# Decoherence of dipolar spin ensembles in diamond

## TL;DR

This study combines theory and experiments to understand how nitrogen impurity spins in diamond cause decoherence of NV center spins, providing a detailed model that explains experimental results across various impurity concentrations.

## Contribution

It introduces a microscopic model and simulations that quantitatively explain NV spin decoherence due to nitrogen spins, resolving previous experimental discrepancies.

## Key findings

- Quantitative agreement between model and experiments across nitrogen concentrations
- Decoherence times $T_2^*$ and $T_2$ explained by many-body contributions
- Decoherence decay shapes derived from individual NV contributions

## Abstract

We present a combined theoretical and experimental study of solid-state spin decoherence in an electronic spin bath, focusing specifically on ensembles of nitrogen vacancy (NV) color centers in diamond and the associated substitutional nitrogen spin bath. We perform measurements of NV spin free induction decay times $T_2^*$ and spin-echo coherence times $T_2$ in 25 diamond samples with nitrogen concentrations [N] ranging from 0.01 to 300\,ppm. We introduce a microscopic model and perform numerical simulations to quantitatively explain the degradation of both $T_2^*$ and $T_2$ over four orders of magnitude in [N]. Our results resolve a long-standing discrepancy observed in NV $T_2$ experiments, enabling us to describe NV ensemble spin coherence decay shapes as emerging consistently from the contribution of many individual NV.