# Detecting Axial Ratio of Microwave Field with High Resolution Using NV Centers in Diamond
## 3 Experiments and Results  
### MW Magnetic Field Detection Using a Single NV Center in Diamond  
The detection of the MW magnetic field is firstly demonstrated with a single NV center in diamond. The experiment setup was based on a home-built confocal microscope [23]. A 532-nm green laser was used to initialize and detect the NV center. A microscope objective (NA = 0.9, Olympus, Kyoto, Japan) was used to focus the laser and collect fluorescence photons. The diamond sample was a single crystal synthetic (100)-oriented electronic-grade type-IIa diamond with dimension of \(2\times 2\times 0.5\) mm\({}^{3}\) from the Element Six company. The diamond sample typically had less than a 0.03 ppb NV concentration before implantation. The investigated individual NV center was generated by \({}^{14}N\) ion implantation. The implantation dosage was \(10^{11}\) cm\({}^{-2}\), and the estimated average depth of NV was about 20 nm. The MW field (R&S SMB 100A signal generator, Munich, Germany) was delivered to the sample via a coplanar waveguide (CPW) fabricated on the top surface of the diamond substrate. The diamond sample was mounted on a NanoCube Piezo System (PI 611.3S, Karlsruhe, Germany) enabling nano-scale scanning. A permanent magnet mounted on a three-axis translation stage applied a bias magnetic field of between zero and roughly 600 G, aligning with the NV axis (z axis). Figure 2b is a fluorescence picture obtained by scanning the diamond sample. The marked bright spot in the picture is a single NV center chosen for MW magnetic field sensing. Second order photon correlation measurement of the bright spot with strong antibunching observed at zero delay \(g_{2}(0)\sim 0.11<0.5\) is proof that a single NV center was investigated [24] (data not shown). To conduct polarization selective MW magnetic field sensing, a bias magnetic field was applied to split the resonant spectra lines corresponding to \(m_{s}=0\leftrightarrow m_{s}=-1\) and \(m_{s}=0\leftrightarrow m_{s}=+1\) transitions. In our experiment, a bias magnetic field of about 500 G was applied. As shown in Figure 2c, the optically-detected magnetic resonance (ODMR) spectra revealed an energy level splitting of 2.86 GHz between the \(m_{s}=-1\) state and \(m_{s}=+1\) state. Although the MW field from the signal generator was linearly polarized, the transition \(m_{s}=0\leftrightarrow m_{s}=-1\) was only sensitive to the \(\sigma_{-}\) MW field when the MW magnetic field strength was not too strong according to the rotating wave approximation in quantum optics [19]. We implemented the measurement of the strength of the \(\sigma^{-}\) circularly-polarized component of the MW magnetic field with the NV center by detecting Rabi frequency. The MW field frequency was adjusted in resonance to the \(m_{s}=0\leftrightarrow m_{s}=-1\) transition. The Rabi frequency detection sequence is shown in Figure 3a. A laser pulse was firstly applied to initialize the NV electron to the ground \(m_{s}=0\) state. Then, an MW manipulation pulse was inserted. Finally, the population of the electron spin state was detected by another laser pulse. To obtain the manipulation frequency of the MW field, the MW pulse varied in time duration. Moreover, a photon count read pulse-2 was applied after the NV center was polarized to the \(m_{s}=0\) state again to provide a reference for drifts of the NV center. Figure 3b shows the Rabi oscillation detected with the MW field source power of about 7.8 mW applied. The oscillation signal was fitted by \(1-C_{0}e^{-t/t_{0}}sin(wt+\phi)\). The manipulation frequency of 0.63 MHz indicated the \(\sigma^{-}\) polarized MW magnetic field strength of \(B_{-}=0.22\) G at the NV center spot perpendicular to the NV axis. According to the fitting error of \(\delta B_{-}=0.0024\) G and detecting time of \(t_{meas}=1000\) s of the Rabi nutation curve, the sensitivity for MW field detection was \(\eta=\delta B\sqrt{t_{meas}}=1.7\)\(\mu\)T/\(\sqrt{\mathrm{Hz}}\). The Rabi oscillation frequency can also be derived by Fourier transformation (Figure 3c).