Chip-Scale Ultra-Low Field Atomic Magnetometer Based on Coherent Population Trapping

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Communication Chip-Scale Ultra-Low Field Atomic Magnetometer Based on Coherent Population Trapping

Hyun-Gue Hong 1,*, Sang Eon Park 1, Sang-Bum Lee 1, Myoung-Sun Heo 1, Jongcheol Park 2 , Tae Hyun Kim 2, Hee Yeon Kim 2 and Taeg Yong Kwon 1

1 Time and Frequency Group, Korea Research Institute of Standards and Science, Daejeon 34113, Korea; [email protected] (S.E.P.); [email protected] (S.-B.L.); [email protected] (M.-S.H.); [email protected] (T.Y.K.) 2 Department of Convergence Sensor, National NanoFab Center, Daejeon 34141, Korea; [email protected] (J.P.); [email protected] (T.H.K.); [email protected] (H.Y.K.) * Correspondence: [email protected]

Abstract: We report a chip-scale atomic magnetometer based on coherent population trapping, which can operate near zero magnetic field. By exploiting the asymmetric population among magnetic sublevels in the hyperfine ground state of cesium, we observe that the resonance signal acquires sensitivity to magnetic field in spite of degeneracy. A dispersive signal for magnetic field discrimination is obtained near-zero-field as well as for finite fields (tens of micro-tesla) in a chip- scale device of 0.94 cm3 volume. This shows that it can be readily used in low magnetic field environments, which have been inaccessible so far in miniaturized atomic magnetometers based on 1/2 coherent population trapping. The measured noise floor of 300 pT/Hz at the zero-field condition is comparable to that of the conventional finite-field measurement obtained under the same conditions.

Citation: Hong, H.-G.; Park, S.E.; This work suggests a way to implement integrated atomic magnetometers with a wide operating Lee, S.-B.; Heo, M.-S.; Park, J.; Kim, range. T.H.; Kim, H.Y.; Kwon, T.Y. Chip-Scale Ultra-Low Field Atomic Keywords: optical magnetometry; coherent population trapping; quantum sensor; chip-scale Magnetometer Based on Coherent atomic device Population Trapping. Sensors 2021, 21, 1517. https://doi.org/10.3390/ s21041517 1. Introduction Academic Editor: Valentina Zhukova Optically pumped atomic magnetometers are the most sensitive room-temperature magnetic sensors, which rely on precision measurements of atomic spin states under Received: 5 January 2021 magnetic fields [1]. The sensitivity surpassing fT/Hz1/2 level has been reported in a Accepted: 19 February 2021 spin-exchange-free regime (SERF) [2], and the absence of cryogenic cooling makes it Published: 22 February 2021 favorable for a wide range of applications, such as tracking of magnetic objects [3,4], space exploration [5], and medical signal detection [6–8]. In particular, miniaturization based Publisher’s Note: MDPI stays neutral on microfabricated vapor cells [9–11] paves the way towards mass-producible low-power with regard to jurisdictional claims in versions of atomic magnetometers, namely chip-scale atomic magnetometers (CSAMs). published maps and institutional affil- Recently CSAMs have been integrated with platforms of real-world applications, such as iations. military systems [12] and wearable medical-imaging instruments [13,14]. Moreover, by exploiting the fact that atom-based measurements provide absolute values via fundamental relations of quantum mechanics, the chip-scale atomic reference platform with in-situ calibration capability have been envisioned [15]. Copyright: © 2021 by the authors. Coherent population trapping (CPT) resonance [16] between two magnetically sensi- Licensee MDPI, Basel, Switzerland. tive sublevels in hyperfine ground states of Alkali atoms is a well-known mechanism used This article is an open access article to implement atomic magnetometers [17]. Although the sensitivity is not as high as that of distributed under the terms and magnetometers, based on direct detection of Larmor precession, the CPT scheme has its conditions of the Creative Commons advantages in robustness and simplicity. For example, since it generally requires a less num- Attribution (CC BY) license (https:// ber of coils, one may expect reduced difficulties related to alignment and crosstalk [18,19]. creativecommons.org/licenses/by/ 4.0/). In the perspective of heterogeneous integration of multiple devices [15,20], it can share

