Coherence of Nitrogen-Vacancy Electronic Spin Ensembles in Diamond

Abstract: We present an experimental and theoretical study of electronic spin decoherence in ensembles of nitrogen-vacancy (NV) color centers in bulk high-purity diamond at room temperature. Under appropriate conditions, we find ensemble NV spin coherence times (T_2) comparable to that of single NVs, with T_2 > 600 microseconds for a sample with natural abundance of 13C and paramagnetic impurity density ~10^15 cm^-3. We also observe a sharp decrease of the coherence time with misalignment of the static magnetic field relative to the NV electronic spin axis, consistent with theoretical modeling of NV coupling to a 13C nuclear spin bath. The long coherence times and increased signal-to-noise provided by room-temperature NV ensembles will aid many applications of NV centers in precision magnetometry and quantum information.

• The paper demonstrates that optimal magnetic field alignment extends NV ensemble coherence times to over 600 microseconds in high-purity diamond.
• The study shows that slight misalignment sharply reduces T2 due to hyperfine interactions with the 13C nuclear spin bath.
• The experimental and theoretical findings advance the design of diamond-based quantum sensors for precision magnetometry and memory storage.

Coherence of Nitrogen-Vacancy Electronic Spin Ensembles in Diamond

The study presented in this paper explores the coherence properties of nitrogen-vacancy (NV) electronic spin ensembles in diamond, an area of significant interest for both quantum information science and precision sensing technologies. The research investigates decoherence mechanisms, coherence lifetimes, and the impact of various external parameters on NV spin properties, specifically in bulk high-purity diamond at room temperature.

Summary of Key Findings

The paper achieves a noteworthy demonstration of long coherence times, $T_2$, for NV spin ensembles in diamond. Under optimal alignment conditions of the static magnetic field with the NV axis, coherence times were observed to exceed 600 microseconds in samples with natural abundance of $^{13}$C and low paramagnetic impurity density. These results are comparable to previous findings in single NV center measurements. This finding is significant as ensemble measurements inherently present increased signal-to-noise ratios, making them highly suitable for applications in precision magnetometry.

The study emphasizes the critical role of the orientation of the magnetic field in relation to the NV spin axis. It is observed that even slight misalignment results in a sharp reduction in coherence time. This phenomenon is consistent with theoretical models indicating that NV spin decoherence is influenced by hyperfine interactions with the surrounding $^{13}$C nuclear spin bath. The alignment of the field allows for optimal rephasing of nuclear spin precessions through coherent echo sequences, which, when compromised, significantly affects coherence.

Numerical Results and Theoretical Implications

Two diamond samples with different NV and nitrogen densities were employed in this study. For the sample with a nitrogen density of approximately $10^{15} \: \mathrm{cm}^{-3}$, ensemble $T_2$ times were over 600 microseconds. In contrast, a higher nitrogen density of about $5\times10^{15} \: \mathrm{cm}^{-3}$ resulted in reduced $T_2$ coherence times around 300 microseconds.

The theoretical exploration in the paper extends the understanding of decoherence mechanisms beyond individual NV centers to ensembles, revealing how distributions in the local spin environment lead to collective behavior different from isolated spins. A model predicting NV ensemble decoherence due to $^{13}$C interactions is presented, incorporating positional and orientation-dependent hyperfine coupling. The model successfully accounts for both the coherence properties with perfect field alignment and the detriments caused by misalignment.

Practical Applications and Future Directions

The ability to maintain long coherence times in NV ensembles at room temperature can enhance applications in precision magnetometry and quantum memory storage. The increase in signal-to-noise ratio through larger NV ensembles facilitates the detection of minute environmental magnetic changes, relevant for both physical and biological applications.

Looking forward, these findings provide a basis for further development of diamond-based quantum sensors and information processing units. The insight into magnetic alignment's impact on coherence can inform strategies to engineer NV hosting diamond materials with tailored spin environments for specific applications. Additionally, coupling of these NV ensembles with superconducting circuits or other quantum devices could further exploit their coherence properties, paving the way for advanced quantum technological applications.

In conclusion, this work represents a crucial step toward optimizing NV diamond systems for quantum technology, highlighting the significant potential for utilizing spin ensembles in real-world applications and setting the stage for future innovations in this domain.