# Investigation of Coherence Time of a Nitrogen-Vacancy Center in Diamond Created by a Low-Energy Nitrogen Implantation

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## Abstract

A nitrogen-vacancy (NV) center in diamond has been investigated extensively because of its promising spin and optical properties for applications to nanoscale magnetic sensing and magnetic resonance of magnetic elements outside the diamond. For those applications, a long decoherence time and positioning of an NV center on the diamond surface are desired. Here, we report the creation of NV centers near the diamond surface using a 3 keV nitrogen implantation and the coherence property of the created NV center.

## 1 Introduction

A nitrogen-vacancy (NV) center in diamond is a promising solid-state system for applications of nanoscale magnetic sensing and magnetic resonance spectroscopy with single spin sensitivity at room temperature [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14], because its extreme sensitivity to the surrounding electron [15, 16, 17] and nuclear spins [18, 19]. The spin sensitivity of those NV-based applications highly depends on the spin decoherence time of NV centers. An NV center near the diamond surface is also highly advantageous for the applications; however, recent studies showed that the decoherence time of NV centers close to the surface tends to be much shorter than that of NV centers inside the diamond crystal [20, 21].

In this article, we will discuss the coherence of an NV center, which was created near the diamond surface using a low-energy (3 keV) \(^{15}\)N implantation process. Such NV centers located several nanometers below the diamond surface will be useful for the NV-based magnetic resonance spectroscopy and sensing applications. We perform measurements and analyses of free-induction decay (FID) and spin echo (SE) decay to investigate dynamics of spin baths surrounding the NV center. We also discuss the spin decoherence time (\(T_\mathrm{d}\)) of the NV center and the extension of \(T_\mathrm{d}\) using a dynamical decoupling sequence.

## 2 Results and Discussion

*b*represents spin-bath coupling constant; \(\tau _\mathrm{C}\) is the correlation time of spin flip-flops within bath spins), [14, 17, 25], the followings represent the decay envelops of FID and SE:

*b*and \(\tau _\mathrm{C}\) as \(4.2 \pm 0.5\,\)μs\(^{-1}\) and \(58 \pm 8\,\)μs, respectively. Based on the obtained

*b*and \(\tau _\mathrm{C}\), the spin bath is in the quasi-static regime (\(b \tau _\mathrm{C} \gg 1\)). In the quasi-static limit, the SE decay is reduced into \(\hbox {SE}(2\tau ) \approx 1/2[1+\exp (-(\tau /T_\mathrm{d})^3)]\) (\(T_\mathrm{d}\) is a characteristic decoherence time).

Furthermore, we employed more advanced pulsed sequences to improve the coherence time of the NV center. Figure 3 shows the applications of the Carr–Purcell–Meiboom–Gill (CPMG) pulse sequence [26, 27]. The pulse sequence of CPMG is shown in the inset of Fig. 3. The CPMG pulse sequence consists of a series of the rephasing \(\pi\) pulses (*N* represents number of \(\pi\) pulses) which suppresses the noise responsible the SE decay. As shown in Fig. 3, the coherence time of the NV center becomes longer, while the number of the \(\pi\) pulses (*N*) in CPMG increases. With the application of the CPMG sequence with 32 \(\pi\) pulses (CPMG-32), we observed that the coherence time (\(T_\mathrm{d}\)) was extended from \(1.7\,\)μs (SE) to 7.2 μs (CPMG-32).

## 3 Summary

In summary, we demonstrated the creation of a shallow NV center with the low-energy nitrogen implantation process. We investigated spin dynamics and the coherence of the NV center using FID, SE, and CMPG techniques. Furthermore, we showed a long coherence time (7.2 μs) of the created NV center using the CMPG technique, which will be useful for the magnetic sensing applications.

## Notes

### Acknowledgements

This work was supported by the National Science Foundation (DMR-1508661 and CHE-1611134), the USC Anton B. Burg Foundation, and the Searle scholars program (S.T.).

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