AC Magnetic Field Sensing Using Continuous-Wave Optically Detected Magnetic Resonance of Nitrogen Vacancy Centers in Diamond
Nitrogen-vacancy (NV) centers in diamond are considered sensors for detecting magnetic fields. Pulsed optically detected magnetic resonance (ODMR) is typically used to detect AC magnetic fields; however, this technique can only be implemented after careful calibration that involves aligning an external static magnetic field, measuring continuous-wave (CW) ODMR, determining the Rabi frequency, and setting the microwave phase. In contrast, CW-ODMR can be simply implemented by continuous application of green CW laser and a microwave filed. In this letter, we report a method that uses NV centers and CW-ODMR to detect AC magnetic fields. Unlike conventional methods that use NV centers to detect AC magnetic fields, the proposed method requires neither a pulse sequence nor an externally applied DC magnetic field; this greatly simplifies the procedure and apparatus needed to implement this method. This method provides a sensitivity of at room temperature. Thus, this simple alternative to existing AC magnetic field sensors paves the way for a practical and feasible quantum sensor.
Nitrogen-vacancy (NV) centers in diamond can be used as sensitive room temperature magnetic field sensors with submicron spatial resolution Wolf et al. (2015); Balasubramanian et al. (2008); Taylor et al. (2008). Many variations of NV center magnetic field sensors exist, such as vector magnetic field sensing via confocal microscopyMaertz et al. (2010); Schoenfeld and Harneit (2011), rapid imaging using charge coupled device (CCD) arraysPham et al. (2011); Le Sage et al. (2013); Steinert et al. (2013); Devience et al. (2015); Glenn et al. (2015), and atomic force microscopy, which provides nanoscale imaging using a nanodiamond or a diamond nanopillar tipMaletinsky et al. (2012); Rondin et al. (2012); Tetienne et al. (2014); Appel et al. (2016); Chang et al. (2017).
To demonstrate a magnetic field sensor, either a pulsed ODMR technique or CW-ODMR technique may be used. The pulsed ODMR technique has been applied to detect both AC and DC magnetic fields Degen (2008); Maze et al. (2008); Taylor et al. (2008). Although the pulsed ODMR technique provides better sensitivity than the CW-OMDR technique, it requires careful calibration before it can detect a magnetic field. This calibration typically involves aligning an external static magnetic field, measuring CW-ODMR, observing Rabi oscillations (to determine the Rabi frequency), controlling the microwave phase, and constructing a pulse sequence. Pulsed ODMR detects high frequency magnetic fields by narrowing the pulse interval, which is technically possible, but this method is not easy from the viewpoint of the coherence time of NV center and the cost of the high speed control device.
In contrast, the CW-ODMR technique can be used to detect DC magnetic fields or low frequency (e.g., kHz) AC magnetic fields, and it is a more convenient technique because it only requires the continuous application of microwaves and an optical laser. Although the sensitivity of CW-ODMR is currently lesser than that of the pulsed ODMR, its simple experimental requirements have led many researchers to use it for practical and feasible magnetic field measurements.
To extend the applications of CW-ODMR method, using CW-ODMR with NV centers in diamond, we developed a method to measure AC magnetic fields up to MHz frequencies. Already, the CW-ODMR method is being used to measure AC magnetic fields in the kHz frequency range; in this technique, magnetic fields are applied to exploit the two level nature of NV centersJensen et al. (2014); Ahmadi et al. (2017); Tashima et al. (2017). In contrast, in the present work, we use the spin-1 properties of NV centers to measure AC magnetic fields with MHz frequencies. Three energy eigenstates exist in the ground state manifold of NV centers, all of which are used for magnetic field sensing. The lowest energy eigenstate is about 2.87 GHz below the two higher energy eigenstates, which themselves have an energy difference in the order of MHz. The idea behind the proposed method is to use this MHz transition frequency to detect AC magnetic fields while the lowest energy eigenstate is continuously excited by the continuous microwave radiation.
