Understanding Decoherence of the Boron Vacancy Center in Hexagonal Boron Nitride

Abstract: Hexagonal boron nitride (hBN) has emerged as a significant material for quantum sensing, particularly due to its ability to host spin active defects, such as the negatively charged boron vacancy (V$\mathrm{B}^-$ center). The optical addressability of the V$\mathrm{B}^-$ center and hBN's 2D structure enable high spatial resolution and integration into various platforms. However, decoherence due to the strong magnetic noise in hBN imposes fundamental limitations on the sensitivity of V$\mathrm{B}^-$ center-based applications. Understanding the phenomena behind decoherence and identifying parameter settings that provide the highest performance are essential for advancing V$\mathrm{B}^-$ sensors. This study employs state-of-the-art computational methods to investigate the decoherence of the V$\mathrm{B}^-$ center in hexagonal boron nitride across a wide range of magnetic field values from 0 T up to 3 T. The provided in-depth numerical and analytical analysis reveals an intricate interplay of various decoherence mechanisms. This study identifies five distinct magnetic field regions governed by different types of magnetic interactions with and within the abundant nuclear spin bath. In addition to magnetic field, the effects of zero-field splitting, nuclear polarization, and different hyperfine coupling terms are studied, representing an important step forward in utilizing V$\mathrm{B}^-$ ensembles in sensing. In particular, this study proposes operation in the moderate $180-350$ mT magnetic field range in chemically pure h$^{11}$B$^{15}$N samples, where the coherence time can reach $1-20$ $\mu$s, significantly exceeding the $\mathcal{O}( 100~\text{ns})$ low-field $T_2$ values.