Precision temperature sensing in the presence of magnetic field noise and vice-versa using nitrogen-vacancy centers in diamond
Adam M. Wojciechowski, Mürsel Karadas, Christian Osterkamp, Steffen Jankuhn, Jan Meijer, Fedor Jelezko, Alexander Huck, Ulrik L. Andersen
PPrecision temperature sensing in the presence of magnetic field noise andvice-versa using nitrogen-vacancy centers in diamond
Adam M. Wojciechowski,
1, 2
M¨ursel Karadas, Christian Osterkamp, Steffen Jankuhn, Jan Meijer, FedorJelezko, Alexander Huck, and Ulrik L. Andersen Center for Macroscopic Quantum States (bigQ), Department of Physics, Technical University of Denmark,Fysikvej 309, 2800 Kgs. Lyngby, Denmark Institute of Physics, Jagiellonian University, (cid:32)Lojasiewicza 11, 30-363 Krak´ow,Poland Department of Electrical Engineering, Technical University of Denmark, Ørsteds Plads, 2800 Kgs. Lyngby,Denmark Institute for Quantum Optics and Center for Integrated Quantum Science and Technology (IQST), Ulm University,Albert-Einstein-Allee 11, 89081 Ulm, Germany Felix Bloch Institute for Solid State Physics, University of Leipzig, 04103 Leipzig,Germany (Dated: 21 February 2018)
We demonstrate a technique for precision sensing of temperature or the magnetic field by simultaneouslydriving two hyperfine transitions involving distinct electronic states of the nitrogen-vacancy center in diamond.Frequency modulation of both driving fields is used with either the same or opposite phase, resulting in theimmunity to fluctuations in either the magnetic field or the temperature, respectively. In this way, a sensitivityof 1.4 nT Hz − / or 430 µ K Hz − / is demonstrated. The presented technique only requires a single frequencydemodulator and enables the use of phase-sensitive camera imaging sensors. A simple extension of the methodutilizing two demodulators allows for simultaneous, independent, and high-bandwidth monitoring of both themagnetic field and temperature.Negatively-charged nitrogen-vacancy (NV) colorcenters have become a popular tool for precisionmagnetic-field sensing at the nano- to milli-meter lengthscales , with a dc sensitivity in the tens of pT/Hz / range and even higher ac sensitivities . At room tem-perature, the energy-level structure of the NV groundstate is sensitive also to temperature fluctuations ;a temperature change of 1 mK causes frequency shiftsequivalent to a few-nT magnetic field change. Thus,the presence of noise in one of these quantities mayimpact the precision of measuring the other quantityunless there is a way of discerning them, for example bytemporal signatures.The temperature of the diamond can be easily read outfrom the optically-detected magnetic resonance (ODMR)spectrum of the NV fluorescence by sweeping a mi-crowave (MW) frequency around 2.8 GHz. The temper-ature is then inferred from the positions of two oppo-site spin transitions corresponding to the same crystal-lographic orientation . Thermometry using pulsed MWprotocols or cw -ODMR has been demonstrated with sin-gle NVs, nanodiamonds and bulk samples . So far,temperature sensing was demonstrated for stationary orslowly-varying conditions at timescales of many secondsto hours. Large-range ( ±
100 K) and high bandwidthtemperature sensing has been shown in Ref. requiring,however, averaging of thousands of measurements. Thisapproach is therefore only suitable for the measurementof well-controlled transients.In this article, we report on a method for recordingtemperature transients on millisecond timescales in asingle-shot measurement while being immune to the mag-netic field that induces comparable resonance shifts. The scheme can also be reversed in order to record magneticsignals that are immune to temperature variations. Suchtemperature transients may be due to laser and/or MWsignals operated in a quasi-continuous mode. Similarconcepts have been introduced for pulsed MW schemes,a magnetometer immune to temperature drifts and athermometer insensitive to magnetic fields .Our approach relies on the simultaneous driving of twotransitions ( m S = 0 ↔ m S = ±