Note that the CW-ODMR technique is compatible with CCD based techniques that have slow camera frame rate. Since CCD cameras detect a wide field, the magnetic field information in diamond may be collected over a wide area in a single measurement. This allows the magnetic field distribution to be rapidly acquired because, unlike other techniques, the magnetic field in diamond does not need to be measured point by point. However, a potential problem of the CCD based scheme is the slow camera operation time (from 100 Hz to 1 kHz). Since the pulse repetition rate exceeds a few MHz for typical AC magnetic field sensing, sophisticated techniques such as the use of optical shutters are requiredPham et al. (2011); Devience et al. (2015). Conversely, because the CW-ODMR technique does not invoke such fast operations, in our AC magnetic field sensors provides a way to adopt the CCD based technique with much more simple experimental setup. Since the CCD based setup can increase the measurement volume of NV centers, the signal from the NV is enhanced and highly sensitive sensing becomes possible. Furthermore, no external static magnetic field is used, the measurement volume can be increased without concern for the uniformity of the static magnetic field.
We start by explaining the theory behind both the conventional methods and the proposed method. The Hamiltonian of an NV center with no external magnetic field is given as follows.
where is a spin-1 operator for electron spin, is the zero field splitting, and is the strain in the x(y) direction. Without loss of generality, we set by defining the axis to pass through the NV center in the direction of the strain. Throughout this letter, we set . The ground state is , and we define the two higher energy eigenstates as and with eigenenergies and , respectively. With zero external magnetic field, two dips appear around 2.87 GHz in CW-ODMR, which is indicative of externally driven transitions from the ground state to higher energy eigenstates such as or Fang et al. (2013); Zhu et al. (2014); Matsuzaki et al. (2016).
We now consider the dynamics of NV centers when both the microwave field and the target AC magnetic field are present. With these external fields, the Hamiltonian of the NV center takes the form , where is given by
where is the gyromagnetic ratio of the electron spin, is the microwave field (target AC magnetic field) amplitude, and is the frequency of the driving microwave field (target AC magnetic field). We assume that is in the order of GHz, whereas is in the order of MHz. In a rotating frame defined by , the effective Hamiltonian becomes . By considering and using the rotating wave approximation, we obtain the following Hamiltonian.
In a different rotating frame defined by , we obtain the following Hamiltonian.
where we have again used the rotating wave approximation.
Importantly, an AC magnetic field in the direction [the fifth term in the Hamiltonian (5)] induces the transition between and when the frequency of the field in resonance with the energy difference between and . Without the AC magnetic field, we can only induce transitions between the ground state and the bright (dark) state  via the microwave radiation with a frequency of () in the conventional CW-ODMR setup. and the applied AC magnetic field and the microwave field can drive transitions from the ground state to the bright and dark states. Thus, the results of CW-ODMR with an applied AC magnetic field should differ from t hose of CW-ODMR without any AC magnetic field.
We now quantify the change in the CW-ODMR signal that occurs because of the AC magnetic fields first focusing on the transition induced between and by the AC magnetic field with a frequency of . We assume a weak amplitude for the AC magnetic field so that we can use time dependent perturbation theory. In the interaction picture, we obtain
By using Fermi’s golden rule, we can show that the transition from the ground state to the higher energy eigenstates (Fig. 1). Thus, applying an external AC magnetic field changes the dip structure in CW-ODMR.
We now describe the details of the diamond sample used in our experiment. We used an ensemble of NV centers in a diamond film on a (001) electronic grade substrate. The isotopically purified diamond film () was grown using nitrogen doped microwave plasma assisted chemical vapor deposition. To both increase the NV center density and improve the coherence timeKleinsasser et al. (2016), the sample was irradiated with ion doses of with 15 keV He ions and was annealed for 24 h in vacuum at 800 . The NV density was estimated to be of the order of .
Now, we explain the experiment of sensing an AC magnetic field using CW-ODMR. For these experiments, we used a homebuilt system for confocal laser scanning microscopy with a spatial resolution of 400 nm. The diamond sample was positioned above the antennaSasaki et al. (2017) used to emit the microwave radiation. A 30 m diameter copper wire is placed in contact with the sample surface to apply the target AC magnetic field, which is detected by measuring the difference in the CW-ODMR spectrum.
