High-resolution vector microwave magnetometry based on solid-state spins in diamond

Abstract

The measurement of the microwave field is crucial for many developments in microwave technology and related applications. However, measuring microwave fields with high sensitivity and spatial resolution under ambient conditions remains elusive. In this work, we propose and experimentally demonstrate a scheme to measure both the strength and orientation of the microwave magnetic field by utilizing the quantum coherent dynamics of nitrogen vacancy centres in diamond. An angular resolution of 5.7 mrad and a sensitivity of 1.0 μT Hz^-1/2 are achieved at a microwave frequency of 2.6000 GHz, and the microwave magnetic field vectors generated by a copper wire are precisely reconstructed. The solid-state microwave magnetometry with high resolution and wide frequency range that can work under ambient conditions proposed here enables unique potential applications over other state-of-art microwave magnetometry.

ARTICLE

Received 11 Nov 2014 | Accepted 12 Feb 2015 | Published 23 Mar 2015

Pengfei Wang1,2, Zhenheng Yuan1, Pu Huang1,2, Xing Rong1,2, Mengqi Wang1,2, Xiangkun Xu1,2, Changkui Duan1,2, Chenyong Ju1,2, Fazhan Shi1,2 & Jiangfeng Du1,2

The measurement of the microwave eld is crucial for many developments in microwave technology and related applications. However, measuring microwave elds with high sensitivity and spatial resolution under ambient conditions remains elusive. In this work, we propose and experimentally demonstrate a scheme to measure both the strength and orientation of the microwave magnetic eld by utilizing the quantum coherent dynamics of nitrogen vacancy centres in diamond. An angular resolution of 5.7 mrad and a sensitivity of1.0 mT Hz 1/2 are achieved at a microwave frequency of 2.6000 GHz, and the microwave magnetic eld vectors generated by a copper wire are precisely reconstructed. The solid-state microwave magnetometry with high resolution and wide frequency range that can work under ambient conditions proposed here enables unique potential applications over other state-of-art microwave magnetometry.

DOI: 10.1038/ncomms7631 OPEN

High-resolution vector microwave magnetometry based on solid-state spins in diamond

1 Hefei National Laboratory for Physics Sciences at the Microsacle and Department of Modern Physics, University of Science and Technology of China, Hefei 230026, China. 2 Synergetic Innovation Centre of Quantum Information and Quantum Physics, University of Science and Technology of China, Hefei, Anhui 230026, China. Correspondence and requests for materials should be addressed to J.D. (email: mailto:[email protected]

Web End [email protected] ).

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Recent advantages in microwave (MW) technology have led to tremendous developments in communications, high-speed electronics and magnetic resonance. Most of these

developments rely on the discovery of nanoscale, high-frequency MW processes13 and materials46. Measurement of MW electromagnetic eld with high spatial resolution is crucial but has been a long-standing problem. Measurements with high sensitivity and angular resolution have been achieved for MW electric eld7,8. It is not so for the measurement of MW magnetic eld vector, despite its importance, for example, in MW antenna test9 and the study of the MW response of materials to the magnetic eld5. Although various approaches, such as coplanar-waveguide-type probe1014, superconducting quantum interference devices15, cold atoms16,17 or spin hall effect lms18, have been applied to measure the MW magnetic eld, the sensor size, the extreme measurement conditions required or the lack of vector measurement ability strongly limit their applications.

In this work, we demonstrate a high-resolution vectorial MW magnetometry based on nitrogen vacancy (NV) centres in diamond. The NV centre is a defect that consists of a substitutional nitrogen atom and an adjacent vacancy in the carbon lattice of diamond. The ground spin triplet state of negatively charged NV centres can be initialized and measured by laser illumination and uorescence intensity under laser illumination, respectively. Owing to its good spin properties, the NV centre has been shown to be a perfect solid-state quantum system for sensing magnetic elds with nanoscale resolution and high sensitivity under ambient conditions19,20. In previous works, NV centres have been utilized in the measurement of oscillating magnetic elds with frequencies ranging from kilohertz19 to megahertz21,22. Here we propose and then demonstrate experimentally a different scheme based on NV centres to realize the measurement of the vector of the MW magnetic eld. The angular resolution and sensitivity are then analysed.

