Electron Spin Noise under the Conditions of Nuclei Induced Frequency Focusing

TL;DR

This paper theoretically investigates electron spin noise in quantum dots under optical pulse pumping, revealing nuclear spin-induced frequency focusing and its impact on the electron spin noise spectrum.

Contribution

It introduces a classical approach to analyze nuclear spin distributions and electron spin noise spectra under non-equilibrium conditions caused by optical pulse trains.

Findings

Electron spin noise spectrum shows sharp peaks at phase synchronization conditions.

Nuclear spin distribution can be directly inferred from the noise spectrum.

Nuclear spin relaxation affects the evolution of the spin distributions and noise spectra.

Abstract

We study theoretically the electron spin noise in quantum dots under non-equilibrium conditions caused by the pumping by a train of circularly polarized optical pulses. In such a situation, the nuclear spins are known to adjust in such a way, that the electron spin precession frequencies become multiples of the pump pulse repetition frequency. This so called phase synchronization effect was uncovered in [Science {\bf 317}, 1896 (2007)] and termed nuclei-induced frequency focusing of electron spin coherence. Using the classical approach to the central spin model we evaluate the nuclear spin distribution function and the electron spin noise spectrum. We show that the electron spin noise spectrum consists of sharp peaks corresponding to the phase synchronization conditions and directly reveal the distribution of the nuclear spins. We discuss the effects of nuclear spin relaxation after the pumping is over and analyze the corresponding evolution of nuclear spin distributions and electron spin noise spectra.