1) using cw , frequency-or amplitude-modulated MW fields with either the sameor the opposite phase of modulation. The common-modeshift of the resonance frequencies with the temperatureand their differential shift with magnetic field change areused for generating the signal of interest from the ODMRspectrum. Depending on the choice of electronic transi-tions and modulation phases (polarity of each contribu-tion), the output signal may contain information aboutthe temperature, the magnetic field or both. Interfer-ence effects that occur due to the simultaneous drivingof transitions that share one sub-state ( m S = 0) areavoided here by addressing distinct and well resolved hy-perfine transitions [Fig.1(a)].We use a [100]-oriented, 2 × × . ultrapure dia-mond crystal ([N] < µ m-thin, isotopically purified ([ C] > . N ([ N] ∼
10 ppm). In order to intro-duce vacancies, the sample was implanted with 1.8 MeVhelium ions with a dose of 10 cm − . The NV concen-tration after 2 hours of annealing at 900 ◦ C is estimatedto be on the order of 0 . − a r X i v : . [ c ond - m a t . m e s - h a ll ] F e b FIG. 1. a) NV ground state level diagram indicating threetypes of interactions influencing the energies. The hyper-fine peak separation for NV is 3.05 MHz. b) ODMR spec-tra recorded with an amplitude (top) and frequency (bot-tom) modulated microwave field in a [110]-oriented bias mag-netic field. The vertical dashed lines indicate MW frequencieswhich are also labeled by the red numbers. The slight asym-metry between the left and right pair of resonances resultsfrom the finite MW antenna bandwidth. scope setup together and a MW antenna structure, withan antenna design similar to that of Ref. . The NV flu-orescence was collected by a NA=0.7 objective (Mitu-toyo M Plan Apo NIR HR) and imaged (30x magnifica-tion) onto a biased photodetector (Thorlabs DET36A).The bottom diamond surface has been anti-reflectioncoated with SiO (95 nm), while the top surface wascoated with Al (300 nm) in order to reflect the fluores-cence and excitation light, and prevent it from passingthrough the samples we intend to place on top of the dia-mond in future experiments. Green laser light at 532 nmwas sent through an acousto-optical modulator (AOM,Isomet M1133-aQ110-1V) and focused on the back focalplane of the objective, resulting in a wide-field ( ∼ µ mspot diameter) illumination with 150 mW of laser powerreaching the diamond. Additional laser light of around75 mW of power was used for quick heating of the dia-mond surface. It was derived from the same laser andsent through an independent AOM to the top surface ofthe diamond, which was painted with a red marker toenhance the beam absorption.The outputs of two MW generators [Stanford Re-search Systems (SRS) SG394] were combined in a powercombiner [Mini-Circuits (M-C) ZFRSC-183-S+] and sentthrough a switch (M-C ZASWA-2-50DR+) to a high-power amplifier (M-C ZHL-16W-43+). Its output is con-nected to the MW antenna through a 3-port circulator(MECA CS-3.000), which allows for monitoring of the reflected power. An external function generator (RigolDG1022) is used to generate the FM or AM signal foreach MW source, providing independent control of themodulation parameters. The photodetector is connectedto the current input of a lock-in amplifier (SRS SR850,10 transimpedance gain) which provides phase-sensitivedemodulation of the fluorescence signal. All data hasbeen recorded with a 40 kHz sine-wave modulation fre-quency and a 100% depth (AM) or ±
500 kHz frequencydeviation (FM). Lock-in time constants of either 100 µ sor 1 ms were used, and the filter roll-off was set to 18dB/octave corresponding to around 1 kHz or 100 Hzbandwidth, respectively. A bias magnetic field of around1.9 mT was aligned in-plane with the diamond surfacealong the [110] direction. An additional set of coils ina near-Helmholtz configuration allowed for fine tuningof the field alignment and for application of additionalmagnetic fields controlled by a data acquisition card. Inthis geometry, the NV center spin resonance frequenciesare sensitive to the magnetic field component parallelto the diamond surface. The resonance position shiftsby ≈ .
