# Efficient Identifying the Orientation of Single NV Centers in Diamond and
Using them to Detect Near Field Microwave

Xuerui Song<EMAIL_ADDRESS>Fupan Feng<EMAIL_ADDRESS>Chunxiao Cai
China Academy of Space Technology (Xi’an), Xi’an, Shaanxi, 710100, P. R. China
Guanzhong Wang  Wei Zhu  Hefei National Laboratory for Physical Science at
Microscale, and Department of Physics, University of Science and Technology of
China, Hefei, Anhui, 230026, P. R. China  Wenting Diao  Chongdi Duan  China
Academy of Space Technology (Xi’an), Xi’an, Shaanxi, 710100, P. R. China

###### Abstract

Arrays of NV centers in the diamond have the potential in the fields of chip-
scale quantum information processing and nanoscale quantum sensing. However,
determining their orientations one by one is resource intensive and time
consuming. Here, in this paper, by combining scanning confocal fluorescence
images and optical detected magnetic resonance, we realized a method of
identifying single NV centers with the same orientation, which is practicable
and high efficiency. In the proof of principle experiment, five single NV
centers with the same orientation in a NV center array were identified. After
that, using the five single NV centers, microwave near field generated by a
$20\,\mu m$-diameter Cu antenna was also measured by reading the fluourescence
intensity change and Rabi frequency at different microwave source power. The
gradient of near field microwave at sub-microscale can be resoluted by using
arry of NV centers in our work. This work promotes the quantum sensing using
arrays of NV centers.

Nitrogen-vacancy(NV) centers are paramagnetic defects within the diamond
lattice, which consist of a substitutional N imputiry adjacent to a vacant
lattice site. Owing to their outstanding optical and spin properties at room
temperature, NV centers have attracted more and more attentions in the fields
of nanoscale quantum sensing and quantum information processing.Degen,
Reinhard, and Cappellaro (2017); Maze  _et al._ (2008); Ariyaratne  _et al._
(2018); Maurer  _et al._ (2012); Bradley  _et al._ (2019); Zaiser  _et al._
(2016) Especially in the fields of quantum sensing, due to the fact that the
NV center can be stablely located colse to the diamond surface at nanoscale or
nanodiamonds,Osipov  _et al._ (2019); Song  _et al._ (2013); Maletinsky  _et
al._ (2012); Ofori-Okai  _et al._ (2012) the spatial resolution of the sensors
based on NV centers have down to nanoscale.Hall  _et al._ (2009); Ariyaratne
_et al._ (2018); Kucsko  _et al._ (2013); Schmitt  _et al._ (2017) This
nanoscale property is quite important in the fields of condense matter physics
and biology research.Casola, Sar, and Yacoby (2018); Wu  _et al._ (2016); Shi
_et al._ (2018); Lillie  _et al._ (2019) Recently, some groups reported that
the near field microwave(MW) sensing using NV centers in diamond have down to
micro even nanoscale resolutions.Wang  _et al._ (2015a); Appel  _et al._
(2015); Shao  _et al._ (2016); Dong  _et al._ (2018); Horsley  _et al._
(2018); Mariani  _et al._ (2018); Chipaux  _et al._ (2015)

Precise detecting of the spatial distribution of the MW near field is crucial
for developing new types of MW devices, chip failure checking, electromagnetic
compatibility analyzing and even solid state physics studying.Wallraff  _et
al._ (2004) Generally speaking, the spatial resolution of the traditional
dipole probe is limited to about $100\,\mu m$. Even worse, during the MW
measuring process, the dipole probe will reconstruct the electromagnetic
field, which can disturb the near field detection.Holloway  _et al._ (2014) In
recent years, new sensors based on alkali vapor cell, superconductor and spin-
torque diode have been developed to detect the near field MW with high
sensitivity.Fang  _et al._ (2016); Couëdo  _et al._ (2019); Fan  _et al._
(2015) However, none of them obtained nanoscale spatial resolution. The
development of near field MW sensors based on NV center will bring an ultimate
solution to this problem.

