High-sensitivity DC magnetic field detection with ensemble NV centers by pulsed quantum filtering technology

Yang Zhang; Zhonghao Li; Yuanyao Feng; Hao Guo; Huanfei Wen; Jun Tang; Jun Tang; Jun Liu; Jun Liu

doi:10.1364/OE.392279

1. Introduction

Precision magnetic field detection using NV^- defects in diamond has drawn increasingly active attention due to its high magnetic sensitivity [1–3], high spatial resolution and nanoscale sensing [4–6]. Depending on its stable two-level spin structure and perfect state-dependent fluorescence properties at ambient conditions [7,8], the NV^- electron spins can be efficiently initialized by laser, precisely manipulated by microwave and indirectly read out by fluorescence without providing extreme temperature, vacuum system or large magnetic field [9]. In the field of quantum sensing, these particular properties have been utilized for many frontier applications, such as high sensitivity DC or AC magnetometry for chips [10,11], high resolution biological cells magnetic imaging [12,13], and sophisticated high-fidelity quantum precision operations [14–16].

The associated magnetic field sensitivity has been both analysed [17] and implemented in chemical vapor deposition (CVD) diamonds with an individual NV^- defect of 300$\textrm{nT}/\sqrt {Hz} $ and low NV^- concentration (ppb level) of 35$\textrm{nT}/\sqrt {Hz} $ [11,18]. However, for those samples with high NV^- concentration (ppm level), although the sensitivity can be improved based on the large number of sensor units, its complex spin interaction mechanism and the power broadening introduced in the measurement seriously affect its sensitivity. As shown in Fig. 1(c), in addition to a pair of target peaks for DC magnetometry, the other 13 obvious peaks are all sideband excitations by paramagnetic resonance impurity. A bad phenomenon called spectral overlap will inevitably occur when we directly use continuous wave optically detected magnetic resonance (CW-ODMR) to obtain the spectral lines [19,20], which eventually leads to poor signal-to-noise ratio (SNR) and even the target signal misidentification.

Fig. 1. (a) CW-ODMR and P-ODMR measurement sequences. (b) Energy-level scheme for the NV^- ODMR dynamics. (c) CW-ODMR spectrum with fifteen obvious peaks (A-O). (d) Experimental Rabi oscillations measurement. The inset shows the Rabi frequency is the square relation of the microwave power$\; {P_{\textrm{MW}}}$.

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These so-called inevitable problems can be solved by a method called pulsed quantum filtering (PQF) technology, which combines pulsed optically detected magnetic resonance (P-ODMR) and pulse shaping techniques. Pulse shaping is an advanced pulsed technique that plays an important role in PQF. Recently, as the performance of arbitrary waveform generator (AWG) continues to upgrade, we can directly use AWG to generate desired amplitude and phase shaped pulses to achieve PQF. Different shaped pulses have different characteristics such as band-selective excitability [20], self-refocusing behavior, robustness and transition region [21,22]. These special properties nowadays have been widely applied to perform high resolution quantum imaging and high fidelity quantum manipulation [23,24], which results in a dramatically improvement for particular applications. In the meantime, some quantum algorithms based on PQF have been reported, which have brought revolutionary promotion for ultrafast time resolution and high-resolution frequency detection [25,26]. In this paper, we first use bulk diamond contains high NV^- concentration demonstrate CW-ODMR measurement and acquire optimized ${{\eta }_{CW}}$ of 12$\textrm{nT}/\sqrt {\textrm{Hz}} $. Then we extract the advantages of PQF to eliminate the power induced broadening and unwanted sideband excitations caused overlap. Finally, we optimize all the sensitivity parameters to obtain ${{\eta }_{pulsed}}$ of 1$\textrm{nT}/\sqrt {\textrm{Hz}} $ and enhance the SNR over 20 dB. Our results indicate the PQF can acquire purer resonance signal and achieve outstanding sensitivity so that it may be applied to a wide range of solid-state sensors to improve their performance.