86 Hz/nT resulting from the geometric factorof cos(90 ◦ − θ B /
2) = (cid:112) /
3, where θ B ≈ . ◦ is thebond angle in diamond. Our experiments were performedat room temperature resulting in temperature-inducedshifts of ∂D∂T (cid:12)(cid:12)(cid:12) ◦ ∼
75 Hz/mK , where D indicatesthe zero-magnetic field splitting parameter.Figure 1(b) shows the cw -ODMR spectra recordedwith a single MW source for two types of modulation.The outermost pairs of resonances are formed by degen-erate pairs of hyperfine transitions belonging to the twodistinct crystallographic directions. This allowed us torecord twice the fluorescence contrast, at the cost of mag-netic shifts being reduced by a factor of (cid:112) / cw -ODMR spectra one can easily determine themagnetic field value by means of measuring the frequencydifference between an appropriate transition pair, for ex-ample 1 and 3 in Fig. 1. For small magnetic fieldchanges causing frequency shifts less than the resonancelinewidth, a high bandwidth readout is possible. Thiscan be accomplished by tuning the MW frequency, f ,to the center (FM) or side (AM) of the resonance wherethe signal, S , has the steepest and approximately linearspectral dependence. The signal detected in-phase withthe modulation reference can be expressed as S ∝ ∂U∂B (cid:12)(cid:12)(cid:12) f ∆ B + ∂U∂T (cid:12)(cid:12)(cid:12) f ∆ T, (1)where U is the ODMR voltage in Fig. 1 and ∆ denotes thechange of the parameter. The last term in 1 is often ne-glected as the temperature variations typically occur onmuch longer time scales than magnetic signals of inter-est. In our experiments we are using a quasi- cw timingprotocol where light and MWs are switched on with alow duty-cycle (interrogation time of 200 ms, repeatedevery 10 s) in order to limit heating of the diamond andpossible interactions with samples on its surface. This FIG. 2. Top panel: timing diagram showing the switching oflaser and MW fields, and the applied heating and magneticfield pulses. The sequence is repeated every 10 s. Bottompanel: Single-shot transient recordings acquired in four dis-tinct configurations: with MW sources tuned to resonanceslabeled 1&2 or 2&4 (see Fig. 1), and their frequency modu-lation having either identical or opposite phases. Recordedsignals reflect changes in the magnetic field (solid blue), tem-perature (dashed red), both at once (solid black) or neitherof those (dashed). The shaded areas indicate time windowswhen no sensing was performed. The lock-in time constantwas set to 1 ms. results in a periodic diamond warm-up and the temper-ature variations can no longer be neglected.Simultaneous driving of several hyperfine transitions,for example those labeled 1 and 2 in Fig. 1(b), is of-ten used to enhance the sensitivity of the diamondprobe because this yields an increase in the fluorescencecontrast . For NV, a double drive may be used andthe signal is then given by S ∝ (cid:18) ∂U∂B (cid:12)(cid:12)(cid:12) f ,φ + ∂U∂B (cid:12)(cid:12)(cid:12) f ,φ (cid:19) ∆ B + (cid:18) ∂U∂T (cid:12)(cid:12)(cid:12) f ,φ + ∂U∂T (cid:12)(cid:12)(cid:12) f ,φ (cid:19) ∆ T, (2)where we have explicitly indicated the modulation phase φ i of the i -th MW driving field with respect to the lock-in reference. In the following, we restrict the modulationphase to be either 0 or 180 degree resulting only in achange of sign in the appropriate partial derivatives.A typical experimental protocol and correspondinglock-in output signals are shown in Fig. 2. The top panelillustrates the pulse sequence that is repeated every 10s. Laser light and MW fields are switched on for 200ms, starting at t = 20 ms. Two additional field pulsesare applied during the measurement. The heating beamis applied between 100 and 150 ms and a 100 nT mag-netic field is switched on between 160 and 200 ms. Thesolid black curve in the bottom part of Fig. 2 shows thelock-in response when the resonances labeled 1 and 2 (c.f.Fig. 1) are driven with an identical FM modulation with φ = φ = 0. We neglect the shaded area in the furtheranalysis as it corresponds to the time when no excitation light is present and a short duration (between 20 and 30ms) of lock-in recovery after switching the laser and MWfields. The central part of the curve shows an oscillationat 50 Hz due to magnetic-field noise in the laboratory anda temperature transient visible as a skew of the oscillat-ing signal. When driving a hyperfine pair of transitionsbelonging to the same electron-spin states with in-phasemodulations, the right-hand side in Eq.(2) simplifies totwice that of a single-drive case described by Eq.