Applied Magnetic Resonance

, Volume 48, Issue 6, pp 571–577 | Cite as

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

  • Chathuranga Abeywardana
  • Zaili Peng
  • Laura C. Mugica
  • Edward Kleinsasser
  • Kai-Mei C. Fu
  • Susumu Takahashi
Original Paper
  • 332 Downloads

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

For the investigation, NV centers were created near the surface of an electric grade diamond crystal (purchased from Element Six; the dimension is \(2 \times 2 \times 0.5\) mm\(^3\)). First, \(^{15}\)N\(^{+}\) ions implantation was performed with the ion energy of 3 keV and the fluence of 10\(^{10}\) N/cm\(^2\). Based on the simulation using the SRIM (the stopping and range of ions in matter) simulator [22], the nominal stopping depth in the present condition is \(5 \pm 2\) nm). After the implantation, the diamond crystal was annealed (850 \(^{\circ }\mathrm{C}\) under 95/5\(\%\) Ar/H\(_2\) gas for an hour, subsequently 460 \(^{\circ }\mathrm{C}\) under air for 24 h) [23].
Fig. 1

Identification of a single NV near the surface of the \(^{15}\)N implanted diamond. a Spatial map of fluorescence signals of the diamond. The dimension of the image is \(3\times 6\) μm\(^2\). The legend contains the color scheme with respect to the FL intensity. The circle indicates the NV center used in the ODMR studies. Inset shows autocorrelation measurement result of the NV. b, c cw ODMR data of the NV center taken without any external magnetic field and at \(B_0=32.0\) mT, respectively. The fit to the Lorentzian function is shown by the solid blue line. The input power of the microwave was 2 dBm. d Pulsed ODMR of the NV taken at \(B_{0} = 32.0\) mT. The blue line represents the fit of the data using two Lorentzian functions. The input power of the microwave was −15 dBm. Amplitudes of bd were normalized by FL intensity taken without applied microwave field at each data point (color figure online)

Optically detected magnetic resonance (ODMR) of the created NV centers was measured using a home-built ODMR setup [14, 24]. Figure 1a shows a fluorescence (FL) image of the diamond sample. We found that FL signals were observed only near the surface of the diamond. Then, we performed autocorrelation (AC) measurements and continuous-wave (cw) ODMR measurements of NV centers. An isolated FL signal of a single NV center used in the rest of the study is indicated in Fig. 1a. The AC measurement data used to confirm the single NV are given in the inset of Fig. 1a. As shown in Fig. 1b, cw ODMR signal at zero magnetic field and room temperature was observed at the microwave frequency of 2.869 GHz. The resonance frequency agrees with the value of the axial term of the zero-field splitting (D-term) for the NV center [1]. In the present study, where we measured 23 NVs, noticeable splitting of the cw ODMR signal due to the presence of the non-axial term of the zero-field splitting (E-term) was not observed, while the splitting is often seen in implanted NVs and NVs in nanodiamonds [28, 29]. As shown in Fig. 1c, cw ODMR measurement was performed by applying a static magnetic field of 32.0 mT aligned along the \(\langle 111 \rangle\) axis of the diamond and showed cw ODMR signal at 1.973 GHz corresponding to the \(m_\mathrm{S}=0 \leftrightarrow -1\) transition of the NV center. Next, we carried out the pulsed ODMR measurements with the application of a single \(\pi\)-pulse for the NV center. The linewidth of cw ODMR spectrum is broaden by the power-saturation and it often makes it difficult to resolve a small hyperfine splitting in ODMR signals. On the other hand, the spectral linewidth taken by the pulsed ODMR is limited by the excitation bandwidth of the microwave pulse, so the spectral resolution can be improved by the pulsed ODMR with a long microwave pulse. We performed the pulsed ODMR with the pulse duration of 850 ns to resolve the \(^{15}N\) hyperfine coupling. As shown in Fig. 1d, we observed two ODMR signals with the hyperfine splitting of 3.1 MHz which agrees with ODMR of \(^{15}\)NV center, and thus, the experiment proves that the observation of a single NV center created by the implantation process. Furthermore, we estimated the yield of the NV fabrication to be \(\sim\)1\(\%\) based on the density of the observed NV centers.
Fig. 2