2. Principle of DC magnetic field sensitivity

CW-ODMR is an easy method because its optical polarization, microwave excitation and readout are carried out simultaneously and has been widely applied in magnetometry [11,27,28,29]. As shown in the upper part of Fig. 1(a), laser continuously polarizes NV^- centers into the brighter fluorescent ${m_s}$ = 0 ground state while microwave frequency is instantaneously tuned to drive NV^- population into the darker fluorescent ${m_s}$= ±1 state, which obey the level scheme of NV^- shown in Fig. 1(b). Without considering ¹⁴N hyperfine interaction, the fluorescence intensity (PL) I of Lorentzian CW-ODMR spectrum as a function of the microwave frequency ${v_m}$ can be written as

(1)$$ I({v_m}) = I(\infty )\left[ {1 - CF\left( {\frac{{{v_m} - {v_0}}}{{{\Delta }f}}} \right)} \right] = I(\infty )\left[ {1 - {C_{CW}}\frac{{{{\left( {\frac{{{\Delta }f}}{\textrm{2}}} \right)}^\textrm{2}}}}{{{{\left( {\frac{{{\Delta }f}}{2}} \right)}^2} + {{\left( {{v_m} - {v_0}} \right)}^{^2}}}}} \right],$$

where $I(\infty )$ is the PL when the spins are off-resonant, F is the spectral line shape, C is the spectral line contrast and $\Delta f$ is the full width at half maximum (FWHM). Differ from single NV^- center, when the spin system contains P1 spins coupled to NV^- spins, the P1 spin flip rate ${{\Gamma }_{P1}}$ should be taken account into the formula of${\; }\Delta f$. Here, we follow the transcendental formula for the P1 spin flip rate [30], is

(2)$${\Gamma _{P1}} = \frac{{\gamma {P_{MW}}}}{{\left( {1 + \frac{{{P_{MW}}}}{{{P_{sat}}}}} \right)}} = \frac{{\gamma f_R^2}}{{\left( {1 + \frac{{f_R^2}}{{f_{sat}^2}}} \right)}},$$

where ${f_R}$ is the Rabi frequency (measured in MHz), as shown in Fig. 1(d), which is the square relation of the microwave power ${P_{MW}}$ [31], the fit parameter ${\gamma }$ and saturated the Rabi frequency ${f_{sat}}$ are denoted by laser power from CW-ODMR measurement. Here, in weak laser excitation, the ${\Delta }f$ can be expressed as

(3)$$\Delta f = {f_{inh}}\textrm{ + }\sqrt {\frac{{\textrm{4}\Gamma _2^{eff}f_R^2}}{{{\Gamma _1} + {\Gamma _p} + {\Gamma _{P1}}}} + {{\left( {\frac{{\Gamma _2^{eff}}}{\pi }} \right)}^2}} ,$$

where ${f_{inh}}$ is the inhomogeneous linewidth limited to ${({\pi T_2^\ast } )^{ - 1}}$, ${\Gamma }_2^{eff} = {{\Gamma }_2} + 1/{{\Gamma }_p}$, ${{\Gamma }_1}$ is the longitudinal relaxation time, ${{\Gamma }_2}$ is the transverse relaxation time and ${{\Gamma }_p}$ is the polarization rate measured through time-resolved PL response measurement. According to Eq. (1), the CW-ODMR contrast ${C_{CW}}$ is

(4)$${C_{CW}} = \frac{{\varepsilon {\Gamma _p}}}{{({1 - \varepsilon } ){\Gamma _1} + {\Gamma _p}}}\frac{{\mathop {({2\pi {f_R}} )}\nolimits^2 }}{{[{\mathop {({2\pi {f_R}} )}\nolimits^2 + \Gamma _2^{eff}({{\Gamma _1} + {\Gamma _p}} )} ]}},$$

where $\varepsilon = ({\alpha - \beta } )/$2$\alpha $ is the difference of PL that characterized by $\alpha $ and $\beta $ between brighter ${m_s}$ = 0 state and darker ${m_s}$= ±1 state. The most classical expression of sensitivity is recognized as

(5)$${\eta _{CW}} = {P_{_F}}\frac{h}{{{G_e}{\mu _B}}}\frac{{\Delta f}}{{C\sqrt R }},$$

where $h/{G_e}{{\mathrm{\mu}} _B}$≈ 36nT$/$kHz is the inverse of the gyromagnetic ratio of the NV^- electronic spins, ${P_F}$ is the numerical parameter related to the specific profile of the frequency frequency-dominated spin response resonance and usually expressed Lorentzian (${P_{Lorentzian}} \approx \; $0.77), the last parameter we should consider is the photon detection rate R which can be calculated by the collected fluorescence ${P_f}$, so we obtain

(6)$$R = \frac{{\lambda {P_f}}}{{hc}},$$

where${\; }h$, c, λ are the Planck constant, light speed and the wavelength (≈ 670 nm) of the collected fluorescence.