Sensors 2021, 21, 1517. https://doi.org/10.3390/s21041517 https://www.mdpi.com/journal/sensors Sensors 2021, 21, 1517 2 of 10

major resources, such as a gigahertz-modulated laser with a chip-scale atomic clock (CSAC). Indeed, the first CSAM was realized on a physics package having the same architecture as the first CSAC [9]. However, to separate the magnetically sensitive transition from the clock transition by many linewidths, the measured field had an offset of ~70 µT, and this has been the case for almost all other CPT-based magnetometers [21,22]. Magnetic sensing near-zero-field, on the other hand, is desirable in some cases where the target field to be measured can be perturbed by the field generated by sensors. Cou- pling between sensors in an array configuration is also minimized for smaller field. In addition, biomagnetic measurement for medical diagnosis often requires a highly shielded environment. There has been a previous attempt to utilize degenerate CPT spectra near zero magnetic field for magnetometers [23], but not in a chip-scale package. Here we report the CPT-based magnetic sensing near zero magnetic field using a millimeter-scale microfabricated vapor cell integrated in a full spectroscopy package of 0.94 cm3. Even in the regime where the linear Zeeman shift is much smaller than the CPT linewidth, we observed a Lorentzian microwave spectrum of 12.1 kHz linewidth, which is the result of combined resonances associated with all magnetic sublevels. The field inhomogeneity in this densely packed assembly was kept low enough so that the superimposed CPT resonance could work as a field discrimination signal under the nulled internal magnetic field. The magnetic sensitivity of the resonance, which arises from the asymmetric population among magnetic sublevels, is compared with the conventional finite-field (10.9 µT and 24.9 µT in this work) measurement based on a single Zeeman- shifted transition. The noise level of the field spectral density amounts to 300 pT/Hz1/2, which is comparable to the finite-field measurement in the same package and operation conditions. Consequently, by just tuning the microwave frequency to the linear Zeeman shift associated with the target field, we obtain a dynamic range of the CSAM extended down to zero-field. This paper is organized as following. We first briefly describe the theoretical expecta- tion in Section2, and the sensor design and associated experimental settings in Section3. We then present CPT spectra and the sensitivity analysis in Section4, and summarize the result in Section5.

2. Theory Although it is possible to describe the system using a full quantum mechanical model [24], it suffices here to deal with simplified analytic formulae in order to obtain an intuitive picture. The CPT spectrum in its simplest configuration is obtained by measuring the laser transmission through atomic vapor, while the frequency difference of a bichromatic field is scanned across the transition frequency of hyperfine ground state [25]. We assume that the total spectrum is comprised of constituent Lorentzian resonances each of which corresponds to the transition between magnetic sublevels. The quantization axis is parallel to the direction of laser propagation, and we only consider the two-photon transitions by which the magnetic quantum number mF in the ground states does not change [26]. Each pair of sublevels is coupled with a bichromatic laser field via excited states in which individual magnetic sublevel is not resolved due to collisional and Doppler broadening. One may here refer to the energy level diagram of cesium shown in Figure1, although our discussion is not limited to specific atomic species. By further assuming that the field inhomogeneity is negligible for simplicity and giving a common linewidth (full width at half maximum, FWHM) of Γ to all resonances, the spectrum reads

M a S(∆ω) = k (1) ∑ 2 2 k = −M (∆ω − 2kγB) + Γ /4

where ∆ω is the microwave frequency detuning from mF = 0 resonance, ak’s represent the relative amplitude of each resonance, γ is the gyromagnetic ratio, B is the applied magnetic SensorsSensors2021 2021, 21, 21, 1517, 1517 3 of 310 of 10