Pulsed ODMR measurements of the created NV. The measurement was performed at \(B_{0} = 32.0\) mT. a\(P(m_\mathrm{S}=0)\) as a function of the microwave pulse duration (\(t_\mathrm{p}\)). The measurement was done at the frequency of 1.973 GHz. The Rabi frequency (\(f_{\mathrm{Rabi}}\)) is \(5.7 \pm 0.1\) MHz was extracted by fitting the data to the function \(1/2[\cos (2 \pi f_{\mathrm{Rabi}} t_{\mathrm{p}})\exp (-(t_{\mathrm{p}}/T)^{2})]\). b Ramsey fringes of the NV center. The pulse sequence is shown on the top panel. The measurement was done at 1.973 GHz. c Spin echo decay of the NV center. The pulse sequence is shown on the top panel

Next, we investigate the coherence of the created NV center using pulsed ODMR experiments. In the pulse measurements, NV was first polarized into the \(m_{\mathrm{S}} = 0\) state by applying the initialization laser pulse (\(\sim\)2 μs). Then, desired MW pulse sequence was applied and the resulting spin state was readout by applying the readout laser pulse (\(\sim\)0.3 μs). During the measurement, the FL intensities of the \(m_\mathrm{S} = 0\) and −1 states were also measured for the reference to map the FL signal to the population of the \(m_\mathrm{S} = 0\) state (\(P(m_\mathrm{S}=0)\)). Figure 2a shows the Rabi oscillation measurement of the NV. By analyzing the data, the frequency of Rabi oscillations (\(f_{\mathrm{Rabi}}\)) was extracted to be \(5.7 \pm 0.1\) MHz. Therefore, \(\pi\)/2 and \(\pi\) pulse lengths were determined to be 44 and 88 ns, respectively. Following to the Rabi measurement, we studied the dynamics of spin baths surrounding the NV center. As shown in Fig. 2b and c, we performed the FID and SE measurements of the NV center. FID and SE decay of NV centers in diamond are often caused due to couplings to fluctuating spin baths surrounding the NV center. By considering the spin baths as classical magnetic noises (\(B_{n}(t))\) where \(C(t) = \langle B_{n}(0)B_{n}(t)\rangle = b^2\)exp(\(-| t |/\tau _\mathrm{C}\)) (the Ornstein–Uhlenbeck (O–U) process; 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:
$$\begin{aligned} \hbox {FID}(t) = \frac{1}{2} - \frac{1}{2} \left[ \cos (\pi A^{\mathrm{NV}}_z t)\right] \exp \left[ -(b \tau _\mathrm{C})^2\left(\frac{t}{\tau _\mathrm{C}}+e^{-t/\tau _\mathrm{C}}-1\right) \right] , \end{aligned}$$
(1)
and
$$\begin{aligned} \hbox {SE}(2\tau ) = \frac{1}{2} + \frac{1}{2}\exp \left[ -(b \tau _\mathrm{C})^2\left( \frac{2\tau }{\tau _\mathrm{C}}-3-e^{-(2\tau )/\tau _\mathrm{C}}+4e^{-(2\tau )/(2\tau _C)}\right) \right] . \end{aligned}$$
(2)
In the present case, the hyperfine coupling \(A^{\mathrm{NV}}_z = 3.1\) MHz (Fig. 1d). By fitting the FID and SE data to Eqs. (1) and (2) simultaneously, we found a good agreement between the data and fit. From the fit result, we also obtained 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).
Fig. 3

Decoherence time (\(T_\mathrm{d}\) of the NV center measured by SE, CPMG-4, CPMG-16, and CPMG-32 sequences. The pulse sequence is given in the inset. SE consists of a single pi-pulse (\(N = 1\)) and CPMG-N consists of N pi-pulses. Lengths of \(\pi\)/2 and \(\pi\) pulses were 44 and 88 ns, respectively. Dashed lines shows the simulations of decay envelope using \(1/2 + 1/2\exp [-(t/T_\mathrm{d})^3]\), where t and \(T_\mathrm{d}\) represent the total evolution time and decoherence time, respectively. The obtained \(T_\mathrm{d}\) values are \(1.7 \pm 0.1\), \(3.1 \pm 0.1\), \(6.4 \pm 0.3\), and \(7.2 \pm 0.3\,\)μs for SE, CPMG-4, CPMG-16, and CPMG-32, respectively

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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Copyright information

© Springer-Verlag Wien 2017

Authors and Affiliations

  1. 1.Department of ChemistryUniversity of Southern CaliforniaLos AngelesUSA
  2. 2.Department of Electrical EngineeringUniversity of WashingtonSeattleUSA
  3. 3.Department of PhysicsUniversity of WashingtonSeattleUSA
  4. 4.Department of Physics and AstronomyUniversity of Southern CaliforniaLos AngelesUSA

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