(1).The situation changes dramatically when two distinctelectron transitions (for example the resonances labeled 2and 4) are driven with the same modulation. The energyderivative on the magnetic field is opposite for the m S = ± ∂U/∂B ) (cid:12)(cid:12)(cid:12) f = − ( ∂U/∂B ) (cid:12)(cid:12)(cid:12) f .Thus, the magnetic-field dependent terms in Eq.(2) can-cel out, and the recorded signal only carries informa-tion on the diamond temperature, which is plotted asa dashed red curve in Fig. 2. Reversing the modulationphase by 180 ◦ on one MW source leads to a simultaneoussign change of both terms at its frequency in Eq.(2). Acommon-mode energy change due to temperature vari-ation is then canceled out and only a differential shiftdue to magnetic-field is recorded, which is plotted as thesolid blue curve in Fig. 2. The remaining fourth combi-nation of driving resonances 1 and 2 with out-of-phasemodulated sources leads to a signal that is immune toboth temperature and magnetic-field variations, which isplotted as the gray dotted curve.In order to further support the attribution of frequencyshifts to in- and out-of-phase drives of the resonances 2and 4, we analyze those signals in more detail in Fig. 3.The top panel in Fig. 3 illustrates that the magnetic sig-nal (blue curve) has a dominant component oscillating atthe mains frequency of 50 Hz with a peak-to-peak am-plitude of 392(4) nT. This signal occurs due to the straylaboratory fields and contains also higher harmonic com-ponents. The observation of the applied 100 nT fieldstep (black dashed trace) is hindered by the mains humand can be seen clearly after subtraction of the latter,as shown by the red curve. The temperature transientsrecorded with and without the heating pulse are shownin the bottom panel. These transients exhibit ∼ ≈ FIG. 3. Relative magnetic field (solid blue) and tempera-ture (dashed red) changes extracted from Fig. 2. Top panel:The response to a change in the magnetic field. The appliedfield step is hindered by large ( ∼
400 nT p − p ) oscillations atthe mains frequency, and recovered by subtraction of the 50Hz component. Bottom panel: Comparison of temperaturetransients recorded with and without the heating pulse. Anadditional laser, when on, increases the heating rate from 5.9K/s to 12.8 K/s as verified by the heating period in the range100-150ms. leveling-off of the temperature transient. The presence ofthe additional heating pulse increases the heating rate to12.9(1) K/s for the duration of the pulse, which corre-sponds to approximately one half of the rate expectedfrom the power impeding on the painted surface.In order to characterize the sensitivity of our setup tothe temperature and magnetic field, we have recorded sig-nals without pulsing the laser or MWs. Time traces of thelock-in output with the length of 1 s were recorded and aroot-mean-square amplitude spectral density was calcu-lated using the Hanning window function. Spectra from50 traces were subsequently rms averaged and the result-ing data is plotted in Fig. 4. In the magnetically sensi-tive configuration (black trace) distinct peaks are visibleat first, second, third and fifth harmonics of the 50 Hzmains frequency. Additionally, an applied 20 nT p − p sine-wave signal is visible at 40 Hz, which serves as a calibra-tion field. The level of the noise floor is ∼ − / up to the lock-in filter roll-off frequency of ∼ ∼ µ K Hz − / is achieved. All recordings show asmall peak around 67 Hz which we attribute to electronicpick-up. The noise floor is about 3 times higher than theoptical shot-noise level for the detected fluorescence andmainly originates from electronic noise in our detectionsystem.Similarly to the frequency modulation of MW sources,AM also provides a way of differential- or common-modesignal cancellation (via slope-polarity change) by tuningthe MW frequency to either side of an appropriate reso-nance. In our experiment we have found that, however, FIG. 4. Recorded noise spectral density in the units ofthe magnetic field and temperature, respectively, with MWstuned to resonances 1 and 3 (see Fig. 1). The magnetic signalcorresponds to opposite modulation phases and shows peaksat the mains harmonics. The temperature signal is recordedwith identical phase modulations and is virtually identical tothe noise floor recorded in the absence of MWs. The sig-nal roll-off around 1 kHz is due to the lock-in filtering witha 100 µ s time constant. Discrete peaks are broadened andhave their amplitudes reduced by a factor of 0.8 due to thewindowing function. FM signals are more immune to laser intensity noise sincethe highest sensitivity is achieved exactly on-resonancewhere the signal output