∆ω 푚 푎 field,where and Mis theis the microwave largest m frequencyF possible. detuning In the limitfrom of small퐹 = 0 resonance, magnetic field푘’s represent where γB is muchthe relative smaller amplitude than Γ, the of each overlapped resonance, spectrum 훾 is the can gyromagnetic be approximately ratio, given퐵 is the as applied magnetic field, and 푀 is the largest 푚퐹 possible. In the limit of small magnetic field ! ! where 훾퐵 is much smaller than ΓM, the overlapped spectrum Mcan be approximately−1 given 4γB∆ω S(∆ω) ≈ 1 ∑ a + ∑ ka + ∑ ka as ∆ω2+Γ2/4 k 2 2 2 k k k = −M (∆ω +Γ /4) k = 1 k = −M (2) 푀 P Q 푀 −1 1 ≡ 2 +4훾퐵∆ωΔ휔 2 푆(∆휔) ≈ ( ∑ ∆푎ω2)++Γ /4 (∆ω2+(Γ2∑/4) 푘푎 + ∑ 푘푎 ) ∆휔2 + Γ2/4 푘 (∆휔2 + Γ2/4)2 푘 푘 푘 = −푀 푘 = 1 푘 = −푀 (2) where, in the last푃 line, P and Q are푄 defined as the sum and difference of a ’s. In principle, ≡ + ∆휔 k there can be∆휔 complicated2 + Γ2/4 dynamics(∆휔2 + Γ among2/4)2 sublevels as all possible transitions occur at the same time, but it turns out that this incoherent sum of spectra well explains experimental where, in the last line, 푃 and 푄 are defined as the sum and difference of 푎 ’s. In princi- observations presented in Section4. During the zero-field magnetometer푘 operation, the ple, there can be complicated dynamics among sublevels as all possible transitions occur microwave frequency is kept near the peak of the spectrum, thereby ∆ω Γ can also be at the same time, but it turns out that this incoherent sum of spectra well explains experi- applied. Thus, the approximated spectrum near ∆ω ≈ 0 is expressed as a peak shifted by mental observations presented in Section 4. During the zero-field magnetometer opera- Q P tion,/ theas themicrowave following frequency equation is kept near the peak of the spectrum, thereby Δ휔 ≪ Γ can also be applied. Thus, the approximated spectrum near ∆휔 ≈ 0 is expressed as a peak P Q 2 Q 4P shifted by 푄/푃 as the followingS(∆ω) ≈ equation − ∆ω − + + (3) 16Γ4 P 32PΓ4 Γ2 푃 푄 2 푄 4푃 푆(∆휔) ≈ − (∆휔 − ) + + (3) where the shifted peak position,16Γ4 Q/P,푃 can32 be푃Γ4 explicitlyΓ2 written as 4γB − × M ka + 1 ka / M a , which is not necessarily zero depending푀 on the where∑k = the1 shiftedk ∑k peak= −M position,k ∑ k푄=/−푃M, cank be explicitly written as 4훾퐵 × (∑푘 = 1 푘푎푘 + −1 푀 relative∑푘 = −푀 푘 amplitude푎푘)/ ∑푘 = −푀 of푎a푘k, ’s.which In fact, is not the necessarily simplest CPT zero configuration depending on considered the relative here ampli- includes onlytude of a single푎푘’s. In beam fact, the of circularlysimplest CPT polarized configuration light (consideredσ+ or σ−), here which includes leads only to asymmetric a single populationbeam of circularly among polarizedthe magnetic light sublevels (휎+ or 휎 owing− ), which to optical leads to pumping asymmetric effect population [24,27]. In a among the magnetic sublevels owing to opticalM pumping effect−1 [24,27]. In aM typical vapor- typical vapor-cell experiment, the factor ∑k = 1 kak + ∑k = −M kak / ∑k = −M ak is order cell experiment, the factor (∑푀 푘푎 + ∑−1 푘푎 )/ ∑푀 푎 is order of unity, which of unity, which means that degradation푘 = 1 푘 of푘 = magnetic −푀 푘 sensitivity푘 = −푀 푘 is not serious unless detri- means that degradation of magnetic sensitivity is not serious unless detrimental effects, mental effects, such as field inhomogeneity and misalignment distort the superimposed such as field inhomogeneity and misalignment distort the superimposed CPT signal. CPT signal.

Figure 1. EnergyEnergy level level diagram diagram of cesium of cesium D1 line D1 linewith with the (conceptual) the (conceptual) steady steady state population state population of ofeach each magnetic magnetic sublevel sublevel expressed expressed as height as height of blue of bars. blue A bars.circularly A circularly polarized polarized light (red) lightis illus- (red) is trated to create dark state resonance between 푚퐹 = 1 states as an example. Likewise, each mag- illustrated to create dark state resonance between mF = 1 states as an example. Likewise, each magnetic sublevels can be coupled by an appropriately tuned bichromatic field. Note that the modulation frequency should be half of 9.192 GHz if the bichromatic fields come from two first-order sidebands of a frequency-modulated laser as in our case.