Figure 2 shows the signal from the conventional CW-ODMR technique (with no external AC magnetic field); the resonance frequency is split by about 4 MHz because of a local magnetic field and strain from impurities in diamondZhu et al. (2014); Matsuzaki et al. (2016). This splitting gives the energy difference between and . ODMR is performed by applying an AC magnetic field with a frequency of and a magnetic field amplitude to induce transitions between and . The result in Fig. 2 shows the difference in the spectrum due to the external AC magnetic field, and it demonstrates the detection of the external AC magnetic fields by CW-ODMR.
Since we use the resonance between and , the frequency band in which AC magnetic fields may be detected is determined by the width of the split in the CW-ODMR spectrum.
As noted in Eq. (5), this splitting may be increased by applying an electric fieldIwasaki et al. (2017), which provides a way to determine which frequency of the AC magnetic field will be detected. Straightforward calculations show that the detectable frequencies range from hundreds of kHz to hundreds of MHz. The lower limit is determined by the resonance linewidth of the ODMR spectrum with 200 kHz currently being the minimum linewidthKleinsasser et al. (2016). However, the upper limit is determined by the breakdown field in diamond. The splitting width due to the Stark effect is given as , so the maximum splitting width is 340 MHz because the Stark shift constant 17 Hz cm/VVan Oort and Glasbeek (1990) and the breakdown electric field of diamond 10 MV/mCollins (1994).
Next, we measure ODMR dependence on the amplitude of the AC magnetic field. The ODMR spectrum with various AC magnetic field amplitudes is shown in Fig. 3 where we set .
While two resonances are observed without applying the AC magnetic fields, the resonance is split into four lines, and the split becomes larger as we increase the amplitude of the AC magnetic fields. This is consistent with our derived formula that represents the resonance .
In Fig. 4(a), we plot the ODMR signal against the amplitude of the AC magnetic field, with the microwave frequency , which is one of the two resonance frequencies obtained with no external AC magnetic field. The signal quadratically depends on the amplitude, which can be quantitatively understood as follows. We represent the two resonances around as the sum of two Lorentzian functions: , where is the linewidth. In this case, we obtain for small , which this shows the quadratic dependence.
To estimate the magnetic sensitivity from the experimental results, we must determine the signal fluctuation where corresponds to the photoluminescence in ODMR Taylor et al. (2008). As shown in Fig. 4(b), the fluctuation decreases with the relation , where is the measurement time. From these experimental observations, we estimate the sensitivity of the method for detecting AC magnetic fields to be . Note that the sensitivity could be improved by using a NV center in diamond with a narrow linewidthKleinsasser et al. (2016) and with an almost perfect preferential orientation of the axisMichl et al. (2014); Fukui et al. (2014); Ozawa et al. (2017) and a high density of the NV centersAcosta et al. (2009); Kleinsasser et al. (2016); Ozawa et al. (2017). In fact, by using the parameters reported in Ozawa et al. (2017), we estimate that the proposed method would have a sensitivity of .
In conclusion, we report a method to detect MHz frequency AC magnetic fields that uses CW-ODMR by exploiting NV centers in diamond. By simply applying a continuous microwave field and optical laser irradiation, the method provides a sensitivity of at room temperature. The experimental setup is very simple because it requires neither an external DC magnetic field nor a pulse sequence. These results pave the way to realize a practical and feasible AC magnetic field sensor.
We thank H. Toida and K. Kakuyanagi for helpful discussions. This work was supported by JSPS KAKENHI Grant No. 15K17732. This work was also supported by MEXT KAKENHI Grants No. 15H05868, No. 15H05870, No. 15H03996, No. 26220602, and No. 26249108. This work was also supported by the Advanced Photon Science Alliance (APSA), JSPS Core-to- Core Program FY2013 Projects No.2, and Spin-NRJ.
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