is close to zero. Our methodcan also be extended to the case of independent modu-lation of MW sources with two distinct frequencies. Thephotocurrent can then be demodulated by two lock-inamplifiers and simultaneously provide information aboutboth the magnetic-field and temperature. On the otherhand, a single demodulator approach as presented herecan be combined with a phase-sensitive camera sensor forwide-field sensing . In such a camera the demodulationis performed on a per-pixel basis and is limited to a singlefrequency for currently available devices.In conclusion, we have demonstrated a modulationtechnique that allows for monitoring of temperature ormagnetic field variations hindered by the presence oflarge noise (or signal) in the other modality. Our methodis based on the in- and out-of-phase modulation of spinresonances belonging to the ground state of negativelycharged nitrogen-vacancy centers, and may be used forprecision, real-time sensing applications, and may eas-ily be extended to a wide-field camera-imaging scenario.The sensitivity presented here is limited by the amount offluorescence light collected and can further be increasedby using a thicker NV sensing layer.We thank Kaare Hartvig Jensen for 3D printing theprototype diamond holder and Kristian Haagsted Ras-musen for coating the diamond. This work was sup-ported by the Innovation Fund Denmark (through theEXMAD and QUBIZ projects), Novo Nordisk Foun-dation (NNF16OC0023514), IQst, DFG, VW Stiftung,ERC, BMBF and EU DIADEMS. F. Jelezko, I. Popa, A. Gruber, C. Tietz, J. Wrachtrup, A. Ni-zovtsev, and S. Kilin, Applied Physics Letters , 2160 (2002). M. W. Doherty, N. B. Manson, P. Delaney, F. Jelezko,J. Wrachtrup, and L. C. L. Hollenberg, Physics Reports ,1 (2013), arXiv:1302.3288. J. R. Maze, P. L. Stanwix, J. S. Hodges, S. Hong, J. M. Taylor,P. Cappellaro, L. Jiang, M. V. G. Dutt, E. Togan, A. S. Zibrov,A. Yacoby, R. L. Walsworth, and M. D. Lukin, Nature , 644(2008). G. Balasubramanian, I. Y. Chan, R. Kolesov, M. Al-Hmoud,J. Tisler, C. Shin, C. Kim, A. Wojcik, P. R. Hemmer, A. Krueger,T. Hanke, A. Leitenstorfer, R. Bratschitsch, F. Jelezko, andJ. Wrachtrup, Nature , 648 (2008). L. Rondin, J.-P. Tetienne, T. Hingant, J.-F. Roch, P. Maletinsky,and V. Jacques, Reports on Progress in Physics , 056503(2014), arXiv:1311.5214. R. Schirhagl, K. Chang, M. Loretz, and C. L. Degen, AnnualReview of Physical Chemistry , 83 (2014). J. F. Barry, M. J. Turner, J. M. Schloss, D. R. Glenn,Y. Song, M. D. Lukin, H. Park, and R. L. Walsworth, Pro-ceedings of the National Academy of Sciences , 14133 (2016),arXiv:1602.01056. T. Wolf, P. Neumann, K. Nakamura, H. Sumiya, T. Ohshima,J. Isoya, and J. Wrachtrup, Physical Review X , 041001 (2015). V. M. Acosta, E. Bauch, M. P. Ledbetter, A. Waxman, L. S.Bouchard, and D. Budker, Physical Review Letters (2010),arXiv:0911.3938. M. W. Doherty, V. M. Acosta, A. Jarmola, M. S. J. Barson, N. B.Manson, D. Budker, and L. C. L. Hollenberg, Physical ReviewB , 041201 (2013), arXiv:1310.7303. D. M. Toyli, C. F. de las Casas, D. J. Christle, V. V. Dobrovitski,and D. D. Awschalom, Proceedings of the National Academy ofSciences , 8417 (2013), arXiv:1303.6730. P. Neumann, I. Jakobi, F. Dolde, C. Burk, R. Reuter, G. Wald-herr, J. Honert, T. Wolf, A. Brunner, J. H. Shim, D. Suter,H. Sumiya, J. Isoya, and J. Wrachtrup, Nano Letters , 2738(2013), arXiv:1304.0688v1. G. Kucsko, P. C. Maurer, N. Y. Yao, M. Kubo, H. J. Noh,P. K. Lo, H. Park, and M. D. Lukin, Nature , 54 (2013),arXiv:1304.1068. H. Clevenson, M. E. Trusheim, C. Teale, T. Schr¨oder, D. Braje,and D. Englund, Nature Physics , 393 (2015), arXiv:1406.5235. Y.-K. Tzeng, P.-C. Tsai, H.-Y. Liu, O. Y. Chen, H. Hsu, F.-G.Yee, M.-S. Chang, and H.-C. Chang, Nano Letters , 3945(2015). K. Fang, V. M. Acosta, C. Santori, Z. Huang, K. M. Itoh,H. Watanabe, S. Shikata, and R. G. Beausoleil, Physical Re-view Letters , 1 (2013), arXiv:1212.1495. P. Kehayias, M. Mr´ozek, V. M. Acosta, A. Jarmola, D. S. Rud-nicki, R. Folman, W. Gawlik, and D. Budker, Physical ReviewB , 245202 (2014), arXiv:1403.2119. M. Mrozek, A. M. Wojciechowski, D. S. Rudnicki, J. Za-chorowski, P. Kehayias, D. Budker, and W. Gawlik, PhysicalReview B , 035204 (2016), arXiv:1512.03996. K. Sasaki, Y. Monnai, S. Saijo, R. Fujita, H. Watanabe, J. Ishi-Hayase, K. M. Itoh, and E. Abe, Review of Scientific Instruments , 053904 (2016), arXiv:1605.04627. X.-D. Chen, C.-H. Dong, F.-W. Sun, C.-L. Zou, J.-M. Cui, Z.-F.Han, and G.-C. Guo, Applied Physics Letters , 161903 (2011). H. A. R. El-Ella, S. Ahmadi, A. M. Wojciechowski, A. Huck,and U. L. Andersen, Optics Express , 14809 (2017),arXiv:1707.00916.22