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3. Experimental Details Our chip-scale magnetometer package is basically identical to the one we used for a compact CPT clock [28]. The core spectroscopy unit is comprised of a vertical cavity surface emission laser (VCSEL), a quarter wave plate (QWP), a micro-fabricated cesium vapor cell, and a photodiode all aligned vertically (Figure2). The current fed to the VCSEL chip is directly modulated so that its spectrum contains multiple sidebands, which are separated by 4.596 GHz from each other. The two first-order sidebands are tuned to induce dark-state resonance between the ground states via the excited state of D1 optical transition (Figure1). The laser beam, which is linearly polarized at the VCSEL output, becomes circularly polarized upon passing through the QWP. It is a single crystal quartz substrate with a coating on one side for power attenuation. Then the laser transmission through the vapor cell is recorded in a photodiode. The vapor cell (Figure3b), which measures 2 × 3 × 1.5 mm3, contains cesium metal, and is filled with neon buffer gas (270 Torr) to avoid wall collision. Due to the collisional broadening by the buffer gas, the Doppler- broadened linear absorption to F’ = 3 and F’ = 4 excited states are merged as a single peak. A pair of coils is built within the package in the axial direction, which is used to create the field to be measured or null out the residual field to set up a zero-field environment. It is patterned on a flexible printed circuit board in Helmholtz configuration. The amplitude of the magnetic field as a function of current injected into the coil is calibrated by using the linear Zeeman coefficient [29], which converts frequency shift to field amplitude, and it turns out to be 9.3 µT per 1 mA. Both the VCSEL and vapor cell are maintained near 80 ◦C, and they are thermally isolated by polyimide bridge structure (Figure3c). To minimize internal magnetic noise induced by current paths near the atom, micro-fabricated elements for temperature sensing and heating are designed to cancel the magnetic field generated from the adjacent current path, and are located only on the substrate holding the VCSEL (Figure3a) . The vapor cell, which is 2 mm away from VCSEL, is thermally conducted via a silicon spacer. The power consumption for the heater, which accounts for most of the device operation power, is about 170 mW. The package is hermetically sealed in a 0.94 cm3 volume where the electric signal paths are interfaced via a ceramic chip carrier to a circuit board. The board distributes signals to off-the-shelf instruments for measurement and control (Figure3d). We employ a compact magnetic shield, which allows us easy characterization of the package [28]. Although imperfect, it could be used, after nulling, for providing a zero-field environment due to small field-inhomogeneity as revealed in the linewidths of CPT spectra for high mF’s. The nulling condition is determined by measuring Zeeman shift for various bias coil currents. In particular, the center of the quadratic Zeeman shift corresponds to the offset field [28], which amounts to 3.02 µT in this case. The zero-field environment is provided by nulling the residual field by the bias coil. We proceed our analysis hereafter by considering the net field at the vapor cell with the compensated offset taken into account. The frequency of VCSEL is stabilized to the Doppler broadened absorption profile using a lock-in amplifier (LIA, Femto LIA-MVD-200-H) and a servo controller (Proportional– Integral–Derivative or PID, custom-made) as shown in Figure2. The direct current (DC) input of VCSEL is provided from a low-noise current source (LNCS, custom-made) while the microwave input comes from a radio frequency signal generator (RFSG, Stanford Research SG386) piloted by an oven-controlled crystal oscillator (OCXO, NEL DFRM). The CPT signal is obtained by using another LIA (Stanford Research SR865) and a frequency modulation–demodulation method. SensorsSensors2021 2021, 21, 21, 1517, 1517 5 of5 of 10 10 Sensors 2021, 21, 1517 5 of 10

FigureFigure 2. 2.Schematic Schematic of of the the magnetometer magnetometer package package and and measurement measurement setup. setup. Inside Inside the the shield shield is is the the Figure 2. Schematic of the magnetometer package and measurement setup. Inside the shield is the spectroscopyspectroscopy unit unit and and the the instruments instruments to to control control it it are are depicted depicted outside outside the the shield. shield. spectroscopy unit and the instruments to control it are depicted outside the shield.