ResultsPrinciples of vector MW magnetometry. The main idea of the MW magnetometry is based on the Rabi oscillation of a solid-state spin driven under resonant MW magnetic eld. The Hamiltonian of the NVs electron spin is H0 DSz2 gB0Sz

gBmw(t) S, where D 2.87 GHz is the zero eld splitting,

g 2.8025 MHz Gauss 1 is the gyromagnetic ratio of the elec

tron spin, S and Sz are the associated spin operator and its z component, and Bmw(t) Bmw cos(2pft) is the MW

magnetic eld. We selectively address the spin operation on transition of ms 02 1 (denoted as |0i and | 1i, respec

tively) with a transition frequency of o0 D gB0 (Fig. 1b). Then

the system can be treated similarly as spin 1/2. The resonance condition o0 f can be fullled by adjusting B0. The component

of the vector Bmw that perpendicular to Sz, denoted as Bmwp, can be treated as the sum of two circular polarized eld with opposite rotating directions. The left-hand rotating circular polarized eld B1 with an amplitude of B1 2

ms=+1

MW

[afii9828]B0

ms=1

ms=0

Diamond

[afii9853] 0

NV

2.87 GHz

B0

Readout

eNV

0

1

Bmw

[afii9825]

B1

B1

Bmwp

Figure 1 | Experimental setup and principle of the MW magnetometry. (a) Schematic view of the setup for the demonstration of vector MW magnetometry. The 532-nm green laser is focused several micrometres below the top surface of the diamond. A copper wire of 22 mm diameter above the diamond plate is used for generating the MW eld. The MW passes through the copper wire and generates a linearly polarized oscillating magnetic eld (red lines). (b) Zeeman splitting of the electron spin of the NV centre. (c) Schematic view of the MW magnetic eld vectors and axis of the NV centre in the laboratory frame. The dark grey surface is perpendicular to the axis of the NV centre. (d) Bloch sphere view of the dynamics of the spin state.

O2r

2O2 cos 2ptO

; 1

where O

O2r do2

q

is the Rabi frequency under off-resonance frequency detuning do o f. In existence of 14N

nuclear spin, the electron spin resonance transition line splits into three peaks with frequencies f mIA, where mI 0,1 denotes

the spin state of 14N nuclear spin (Fig. 2a). As a result, there are two frequencies Ofast and Oslow in the Rabi oscillation curve

fullling the relation of Ofast2 Oslow2 A2. Oslow is the Rabi

frequency of the on-resonance peak and indicates B1 value. The other factor is the inhomogeneous line broadening effect caused by the spin bath noise that dominates the signal decay. The broadened line shape can be characterized by adding a Gaussian type noise to the electron spin2325:

PmIo kI p2

p

2 Bmwp directly drives the spin rotation (Fig. 1c). The Hamiltonian H0 can be simplied in the rotation frame as Hr gB1Sx (Fig. 1d), which results in the spin

state oscillating between |0i and | 1i with Rabi frequency

Or gB1. In the Bloch sphere representation, the spin state vector

rotates around B1 by an angle of a 2pgB1t after a sensing

time t.

Decoherence of the NV spin states needs to be taken into account in an actual case. After considering the interaction between NV and the 14N nuclear spin and the noise due to 13C nuclear spin bath, we have the whole Hamiltonian H H0

S A I QIz2 bSz, where I is the 14N nuclear spin operator, A is

the hyperne coupling tensor and b denotes the effective

uctuation magnetic eld of the noise23,24. There are two factors need to be considered. One is the off resonance due to the hyperne interaction with the nitrogen nuclear spin. The probability on |0i under off resonance MW driving is written as25

po

1

2

r T 2e o f mIA

2T 22p2 ; 2

where kI is the relative height of each peak and T2* is the electron spin dephasing time. The nal signal can be obtained from integration of all the off-resonance contributions in the three peaks:

~po X

mI0; 1

Z

PmIopodo: 3

The magnetic eld vector can be reconstructed by making use of

1

1

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NATURE COMMUNICATIONS | DOI: 10.1038/ncomms7631 ARTICLE

0

1

f

Bmwp = 2.106 Gauss

Fluorescence

change (%)

1

Probability on0

0.5

0 1 2 3

2,595 2,600 2,605 MW frequency (MHz)

MW duration time [afii9848]MW (s)

*

4

Laser

MW

Phonton count

Amplitude (a.u.)

B mwp(Gauss)

5

0

[afii9848]mw

2

Initialization Readout

Sensing

0 5 10

0 0.00 0.01 0.02

Frequency (MHz)

MW source power (W1/2)

Figure 2 | Experiment results of the MW magnetic eld amplitude measurement. (a) Electron spin resonance lines of the NV centres. (b) Pulse sequence of vector MW magnetometry. The 5-ms laser pulse and 2-ms waiting time initialize the NV centre to |0i. Then the MW is on and the NV centre sense the

MW magnetic eld. Finally, the laser is on and the amount of photons is counted to determine the spin state. (c) Rabi oscillations. Each point of the data is repeated for 1.5 105 times to increase the signal to noise ratio. The tting yields Bmwp (2.1060.002) 10 4 T and a sensitivity of 1.0 mT Hz 1/2. (d)

Fourier transformation of Rabi oscillations in c, with a red line connecting the data. The frequencies of the peak (*) and the other one are 4.17 MHz and4.68 MHz. (e) Measured projected MW magnetic eld versus MW source power.

