefunction shape on spectral diffusion and provides wavefunction dependent decoherence time formulas for a free induction decay as well as spin echoes and concatenated dynamical decoupling schemes for enhancing coherence. We also discuss a dephasing of a qubit encoded in singlet-triplet states of a double quantum dot. A central theoretical result of this work is the development of a continuum approximation for the spectral diffusion problem which we have applied to GaAs and InAs materials specifically.