Figure 3. (a) Optical image of the substrate on which the VCSEL and the elements for temperature Figurecontrol 3. are(a) Optical mounted. image (b) The of the micro substrate -fabricated on on which which vapor the the cell VCSEL VCSEL with a and andseparate the the elements elements room for for for a cesiumtemperature temperature dis- control are mounted. (b) The micro-fabricated vapor cell with a separate room for a cesium dis- controlpenser, are which mounted. is activated (b) The by micro-fabricated an infrared laser vapor after cell bonding. with a separate(c) Flexible room printed for a cesium circuit dispenser,board penser, which is activated by an infrared laser after bonding. (c) Flexible printed circuit board whichframe is holding activated polyimide by an infrared suspensions. laser after (d) bonding. The printed (c) Flexible circuit board printed with circuit a socket board used frame for holding inter- framefacing holding the signal polyimide from the suspensions. physics package. (d) The printed circuit board with a socket used for inter- polyimidefacing the signal suspensions. from the (d physics) The printed package. circuit board with a socket used for interfacing the signal from the physics package. The frequency of VCSEL is stabilized to the Doppler broadened absorption profile The frequency of VCSEL is stabilized to the Doppler broadened absorption profile usingFor a closed-loop lock-in amplifier operation, (LIA, the Femto servo LIA controller-MVD- (Stanford200-H) and Research a servo SIM960) controller stabilizing (Propor- using a lock-in amplifier (LIA, Femto LIA-MVD-200-H) and a servo controller (Propor- thetional microwave–Integral frequency–Derivative is or enabled PID, custom and the-made) feedback as shown signal in isFigure analyzed 2. The by direct a dynamic current tional–Integral–Derivative or PID, custom-made) as shown in Figure 2. The direct current signal(DC) analyzerinput of VCSEL (DSA, is Stanford provided Research from a low SR785).-noise For current open-loop source operation,(LNCS, custom the servo-made) (DC) input of VCSEL is provided from a low-noise current source (LNCS, custom-made) controllerwhile the is microwave disabled and input the signalcomes fromfrom LIAa radio is directly frequency recorded signal by generator the DSA. (RFSG, Stan- whileford the Research microwave SG386) input piloted comes by from an a oven radio-controlled frequency crystalsignal generator oscillator (RFSG, (OCXO, Stan- NEL 4.fordDFRM). Results Research The CPT SG386) signal piloted is obtained by an by oven using-controlled another LIA crystal (Stanford oscillator Research (OCXO, SR865) NEL and DFRM). The CPT signal is obtained by using another LIA (Stanford Research SR865) and a frequencyIn this section, modulation we investigate–demodulation the resulting method. spectrum and corresponding field measurement.a frequencyFor closed The modulation typical-loop operation, CPT–demodulation microwave the servo spectramethod. controller for sufficiently (Stanford large Research fields SIM960) of 10.9 µ stabiliz-T and 24.9ingµ FortheT are microwaveclosed shown-loop in frequency Figureoperation,4a. Thereis the enabled servo are well-resolved andcontroller the feedback (Stanford seven signal resonances, Research is analyzed SIM960) which by originate a stabiliz- dynamic ing the microwave frequency is enabled and the feedback signal is analyzed by a dynamic fromsignal magnetic analyzer sublevels (DSA, Stanford ranging Research from mF S=R785).−3 to For +3 open with-loop the change operation, of m theF being servo zero con- (Figuresignaltroller analyzer1 ).is Thedisabled central (DSA, and one Stanford the corresponds signal Research from to LIA the SR785). so-calledis directly For clockopen recorded- transition,loop byoperation, the which DSA. the is insensitive servo controller is disabled and the signal from LIA is directly recorded by the DSA.

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4. Results In this section, we investigate the resulting spectrum and corresponding field measurement. The typical CPT microwave spectra for sufficiently large fields of 10.9 μT and 24.9 μT are shown in Figure 4a. There are well-resolved seven resonances, which originate Sensors 2021, 21, 1517 6 of 10 from magnetic sublevels ranging from 푚퐹 = −3 to +3 with the change of 푚퐹 being zero (Figure 1). The central one corresponds to the so-called clock transition, which is insensitive to magnetic field in the first order. Its resonance frequency has an offset from the exact halfto magneticof ideal clock field in transition the first order. frequency Its resonance (4,596,316 frequency kHz) has by an~45 offset kHz from due theto combined exact half effects ofof ligh idealt shift, clock pressure transition shift, frequency second (4,596,316-order Zeeman kHz) by ~45 shift kHz etc. due The to linewidth combined effects(FWHM) of of the light shift, pressure shift, second-order Zeeman shift etc. The linewidth (FWHM) of the clock transition is 6.8 kHz while other resonances are broadened by ~1.76 kHz × |푚퐹| due clock transition is 6.8 kHz while other resonances are broadened by ~1.76 kHz ×|mF| due toto field field inhomogeneity. inhomogeneity.