As shown in the right section of Fig. 1, the ground state of electron spin of
the NV center is a spin triplet ${}^{3}A_{2}$ with a zero field splitting of
$D=2.87\,GHz$. The oscillation between $|0\rangle$ and $|\pm 1\rangle$ ground
states can be driven by a resonant MW magnetic field as
$\hbar\omega=D\pm\gamma B_{Z}$, where $B_{Z}$ is a static magnetic field along
the axis of NV center, $\gamma=2.8025\,MHz/Gauss$ is the gyromagnetic ratio of
the electron spin. The MW magnetic field is written as
$\boldsymbol{B}_{MW}(t)=\boldsymbol{B}_{MW}cos(\omega t)$, where
$f=\frac{\omega}{2\pi}$ is the MW frequency. By carrying out the optical
detected magnetic resonant (ODMR), the resonant frequency of the MW field can
be obtained. By adding static magnetic field $\boldsymbol{B}$, $|\pm 1\rangle$
can be further splitted, which varies the resonant MW field frequency from kHz
to sub-THz.Aslam  _et al._ (2015) Additionally, the Rabi frequency of the spin
state oscillation $\Omega$ is proportional to the component of the MW field in
a plane perpendicular to the NV axis as $\Omega=\gamma B_{MW\perp}$. At last,
by using NV centres at the four different axes, the total amplitude $B_{MW}$
and the orientation of the vector can be obtained by mearsuring different
$B_{MW\bot}$. By doing this, nonivasive detecting of near field MW magnetic
field at nanoscale resolution obtained.Wang  _et al._ (2015a); Appel  _et al._
(2015)

Traditionally, to measure field at nanoscale resolution, scanning should be
carried out by combining the NV sensors with AFM tip, which is highly
requirement in practice.Appel  _et al._ (2015); Maletinsky  _et al._ (2012);
Degen (2008) Alternatively, by measuring field using NV centers at different
sites, NV center arrays in the diamond have the potential in the fields
nanoscale quantum sensing.Momenzadeh  _et al._ (2015); Wang  _et al._ (2015b);
Fukami  _et al._ (2019) Howerer, determining their orientations one by one is
resource intensive and time consuming. In this work, using shallow NV center
arrays in diamond, a method by combining scanning confocal fluorescence image
and optical detected magnetic resonance was developed to efficiently identify
the NV centers with same orientation. The relative MW amplitude distribution
is obtained by measuring the fluorescence intensity and the Rabi oscillation
of the single NV center at different sites of the arrays. The spatial
resolution of near field MW sensors based on array of NV centers in this work
is hundreds of nanometers which consists with the optical microscope.

Figure 1: Experiments and principle illustrating of the work. Left, shallow
array of NV centers with different orientations were located close to the
diamond surface within nanometers. The near field MW was generated by a
$20\,\mu m$-diameter Cu antenna which lays tens of micrometers above the
diamond surface. The NV center was exciated by $532\,nm$ green laser. The red
fluorescence was collected by an objective and then detected by an APD. Right,
energy level of the ground state of the electron spin of NV center.

The sample used in this work was a $2\times 2\times 0.5\,mm^{3}$ high-quality
electronic grade diamond with natural isotopic concentration of ${}^{13}C$
(1.1%) from Element Six. The NV center array was prepared by implanting
$8\text{\,}keV$ ${}^{14}N_{2}^{+}$ molecules with a fluence of $8\times
10^{10}\,{}^{14}N_{2}^{+}/cm^{2}$. The implantation angle is $7^{\circ}$
through $60\,nm$ diameter apertures which were patterned using electron beam
lithography in a 300-nm-thick polymethyl methacrylate (PMMA) layer deposited
on the diamond surface.Feng  _et al._ (2016); Wang  _et al._ (2015b); Toyli
_et al._ (2010) After implantation, the sample was annealed $2h$ at
$1050\,^{\circ}C$ in a vacuum at $2\times 10^{-5}\,Pa$ to induce vacancy
diffusion to form NV centers. According to SRIM simulation of the stopping of
nitrogen ions in diamond chip, the most probable stopping position of the
implanted nitrogen ions was $6.5\,nm$ below the diamond surface.Ziegler,
Ziegler, and Biersack (2010) After paperation of the NV center arrays, the
diamond sample was placed in the set-up shown in Fig.1. The scanning confocal
fluorescence image of the NV center array with a $10\times 10\,\mu m^{2}$
region was shown in Fig. 2(a). The fluence of the ${}^{14}N_{2}^{+}$ molecules
and the size of the apertures used during the implantation ensure that most of
the bright pots in the arrays was single NV center, which consistents with the
ODMR experiments. It should be noted that due to the low enengy of the
implanting ions, creation of the NV centers were unsuccessful in some sites.

