Spectrum of an electron spin coupled to an unpolarized bath of nuclear spins

TL;DR

This paper analyzes electron spin decoherence in quantum dots caused by hyperfine interactions with nuclear spins by diagonalizing the Hamiltonian in high magnetic fields, revealing Gaussian tails in the density of states and implications for noise reduction.

Contribution

It provides a theoretical framework for understanding the spectral properties of an electron spin coupled to an unpolarized nuclear bath in high magnetic fields.

Findings

Density of states exhibits Gaussian tails.

Level spacing varies exponentially and super-exponentially.

Selecting states from the distribution wings can reduce noise.

Abstract

The main source of decoherence for an electron spin confined to a quantum dot is the hyperfine interaction with nuclear spins. To analyze this process theoretically we diagonalize the central spin Hamiltonian in the high magnetic B-field limit. Then we project the eigenstates onto an unpolarized state of the nuclear bath and find that the resulting density of states has Gaussian tails. The level spacing of the nuclear sublevels is exponentially small in the middle of each of the two electron Zeeman levels but increases super-exponentially away from the center. This suggests to select states from the wings of the distribution when the system is projected on a single eigenstate by a measurement to reduce the noise of the nuclear spin bath. This theory is valid when the external magnetic field is larger than a typical Overhauser field at high nuclear spin temperature.