FigureFigure 4. 4. (a(a) )Coherent Coherent populationpopulation trapping trapping (CPT) (CPT) spectra spectra as a functionas a function of microwave of microwave frequency frequency for for finitefinite-field-field measurement measurement(blue (blue for for 10.9 10.9µT μT and and red red for 24.9for 24.9µT) andμT) zero-fieldand zero measurement-field measurement (black) (black) showingshowing all all possible possible resonances resonances betweenbetween magnetic magnetic sublevels sublevels given given the the magnetic magnetic field. field. (b) CPT(b) CPT spectraspectra for for a a series series ofof smallsmall magnetic magnetic fields fields varying varying near near 0 µT. 0 μT.

ForFor conventional conventional CPT-magnetometry,CPT-magnetometry, one one of the of magneticallythe magnetically sensitive sensitive resonances resonances withwith significant significant amplitude is is chosen chosen as aas discriminator a discriminator for the for magnetic the magnetic field. Since field. the Since the amplitude of the signal itself for mF = 2, 3 is smaller than those of mF = 0, 1 due to the amplitude of the signal itself for 푚퐹 = 2, 3 is smaller than those of 푚퐹 = 0, 1 due to the broadening, we chose mF = 1 transition for our finite-field measurement. The absence broadening, we chose 푚퐹 = 1 transition for our finite-field measurement. The absence of of signal associated with transitions of different mF’s indicates that the bias field is well- signalaligned associated to the laser with propagation transitions direction. of different As mentioned 푚퐹’s indicates in Section that2, thethe asymmetry bias field is well- alignedwith respect to the to laser the clockpropagation transition direction. is apparent As due mentioned to the optical in Sec pumpingtion 2, the by circularlyasymmetry with respectpolarized to the light. clock The transition field discrimination is apparent signal due isto obtained the optical from pumping the demodulated by circularly LIA polar- izedoutput light. by The sweeping field thediscrimination bias magnetic signal field with is obtained the microwave from frequency the demodulated fixed near eachLIA output resonance associated with mF = 1. Both signals for 10.9 µT and 24.9 µT show the same level of discrimination, which is 2.1 V/µT as given by linear fitting (Figure5).

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Sensors 2021, 21, 1517 by sweeping the bias magnetic field with the microwave frequency fixed near each reso- 7 of 10 nance associated with 푚퐹 = 1. Both signals for 10.9 μT and 24.9 μT show the same level of discrimination, which is 2.1 V/μT as given by linear fitting (Figure 5).

Figure 5. The lock-inFigure amplifier 5. The lock (LIA)-in amplifier signal as (LIA) a function signal of as the a function axial magnetic of the axial field magnetic applied to field the applied atom. The to the microwave frequency is tunedatom. to measureThe microwave each target frequency field of is 0.0 tunedµT (black), to measure 10.9 µ eachT (blue), target and field 24.9 ofµ 0.0T (red). μT (black), Green curve:10.9 μT linear fitting (blue), and 24.9 μT (red). Green curve: linear fitting near zero-crossing for each dispersive curve. near zero-crossing for each dispersive curve.