NV centres with four different orientations (Fig. 3a), [111], [111], [111], [111] (labelled as 1, 2, 3, 4). The static magnetic eld can be aligned subsequently to each of the four orientations, and then the set of NV centres of the orientation is selectively driven and its Rabi oscillation is measured to deduce the relevant projected MW magnetic eld Bi;expmwp (i 1, 2, 3 and 4), which is

related to Bmwp, as shown in Fig. 1c, by

Bimwp Bmw eiNV

i 1; 2; 3 and 4

: 4 The four relations in equation (4) are over-complete but theoretically consistent in determination all the three components of Bmw (Bx, By, Bz). Actually, any three of them

should be sufcient, except for the exceptionally few singular points such as Bmwp being along [100], [010] or [001]

(Supplementary Note 1). Hence the sensor can be a nanosized diamond with three or more appropriate NV centres. For the sample with NV centres of all the four orientations used here, we can make use of the over-completeness by applying Maximum-likelihood estimation method to the data to obtain the best estimation of the magnetic vector. The likelihood can be written as

/ Y

Bi;expmwph i2

5

Maximizing c will nd the optimum value of the vector according to Bayes theorem (Supplementary Note 4). The MW magnetic eld can be uniquely determined in this way.

Experimental demonstration of the magnetometry. The probe head of the setup is shown in Fig. 1a. For the ease of demonstration, we use a chemical vapour deposition synthesized, type IIa diamond plate of 50 mm in thickness from Element Six, rather than a nanodiamond that contains NV centres as the magnet-ometer. The average distance between each NV centre is less than 100 nm, and there are B20 NV centres in the laser spot. The static magnetic eld B0 is aligned to the axis of each NV centre group to avoid ground-state mixing. The MW electronic circuits

are designed to be 50 O impedance and the total power reection is reduced to S11o 10 dB, so that a highly linearly polarized

MW magnetic eld is generated. As the relative permeability of diamond crystal is B1.0000, the magnetic eld inside the diamond should be the same as that outside of it. In our demonstration, we x the applied static eld to B0E94.34 Gauss, and the corresponding frequency for the MW eld is f 2.6000 GHz.

The pulse sequence and the measured Rabi oscillation results are shown in Fig. 2b. Figure 2c shows an example of Rabi oscillations under the MW source power of 0.13 mW. By tting the curve, we derive the projected MW magnetic eld strength. Bmwp (2.1060.002) 10 4 T (see Supplementary Note 2 and

3 for details). The tting result is conrmed by the Fourier transformation of the data in the frequency domain (Fig. 2d). By varying the MW source power, we nd that proportionality of the projected MW magnetic eld strength deduced from the measured Rabi oscillation to the square root of the MW source power holds in a wide Bmwp range (Fig. 2e and Supplementary

Fig. 1).

Further demonstration to show the angular resolution was performed by using the vector MW magnetometry to measure in a series of space locations the strength and orientation of the linearly polarized MW magnetic eld generated by a copper wire of B5 mm in length. The copper wire is much longer than the distance between the copper wire and the diamond surface, and so can be treated as indenitely in length. The MW magnetic near eld has a magnitude inversely proportional to the distance to the wire and an orientation along the tangent as Amperes circuital law. We scan the laser spot in a line to measure Rabi Oscillations. The scanning line is divided into 150 points with a step of B130 nm and several micrometres below the diamond surface (Fig. 3b). By controlling the orientation of the static magnetic eld, we measure the Rabi oscillations of the NV centres of all the four groups in each point. In prior, the diamond is put at an angle of 0.37 rad with the copper wire to avoid the singular point (Supplementary Fig. 2). The experiment results are shown in Fig. 3c (see Supplementary Table 1 for the tting parameters). All

4 exp

1

2s2i Bimwp Bx; By; Bz

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[111]

[111]

Copper wire

z

[111]

[afii9835]

[afii9850] x

[111]

r0

Air

y

Diamond

Bmw

z

x y

[afii9835]

Bmw

4 T)

3

B mwp(10

2

1.6

Angle (rad)

1.4

10 5 10

5

0

Position (m)

Figure 3 | Experiment results of vector MW magnetometry. (a) Denition of the vector and angle. (b) Schematic view of the MW magnetic eld distribution and the scanning line. In the near eld, the oscillation current in the copper wire generates a linearly polarized magnetic eld with a direction perpendicular to the copper wire and along the tangent. The coordinate is set as follows: x is along the copper wire, y is perpendicular to the copper wire and parallel to the diamond surface, and z is vertical to the diamond surface. The scanning line (black line) is made below the copper wire and along the y axis. (c) Measured Bmwp with the magnetic eld along [111] (triangle), [111] (diamond), [111] (rhombic) and [111] (hexagon). The tting curve to the data (dashed line) gives the distance r0 47.49 mm.

