# Influence of the nuclear Zeeman effect on mode locking in pulsed semiconductor quantum dots

## TL;DR

This paper investigates how the nuclear Zeeman effect influences mode locking in pulsed semiconductor quantum dots, revealing that it can alter resonance conditions and depends on nuclear species and g-factors.

## Contribution

It provides a quantitative analysis of the nuclear Zeeman effect's impact on mode locking, considering multiple nuclear species and their individual g-factors.

## Key findings

- Nuclear Zeeman effect can exchange resonant and non-resonant frequencies.
- Resonance positions depend on individual nuclear g-factors in multi-species models.
- The effect is significant when nuclear Zeeman energy is comparable to hyperfine interaction.

## Abstract

The coherence of the electron spin in a semiconductor quantum dot is strongly enhanced by mode locking through nuclear focusing, where the synchronization of the electron spin to periodic pulsing is slowly transferred to the nuclear spins of the semiconductor material, mediated by the hyperfine interaction between these. The external magnetic field that drives the Larmor oscillations of the electron spin also subjects the nuclear spins to a Zeeman-like coupling, albeit a much weaker one. For typical magnetic fields used in experiments, the energy scale of the nuclear Zeeman effect is comparable to that of the hyperfine interaction, so that it is not negligible. In this work, we analyze the influence of the nuclear Zeeman effect on mode locking quantitatively. Within a perturbative framework, we calculate the Overhauser-field distribution after a prolonged period of pulsing. We find that the nuclear Zeeman effect can exchange resonant and non-resonant frequencies. We distinguish between models with a single type and with multiple types of nuclei. For the latter case, the positions of the resonances depend on the individual $g$ factors, rather than on the average value.