Next, we considerNext, wethe considercase near- thezero case-field. near-zero-field. The CPT spectrum The shown CPT spectrum in Figure shown 4a is com- in Figure4a is prised of a singlecomprised dispersion of a single curves, dispersion which is the curves, result which of accumulation is the result of of resonance accumulation signals, of resonance 푚 thereby aboutsignals, two times thereby larger about in twoampl timesitude largerthan that in amplitude of 퐹 = 1 than resonance that of musedF = for 1 resonance finite- used for field measurement.finite-field The measurement. linewidth of the The merged linewidth resonance of the merged is 12.1 resonancekHz, which is is 12.1 only kHz, two whichis only times broadenedtwo-times compared broadened to that comparedof the magnetically to that of insensitive the magnetically clock transition. insensitive clock transition. The variationThe of variationresonance of fre resonancequencies frequencieswith respect withto the respect magnetic to the field magnetic near 0 μT field is near 0 µT shown in Figureis shown 4b. The in Figure frequency4b. The sensitivity frequency measured sensitivity by the measured shift of zero by the-crossing shift of is zero-crossing3.7 kHz/μT, whichis 3.7 is kHz/ aboutµT, the which same is as about that the of finite same-field as that measurement of finite-field for measurement 푚퐹 = 1 (3.5 for mF = 1 kHz/μT) [29].(3.5 Based kHz/ onµT) the [29 simple]. Based expression on the simple in Equation expression (3), we in can Equation estimate (3), the we fre- can estimate quency shiftthe upon frequency magnetic shift field upon variation magnetic by extracting field variation 푎푘’s byfrom extracting data shownak’s in from Figure data shown in 4a. The estimationFigure4 givesa . The 6.5 estimation kHz/μT, which gives is 6.5 1.85 kHz/ timesµT, more which sensitive is 1.85 timesthan the more measur sensitiveed than the value. Sincemeasured we assumed value. the same Since linewidth we assumed of Γ thefor sameeach resonance linewidth in of theΓ for simple each theory, resonance in the we attributesimple this discrepancytheory, we attribute to additional this discrepancy broadening to additional for larger broadening 푚퐹 ’s, which for larger bringsm F’s, which about imperfectbrings overlap about imperfectof each resonance. overlap of each resonance. As the fieldAs deviate the field from deviate the exac fromtly thenulled exactly condition, nulled the condition, overlap the of the overlap degenerate of the degenerate resonance becomesresonance imperfect, becomes imperfect,and consequently and consequently leads to reduction leads to reduction of the signal of the ampli- signal amplitude. tude. The magneticThe magnetic field discrimination field discrimination signal signal obtained obtained by scanning by scanning the bias the field bias is field also is also com- compared topared those to of those finite of field finite magnetometry field magnetometry in Figure in 5. Figure The slope5. The of 1.9 slope V/μT of is 1.9 again V/ µ T is again similar to thatsimilar of finite to that-field of finite-field magnetometry magnetometry under the under same theexperimental same experimental conditions conditions ex- except cept the valuethe valueof microwave of microwave frequency. frequency. The amplitude The amplitude of the of CPT the CPT signal signal itself itself is not is notas as large as large as thatthat in inthe the frequency frequency-scanned-scanned signal signal due due to to the the aforementioned aforementioned imperfection inin the overlap the overlapof of degenerate degenerate signals signals as as the the field field deviates deviates from from zero. zero. Based Based on on the the CPT CPT analysis anal- so far, we ysis so far, weexpect expect the the similar similar level level of noiseof noise sensitivity sensitivity for for the the ultra-low ultra-low field field measurement measure- to that of ment to thatthe of conventionalthe conventional finite-field finite-field measurement. measurement. Now we presentNow wethe presentmagnetic the field magnetic spectrum field measured spectrum in measured both the inopen both-loop the mode open-loop mode and closed-andloop closed-loop mode to discuss mode the to discusssensitivity the of sensitivity our CSAM, of our which CSAM, shows which an extended shows an extended dynamic range.dynamic The range.spectrum The in spectrum the open in-loop the mode open-loop is obtained mode isby obtained Fourier byanalysis Fourier of analysis of 1/2 LIA signal withLIA signalthe servo with being the servo inactive. being About inactive. 300 pT/Hz About1/2 300 of noise pT/Hz floor ofabove noise tens floor of above tens Hertz is identifiedof Hertz for is all identified three target for all magnetic three target fields, magnetic including fields, zero including (Figure 6a). zero By (Figure de- 6a). By tuning the detuningmicrowave the frequency microwave far frequencyenough to faravoid enough any CPT to avoid resonance any CPT (~1 MHz), resonance we (~1 MHz), could verifywe this could floor verify for all this frequency floor for ranges all frequency down to ranges DC (gray down curve to DCin Figure (gray curve6a). The in Figure6a). The low frequency feature is the result of ambient magnetic field penetrated through the shield, and varies depending on the magnetic environment in the vicinity of the sensing module. The electronic noise limit is measured to be 100 pT/Hz1/2 by turning off the

VCSEL current (green curve in Figure6a). The result of closed-loop measurement (servo Sensors 2021, 21, 1517 8 of 10

low frequency feature is the result of ambient magnetic field penetrated through the Sensors 2021, 21, 1517 shield, and varies depending on the magnetic environment in the vicinity of the sensing8 of 10 module. The electronic noise limit is measured to be 100 pT/Hz1/2 by turning off the VCSEL current (green curve in Figure 6a). The result of closed-loop measurement (servo bandwidth ~1 kHz) obtained by stabilizing the microwave frequency to the peak of CPT reso- bandwidth ~1 kHz) obtained by stabilizing the microwave frequency to the peak of CPT nance shows the consistent result as in Figure 6b. We attribute the large peaks at 11 Hz resonance shows the consistent result as in Figure6b. We attribute the large peaks at 11 Hz and 60 Hz to electric noise from instruments. and 60 Hz to electric noise from instruments.