(d) y (diamond) and j (circle) calculated from the data in c. The dashed line is the tting curve to the data. The tting yields the angular resolution of dy 5.7 mrad and dj 9.9 mrad.

the three components of the vector Bmw are then deduced by utilizing maximum-likelihood estimation method, and so the orientation of the vector is obtained (Supplementary Note 5). The orientation of Bmw versus position is shown in Fig. 3d, together with theoretically predicted lines. The experiment result of j and y perfectly matches the theoretical predictions of the MW magnetic eld. The minimum angular resolution achieved is do 5.7 mRad, which can be further improved by increasing the

detecting time or photon collection efciency26,27.

DiscussionIn conclusion, we have proposed a vector MW magnetometry scheme using NV centres in diamonds with high sensitivity and spatial resolution and under ambient conditions, and then carried out experimental demonstration of the amplitude and angular sensitivity with the measurement of the MW magnetic eld vector generated by an innitely long copper wire. In our demonstration, the spatial resolution is only diffraction limited, which gives a sensor size of B230 nm (see Methods section). The capability of the vector MW magnetometry based on the NV centre is not limited by what we demonstrate here. By adopting wide-eld imaging technology, a two-dimensional reconstruction of the MW magnetic eld can be realized28,29. Based on solid-state spins of NV centre in diamond, the sensor size can be

reduced to ten nanometre scale by a well-treated nanodiamond30. Also the working frequency can be extended to sub-terahertz band continuously by an external static eld 8.6 T (ref. 31) and reach terahertz under 35 T, which is available in the current technology.

Our solid-state MW vector magnetometry will directly nd its application in testing the MW electronics and materials. Owing to long-term stability of the NV centre, it can also serve for the purpose to stabilize the amplitude of the MW. Moreover, by combining the NV centres with a scanning probe microscopy, the NV centre-based scanning near-eld vector MW magnetometry can be used in studying antenna radiation as a non-destructive measurement9. Finally, as the sensor can be downsized to nanometre scale, our scheme may promote the ferromagnetic resonance imaging32 to the nanoscale.

Methods

Experiment setup. Our setup is based on our homebuilt confocal microscopy. A temperature-stabilized diode laser (CNI MGL-III-532) is used for the initialization and readout of quantum states. The laser beam passes through a double-pass acoustic optical modulator (Crystal Technology 3200-121) to reach an isolation of about 60 dB. Then it enters a single-mode bre acting as a spatial lter. A high numerical aperture (NA) objective lens (Olympus UPLSAPO 100XO) is used for the laser focusing and uorescence collection. A high-resolution scanner (Asylum research) and fast steering mirror (Newport FSM-300) is used for the laser scanning. The magnetic eld is applied by a permanent magnet on a three-dimensional translation stage. The uorescence passes through a band-pass lter with 650775 nm and 20 mm pinhole to the APD (Perkin Elemer SPCM-AQRH-14), which limit the optical detection size to be diffraction limited. The MW generated by a MW source (Agilent N5181B) is cut to square wave pulse by an MWPIN switch (CMCS0947A-C1, 3 ns rising time). An amplier (Mini-circuits ZHL-16 W-43 ) is used to amplify the MW signal.

Thermal drift. The experimental measurements in this demonstration last for a month, so the long-term stability of the whole setup is crucial. First, we put the whole probe head in a chamber with temperature stability of 50 mK to reduce mechanical thermal drift, which enables us to focus on the same point for a long time without any drift. Second, we put some diamond nanocrystal with NV centres on the diamond surface for locating and carrying out position feedback. Finally, the most important thing is to keep all the MW circuit stable to 0.5 K and keep a constant output power, so that the MW magnetic eld amplitude remains stable during the measurement.

Sensor size and spatial resolution. In our demonstration, the diamond sample is rather big, and the spatial resolution is the pinhole size divided by the magnication of the objective lens, with the low limit being the Abbe diffraction limit, which can be written as:

d

l2 NA

6

With our band-pass lter wavelength, lB650 nm, we obtain dB230 nm. However, a well-selected nanosized diamond could be used to reach a nanoscale spatial resolution.

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Acknowledgements

We thank Professor Fei Xue and Professor Xidong Wu for useful discussions. This work was supported by the National Key Basic Research Program of China (Grant No. 2013CB921800), the National Natural Science Foundation of China (Grant Nos.11227901, 31470835, 91021005 and 11275183) and the CAS, and the Fundamental Research Funds for the Central Universities.

Author contributions

P.W., Z.Y., F.S. prepared the setup and performed the experiments; P.W., X.R. built the microwave circuits; X.X. and M.W. designed and fabricated the microwave delivery device; J.D. supervised the setup and experiments. All authors discussed the results and participated in writing the manuscript.

Additional information

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