Using P-ODMR method, as shown in the lower part of Fig. 1(a), can avoid optical and microwave power broadening for the spin resonances. Several microseconds delay after the end of the laser pulse for polarization ensures the populations trapped in the metastable state return to the ground state by non-radiative transition. To reduce the noise from laser and the spin lattice relaxation, it is necessary to add another cycle without applying microwave ${\pi }$ pulse as reference. The spectrum is obtained by stepping the frequency of microwave pulse and synchronously processing recorded PL signals. In this work, optimizing the polarization laser pulse time ${t_p}$ and readout integration time ${t_I}$ through time-resolved fluorescence measurements is especially important to obtain a high contrast$\; {C_{pulsed}}$. Different from the ${\eta _{CW}}$ expressed in Eq. (5), since the PL readout part is carried out separately, the optimized P-ODMR DC magnetic field sensitivity ${\eta _{pulsed}}$ is expressed as

(7)$${\eta _{pulsed}} = {P_F}\frac{h}{{{G_e}{\mu _B}}}\frac{{\Delta f}}{{{C_{pulsed}}}}\sqrt {\frac{{{t_p} + {t_I} + T_2^{\ast }}}{{\sigma R{t_I}}}} ,$$

where ${\sigma }$ is the PL collection efficiency (about 1% in this work), the resonance profile ${P_F}$ here is given by a convolution of the natural $\textrm{T}_2^{\ast }$-limited line profile and additionally broadening from the NV^- spin’s response to a fixed-duration, detuned microwave π pulse [32]. Under our condition, excessive microwave power would badly affect the natural $\textrm{T}_2^{\ast }$-limited line profile, so we need to choose a proper shaped pulse as a band-pass quantum filter to suppress those unwanted resonant excitation peaks on the spectrum. We also notice that once those unnecessary resonance excitations, the spectrum shape will behave Gaussian (${P_{Guassian}} \approx $ 0.77) which is the same ${P_F}$ as single NV^- center. With the number of effective excitation NV^- defects${\; }n = R{t_I}$ and$\; {t_p} \gg {t_I} + T_2^\ast $, the simplified ${\eta _{pulsed}}$ for Eq. (8) is given by

(8)$${\eta _{pulsed}} = 0.77\frac{h}{{{G_e}{\mu _B}}}\frac{{\Delta f}}{{{C_{pulsed}}}}\sqrt {\frac{{{t_p}}}{n}} .$$

In Eq. (8), n can be calculated by

(9)$$n = N\frac{\kappa }{{1 + \kappa }},$$

where N is the total NV^- defects in effective excitation region,${\; }\kappa $ is the laser excitation rate defined as $\kappa = {P_{opt}}/{P_{sat}}\; $. Finally, though fitting a simple model

(10)$${P_f} = A\frac{{{P_{excite}}}}{{{P_{excite}} + {P_{sat}}}},$$

${P_{sat}}$ can be estimated about 1.3W and we can get the value $\kappa $ for each setting of our laser power.

3. Sample and experimental setup

The sample (5mm*5mm*0.5 mm, Type 1b, Element Six, $[{100} ]$ surface) used in this experiment is produced by high-pressure and high-temperature (HPHT) methods with high initial N concentration (∼50 ppm) and natural 1.1% ¹³C abundance. In order to create more NV^- centers for magnetometry, the diamond is irradiated by using 10 MeV electrons for 4 hours to a total dose of 1.8×10¹⁸cm² and followed by annealing in vacuum for 1.5 hours at 850°C, resulting in the NV^- concentration of about 3 ppm. Since the total excited NV^- defects number n contributing to the fluorescence signal is also determined by the optical and microwave excitation volume, we estimated the volume of the microwave uniform field ∼ 2×10⁻² mm³ (uniformity error < 1%). The beam is focused with a diameter of 50um onto the sample to initialize and read out NV^- defects spin, we calculate the typically effective microwave uniform excitation volume ∼ 9.8×10⁻⁴ mm³. With the HPHT sample NV^- density of 3 ppm, we estimate NV^- defects number n ∼ 5.18×10¹¹ contributes to the signal.