FigureFigure 6. 6.( a(a)) Field Field noise noise spectral spectral density density obtained obtained by by Fourier Fourier analysis analysis of of the the LIA LIA output output in in the the open loopopen mode. loop mode. Black: Black: 0.0 µ 0.0T, blue:μT, blue: 10.9 10.9µT, andμT, and red: red: 24.9 24.9µT. μT. For For reference reference purpose, purpose, the the results results for for completely off-resonant microwave frequency (gray) and in the absence of laser light (green) completely off-resonant microwave frequency (gray) and in the absence of laser light (green) are are overlaid. (b) Field noise spectral density obtained from the feedback signal of PID servo con- overlaid. (b) Field noise spectral density obtained from the feedback signal of PID servo controller in troller in the closed loop-mode. Same color code as (a) for target magnetic fields. the closed loop-mode. Same color code as (a) for target magnetic ﬁelds.

WeWe believe believe that that there there is is room room for for further further improving improving the the sensitivity sensitivity of of this this magnetome- magnetom- ter.eter. First, First, it it would would be be favorable favorable to to achieve achieve higher higher density density of of atoms atoms by by increasing increasing the the cell cell temperature.temperature. InIn fact,fact, thethe temperaturetemperature ofof microfabricatedmicrofabricated vaporvapor cellcell isis around around 100 100◦ °CC for for mostmost CSAMs CSAMs based based on on cesium cesium [ 18[18,30].,30]. Secondly,Secondly, the the CPT CPT linewidth linewidth itself itself can can be be improved improved byby reducing reducing the the laser laser beam beam divergence divergence if weif we implement implement a micro-lens a micro-lens in the in package.the package. In our In case,our case, the diverging the diverging beam beam with awith half a angle half angle of 20◦ ofpasses 20° passes through through the cell. the For cell. a collimatedFor a colli- beam,mated the beam, intrinsic the intrinsic linewidth linewidth of CPT signal of CPT as signal low as as 2 kHzlow hasas 2 been kHz obtainedhas been by obtained using the by sameusing VCSEL the same and VCSEL vapor cell and in vapor a separate cell in tabletop a separate experiment tabletop (not experiment shown). Lastly,(not shown). since theLastly, magnetic since the sensitivity magnetic comes sensitivity from thecomes asymmetric from the population,asymmetric increasingpopulation, the increasing optical pumpingthe optical efﬁciency pumping is efficiency another way is another for improvement. way for improvement.

5. Conclusions In conclusion, we demonstrated the operation of a CPT-based chip-scale magnetometer near zero magnetic field in a miniaturized package. In spite of densely assembled components in our chip-scale device of 0.94 cm3 in volume, the field inhomogeneity induced by internal parts was small enough to preserve the dispersive CPT spectra, even when they are all superimposed in the absence of magnetic field. We observed a similar level of magnetic sensitivity of resonance frequency to that of the individual CPT resonance of nonzero mF even in the ultra-low field environment. We also analyzed performances Sensors 2021, 21, 1517 9 of 10

of the zero-field and finite-field magnetometers, both of which are comparable under the same condition. Further improvements are expected by optimizing the temperature and beam divergence. This work demonstrates successful operation of CPT-based CSAMs in a field range, which has been considered inaccessible. It also paves a way to further augment the simplicity of CSAMS, for example, by enabling operation without bias coils.

Author Contributions: Conceptualization, H.-G.H. and T.Y.K.; fabrication, J.P., T.H.K. and H.Y.K.; measurement and characterization, H.-G.H., S.E.P., S.-B.L., M.-S.H. and T.Y.K.; data analysis, H.-G.H.; writing—original draft preparation, H.-G.H.; writing—review and editing, all authors; supervision, T.Y.K. All authors have read and agreed to the published version of the manuscript. Funding: This research was funded by KRISS; grant number KRISS–2020–GP2020-0001. Institutional Review Board Statement: Not applicable. Informed Consent Statement: Not applicable. Data Availability Statement: The data presented in this study are available on request from the corresponding author. Acknowledgments: We acknowledge Tae Gyun Kim and Tae Hyun Jun for support with printed circuit boards. We are also grateful to Jae Hoon Lee for valuable comments on the manuscript. Conﬂicts of Interest: The authors declare no conﬂict of interest.

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