Figure 2: Efficient identifying the orientation of NV centres in diamond.(a)
Scanning confocal fluorescence image of NV center array with a $10\times
10\,\mu m^{2}$ region. (b) ODMR spectrum of the NV center as pointed in Fig.
2(a). Upper spectrum, $B=0$. Lower spectrum, $B\neq 0$. (c) Under continues MW
exciation with resonance frequency at $2.794\,GHz$ ($2.949\,GHz$), the
scanning confocal fluorescence image of the region of Fig. 2(a) was recorded
again. (d) Imaging of the five single NV centers with the same orientation.

Then, by combining scanning confocal fluorescence image and optical detected
magnetic resonance, we realized a method which can fast identify single NV
centers with the same orientation, so called scanning optical detected
magnetic resonance (SODMR) method. By sweeping the MW frequency using the
$20\,\mu m$-diameter Cu antenna under continuous $532\,nm$ green laser
exciation, the ODMR of a single NV center that randomly selected ( pointed by
an black arrow in Fig. 2(a)) under zero magnetic field was measured. The dip
of the ODMR spectrum (Fig. 2(b)) located at $2.87\,GHz$ corresponds to the
transition between $|0\rangle$ and $|\pm 1\rangle$ states. After that, a
static magnetic field $\boldsymbol{B}$ generated by an electromagnet was
applied to the NV center to further split the $|\pm 1\rangle$ states. At this
condition, as shown in lower spectrum of Fig. 2(b), the two dips located at
$2.794\,GHz$ and $2.949\,GHz$ correspond to the transitons of
$|0\rangle\leftrightarrow|-1\rangle$ and $|0\rangle\leftrightarrow|+1\rangle$
respectively. As the resonance frequency of the A-point is known, the NV
centers with the same orientation can be identified immediately by our SODMR
method introduced here. By applying continues MW exciation at $2.794\,GHz$
($2.949\,GHz$), the scanning confocal fluorescence image of the same region of
Fig. 2(a) was recorded again. The dramatically decreased fluorescence
intensity of the A-point in Fig. 2(c) confirmed that magnetic resonance
occured during scanning counting of the fluorescence of A. As same as A, the
fluorescence intensity of the other four single NV centers marked as B,C,D and
E, which have the same orientation as A, also decreased. As a comparison, the
fluorescence intensity of the other NV centers, which have different
orientation with A, showed litte change. To further improve the efficiency of
identifying of the NV centers with the same orientation, the contrast diagram
of the fluorescence intensity was normalization as $\frac{I_{res}-I_{no-
MW}}{I_{no-MW}}$, where $I_{res}$ (Fig. 2(c)) was the fluorescence of NV
centers under microwave radiation and $I_{no-MW}$ (Fig. 2(a)) was that of
without MW. As shown in Fig. 2(d), five of the single NV centers with the same
orientation obviously displayed. The method of identifying of the single NV
centers with the same orientation introduced here is more efficiency for
arrays with a mass of NV centers.Toyli  _et al._ (2010); Hausmann  _et al._
(2011)

Figure 3: Using the five NV centers identified, MW near field generated by a
$20\,\mu m$-diameter Cu antenna was measured. (a) Scanning confocal
fluorescence image of one of the single NV center at MW power of $0.04\,mW$.
(b) NV fluorescence change VS MW source power.(c) Example of Rabi oscillation
of single NV center. Insert, FFT of the Rabi oscillation.(d) Square of Rabi
frequency($\Omega^{2}$) versus MW source power.