As shown in Fig. 2, experiments have performed with a home-built confocal-microscope system at room temperature. An acousto-optic modulator (Crystal Technology, AOMO 3350-199) is set to generate laser pulses. The stimulated fluorescence passes through a 532 nm notch filter and a 650 nm long pass filter to remove any background pump laser and is terminally focused into an avalanche photo diode (Thorlabs, APD130). The APD output signal is acquired with a data acquisition card (Gage Applied, CSE161G2). An arbitrary waveform generator (Tektronix, AWG5204) is used to generate microwave pulses while a microwave source (Keysight, N8153B) outputs continuous frequency-swept microwave signal for CW-ODMR experiment. A power amplifier (CBA6G015C) is used to amplify microwave to provide sufficient Rabi frequency. Finally, the microwave radiates to the sample through a self-designed microstrip antenna terminated with an external 50${\Omega }$ load. A pair of cylindrical permanent magnet is mounted on a multi-axis moving stage to add a magnetic bias field B₀ parallel to one of four NV axes.

Fig. 2. Detailed experimental device diagram for both CW-ODMR and PQF measurements.

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4. Results and discussion

For CW-ODMR measurement, as shown in Fig. 3(a), raising ${P_{\textrm{MW}}}$ can significantly increase ${\Delta }f$, ${\textrm{C}_{CW}}$ and some side resonances appear caused by the coupling between NV^- and P1 spins when the ${P_{\textrm{MW}}}$ exceeds the value of central resonance saturation, resulting in the spectral could be hardly fitted by Eq. (1). As the increases, those microwave-sensitive resonance spectrums would seriously broaden or even overlap the target resonance signals so as to cause sensor fail to recognize the target resonance signal. According to Fig. 3(e), the SNR of CW-ODMR spectrum is calculated to be 27.7 dB by its power spectrum density of signal and noise. It should be noted that the excited-state optically detected magnetic resonance (ES-ODMR) technique can further enhance sensitivity under a magnetic field of about 510 Gauss with single NV^- defect [11,18,33]. But for high concentration samples with a large excitation volume, the ${\Delta }f$ cannot be effectively narrowed because of the existence of high ¹³C concentration and the spectra suffers a significant decrease in ${C_{CW}}$ with increasing magnetic field due to the cross relaxation of the NV^- defects with the P1 spins. Meanwhile, it is very difficult to keep the specific magnetic field in such a large excitation volume because of the gradient distribution of the magnetic field. According to Eq. (5), the best CW-ODMR shot-noise-limited magnetic field sensitivity ${\eta _{CW}}$ is estimated to be 12$\textrm{nT}/\sqrt {\textrm{Hz}} $.

Fig. 3. (a) Linewidth broadening and overlap with different input microwave powers ${P_{\textrm{MW}}}$ in CW-ODMR measurement. Solid lines: Lorenzian function fitting curves with different$\; {P_{\textrm{MW}}}$. (b) PQF measurement with different$\; {P_{\textrm{MW}}}$. Solid lines: Gaussian function fitting curves with different$\; {P_{\textrm{MW}}}$. The insets in (a) and (b) show the curve of target resonance frequency changing with different$\; {P_{\textrm{MW}}}$. (c) The changes of the contrast and linewidth in CW-ODMR measurement. (d) The changes of the contrast and linewidth in PQF measurement. (e-f) The power spectrum density of the signal and noise in CW-ODMR and PQF.

