Spin echo decay at low magnetic fields in a nuclear spin bath

TL;DR

This paper studies the spin echo decay of an electron in quantum dots interacting with nuclear spins at very low magnetic fields, using both numerical simulations and analytical theory, revealing new insights into decoherence mechanisms.

Contribution

It demonstrates the validity range of the effective pure dephasing Hamiltonian and uncovers the oscillatory behavior of the spin echo signal in homonuclear baths at low fields.

Findings

Analytical theory matches numerical simulations at fields above the Overhauser field.

Spin echo signals in homonuclear baths oscillate with nuclear Zeeman frequency.

Qualitative differences between homonuclear and heteronuclear baths persist at low fields.

Abstract

We investigate theoretically the spin echo signal of an electron localized in a quantum dot and interacting with a bath of nuclear spins. We consider the regime of very low magnetic fields (corresponding to fields as low as a militesla in realistic GaAs and InGaAs dots). We use both the exact numerical simulations and the analytical theory employing the effective pure dephasing Hamiltonian. The comparison shows that the latter approach describes very well the spin echo decay at magnetic fields larger than the typical Overhauser field, and that the timescale at which this theory works is larger than previously expected. The numerical simulations are also done for very low values of electron spin splitting at which the effective Hamiltonian based theory fails quantitatively. Interestingly, the qualitative difference in the spin echo decay between the cases of a homonuclear and a heteronuclear bath (i.e. bath containing nuclear isotopes having different Zeeman energies), predicted previously using the effective Hamiltonian approach, is still visible at very low fields outside the regime of applicability of the analytical theory. We have found that the spin echo signal for a homonuclear bath oscillates with a frequency corresponding to the Zeeman splitting of the single nuclear isotope present in the bath. The physics behind this feature is similar to that of the electron spin echo envelope modulation (ESEEM). While purely isotropic hyperfine interactions are present in our system, the tilting of the electron precession axis at low fields may explain this result.