As has been reported, the MW power influences the contrast of the ODMR
spectrum.Jensen  _et al._ (2013); Dréau  _et al._ (2011) Therefore, on the
condition of resonance, the power of MW near field can be indirectly read out
by measuring the fluorescence intensity change of the NV centers.Appel  _et
al._ (2015); Yang  _et al._ (2019) Utilizing the five NV centers with the same
orientation identified above, the relative component of the MW field amplitude
in a plane perpendicular to the NV axis $B_{MW\perp}$ was studied by measuring
the fluorescence intensity and Rabi oscillation frequency $\Omega$. Fig. 3(a)
shows the scanning confocal fluorescence image of single NV center at MW power
of $0.04\,mW$. The corresponding fluorescence intensity was obtained by sum
the total counts within a circle around the center of fluorescence spot with a
radius of $200\,nm$. Fig. 3(c) shows an example of the Rabi oscillation, and
the Rabi frequency was obtained by carrying out the FFT of the data(insert in
Fig. 3(c). The measured projected fluorescence intensity and square of Rabi
frequency($\Omega^{2}$) versus MW source power were shown in Fig. 3(b) and
Fig. 3(d) respectively. From Fig. 3(b) we can see that, with the increasing of
the MW source power from $0$ to $0.02\,mW$, the NV fluourescence intensity
sharply decreased. From $0.02$ to $0.1\text{\,}mW$, the fluourescence
intensity drecreased steadly, indicating that a saturation effect exists under
strong MW source power.Dréau  _et al._ (2011) This result demonstrated that
the method of measuring the relative MW intensity by reading the NV
fluourescence intensity change is more faithful under weaker MW power
excitation. Additionally, under strong MW excitation(e.g. $0.1\,mW$), the NV
fluourescence intensity change of A,C,E is more obvious than B and D, which
consistents with the fact that the later two NV centers are more far-away from
the Cu MW antenna, as the configuration shown in Fig. 1 and Fig. 2(c). Fig.
3(d) shows the proportional relationship of the square of Rabi frequency
($\Omega^{2}$) versus MW source power as $\Omega^{2}\propto P$. The reslut
datas were fitted by linearity curves. The gradient of the MW was precisely
reflected by the slopes of the linearity curves as $E>C>A>D>B$, which is
consistent with the configuration of the five NV centers shown in Fig. 2(c),
except for the spot of B. The unusual of spot B was also shown in the Fig.
3(b) under strong MW power(e.g. $0.1\,mW$), which indicated the distribution
of MW near field is not simply linearity with the distance of the
antenna.Appel  _et al._ (2015) The result indicated that the gradient of near
field MW at sub-microscale can be resoluted by using arry of NV centers in our
work. In this paper, only the relative MW amplitude component perpendicular to
the quantum axis of the five NV centers with the same orientation was
obtained. The MW amplitude vector can be reconstructed by further measuring
the Rabi frequency or fluourescence intensity change by using the NV centers
in other three axis.Wang  _et al._ (2015a) In this work, near field MW was
detected by reading the fluourescence intensity change and Rabi frequency.
Compared with the method by reading the fluourescence intensity change, the
method by detecting the Rabi frequency is more convincing to refelct the
distribution of the near field MW at high power.

In conclusion, by combining scanning confocal fluorescence images and optical
detected magnetic resonance, we realized a method which can fast identify
single NV centers with the same orientation. By using an array of single NV
center in diamond, five single NV centers with the same axis were identified
in a $10\times 10\,\mu m^{2}$ region which demonstrated that the method is
practicable and high efficiency. After that, the relative component of the MW
field amplitude in a plane perpendicular to the NV axis was studied by
measuring the fluorescence intensity and Rabi oscillation frequency. The
gradient of near field MW at sub-microscale can be resoluted by using arry of
NV centers in our work. The method of identifying the orientation of single NV
centres in diamond introduced here can also be used to classify spins with
different orientations in other solid crystals such as SiC.Wang  _et al._
(2017) By designing the unique configuration, the near field MW sensor using
the NV center array introduced here have the potential in the field of chip
failure checking.

###### Acknowledgements.

This work was supported by the Natural Science Foundation of China (Grant No.
11505135 and No. 61501368) and the National Key Laboratory Foundation (Grant
No. 6142411185307).

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