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Using PQF can well eliminate the broadening caused by synchronous excitation of laser and microwave, so we can stimulate more NV^- defects by increasing laser power to further improve sensitivity. Meanwhile, benefiting from the amplitude modulation function of AWG, we can compile specific ${\pi \; }$pulse to suppress the redundant flip of other sublevels. Here, we create a Gaussian pulse with narrowband excitation and good robustness characteristics to manipulate electron spin states. As shown in Figs. 3(b) and 3(f), we find the data can be well fitted by Gaussian function and the SNR of 56.9. According to Eqs. (5) and (8), we note the ratio between the linewidth and contrast is an important factor for sensitivity. As shown in Figs. 3(c) and 3(d), the optimized methods in this work intuitively displays a narrower linewidth, a higher contrast and a better ratio between the two, which will be beneficial to sensitivity when compared to CW-ODMR measurement.

In order to guarantee NV^- defects to be polarized to ${m_s}$ = $0$ state within the excitation region as many as possible, we optimize ${t_p}$ to ensure the defects those at the rim of the Gaussian beam can be polarized completely and ${t_I}$ to achieve higher ${\textrm{C}_{pulsed}}$ through time-resolved fluorescence measurements in Figs. 4(a) and 4(b). Then wait few microseconds to make sure that all the populations trapped in the metastable state return to the ground state by the non-radiative transition before applying microwave ${\pi }$ pulse. During the experiment, we find when the laser power increases, the ${f_R}$ decreases if we do not calibrate the input microwave power. This is because as more defects are excited, the original energy can't make the Rabi frequency reach the expected value. Hence, to avoid introducing pulse error, we need calibrate the microwave power to match the ${f_R}\; $once the laser power changes.

Fig. 4. (a) Time-resolved PL response of ensemble NV^- centers to optimize laser polarization time$\; {t_p}$. The inset shows the ${t_p}$ as a function of the laser power in different Rabi frequency$\; {f_R}$. (b) Optimal integration time ${t_I}$ in different laser power.

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According to the data shown in Figs. 3(a) and (b) and Figs. 5(a)-(d), we notice${\; \Delta }{f_{PQF}} < {\; \Delta }{f_{CW}}$ and ${C_{PQF}} > \; {C_{CW}}$ for the same condition due to the spin inversion period in PQF is absence of laser. This sequential method successfully decouples the influence of the simultaneous excitation of laser and microwave. In Figs. 5(a) and 5(c), measurements of the contrast are well fitted using Eq. (4) with the fixed fitting parameters $\varepsilon $ = 0.3, ${\Gamma }_2^{eff} \approx $ 2 MHz and ${{\Gamma }_p}$ is the free fitting parameters here. We note in order to achieve high contrast, ${{\Gamma }_p}$ should be larger than${\; }{{\Gamma }_1}({1 - \varepsilon } )$. At lower optical power with higher$\; {f_R}$, the contrast will increase at first because of low insufficient polarization. Once excited with lower${\; }{f_R}$, thus the value of ${{\Gamma }_p}$ exceeds$\; {({2\pi {f_R}} )^2}/{\Gamma }_2^{eff}$, the contrast will decrease at higher laser power. In Figs. 5(b) and 5(d), measurements of the linewidth are also well fitted using Eqs. (2) and (3) with the fixed fitting parameters$\; {f_{inh}} \approx 7\textrm{MHz}$, ${\; }{{\Gamma }_1}/{\Gamma }_2^{eff} \approx $10⁻³ and the free fitting parameters ${{\Gamma }_p}/{\Gamma }_2^{eff}$,${\; \gamma }/{\Gamma }_2^{eff}$.We find the value of ${\; }{{\Gamma }_p}/{\Gamma }_2^{eff}$ is linearly increasing with laser power while the value of ${\gamma }/{\Gamma }_2^{eff}$is irregular, causing an abnormal phenomenon that the $\Delta f$ decreases when the laser power increases. It is probably due to complex NV^–P1 simultaneous spin flips mechanism [19]. Consistent with Eq. (3), as the microwave pulse length increases (equivalent to reducing microwave power for CW-ODMR), ${\Delta }f$ becomes sharper and reaches the limited inhomogeneous linewidth${\; \Delta }{f_{inh}} \approx {({\pi T_2^\ast } )^{ - 1}}$. By using Eq. (8), we perform the corresponding DC magnetic field sensitivity with PQF in Figs. 5(e) and (f). From this result, it indicates we can continue to optimize the sensitivity by increasing the laser power and locking the corresponding optimal Rabi frequency. At last, having consolidated more than 200 sets of data, a contour plot of ${\eta _{CW}}$ and ${\eta _{PQF}}$ as a function of laser excitation rate $\kappa $ and Rabi frequency ${f_R}$ are drawn in Figs. 6(a) and (b), showing that the sensitivity of our method is better than CW-ODMR in gradient uniformity and the optimized shot-noise-limited magnetic field sensitivity ${\eta _{PQF}}$ is about 1$\textrm{nT}/\sqrt {\textrm{Hz}} $ which is enhanced by one order of magnitude than$\; {\eta _{CW}}$

Fig. 5. (a-d) Hollow point: Experimental results of PQF contrast and linewidth as a function of the laser excitation rate $\kappa $ and Rabi frequency$\; {f_R}$. (e-f) The corresponding DC magnetic field sensitivity with PQF. Solid lines: Fits to the contrast, linewidth and sensitivity.

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Fig. 6. Contour plot of (a) CW-ODMR and (b) PQF DC magnetic field sensitivity as a function of laser excitation rate $\kappa $ and microwave power$\; {P_{\textrm{MW}}}$.

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5. Conclusion and outlook

In conclusion, we use CW-ORMR and PQF techniques to study the DC magnetic field sensitivity in high NV^- density diamond. For CW-ODMR, the sensitivity is seriously affected by power and interference noise spectrum. By using PQF technology and optimizing each parameter, the power induced linewidth broadening and NV^–P1 simultaneous spin flips induced overlap are well eliminated. And then, after sorting out the overall data, we also find an important detail that this technology can dramatically suppress the resonance frequency drift caused by the change of laser and microwave power, which means that it has the application prospect of maintaining the stability of sensor performance in the complex and changeable environment. Finally, we use this powerful way to enhance SNR from 27.7 dB to 56.9 dB and the DC magnetic sensitivity by an order of magnitude to CW-ODMR. In this work, we still have to make great efforts to further improve DC magnetic sensitivity, such as designing a special microwave resonator to expanding the uniform region of microwave radiation [34–36], ¹³C isotope purification of samples with high NV color center concentration to enhance dephasing time, improvement of N-NV^- conversion efficiency to sharpen the linewidth and promoting the NV excitation efficiency and the fluorescence collection efficiency to improve readout fidelity [30,37]. The best projected shot-noise limited sensitivity we predict will be by more than three orders of magnitude to 10$\textrm{pT}/\sqrt {\textrm{Hz}} $ level. The techniques in this paper would be a practical approach to acquire higher magnetic sensitivity, frequency resolution, and SNR in nanoscale magnetic sensor, biomedical living cells imaging and many other optical frontier fields.

Funding

China Postdoctoral Science Foundation (2018M641684); National Postdoctoral Program for Innovative Talents (BX20180276); Applied Basic Research Project of Shanxi Province (201901D111011(ZD)); Key Laboratory of Shanxi Province (201905D121001); National Science and Technology Planning Project (2017YFB0503100); Special Fund for Key Scientific Instruments of the National Natural Science Fundation of China (61727804); National Natural Science Foundation of China (51635011, 51727808, 51922009); Shanxi Provincial Research Foundation for Basic Research, China (201801D221202); Key Research Foundation of Shanxi Province (201803D121067); Science and Technology Innovation project of the Higher Education of Shanxi Province (2019L0558); Natural Science Foundation of the North University of China (XJJ201808); Shanxi Province Science Foundation for Youths (201901D211254); Shanxi “1331Project” Key Subjects Construction, China.

Disclosures

The authors declare no conflicts of interest.

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High-sensitivity DC magnetic field detection with ensemble NV centers by pulsed quantum filtering technology

Abstract

1. Introduction

2. Principle of DC magnetic field sensitivity

3. Sample and experimental setup

4. Results and discussion

5. Conclusion and outlook

Funding

Disclosures

References

Cited By

Figures (6)

Equations (10)

Optics Express