Magnetometry using sodium fluorescence with synchronous modulation of two-photon resonant light fields RAGHWINDER SINGH GREWAL, MAURICIO PULIDO, GOUR PATI, RENU TRIPATHI * Division of Physics, Engineering, Mathematics and Computer Science, Delaware State University, Dover, DE 19901, USA *Corresponding author: rtripathi@desu.edu

Received XX Month XXXX; revised XX Month, XXXX; accepted XX Month XXXX; posted XX Month XXXX (Doc. ID XXXXX); published XX Month XXXX

We report a new technique for generating magnetic resonance with synchronous modulation of two-photon resonant light fields. Magnetic resonances in fluorescence from a sodium cell are measured to demonstrate suitability of this technique for remote magnetometry. A strong magnetic resonance with its dip corresponding to the Larmor frequency is produced in the presence of a transverse magnetic field. An additional resonance at 3ΩL is observed, which can be used to determine the magnetic field orientation. We have developed a theoretical model based on the density matrix equations to verify our experimental observations. An average magnetic field sensitivity of 41 /√ is measured using light duty cycles ranging from 35% to 10%. We have discussed possible changes that can be made to improve the sensitivity of this scheme further.

OCIS codes: (270.1670) Coherent optical effects; (020.1335) Atom optics; (020.7490) Zeeman effect; (300.6280) Spectroscopy, fluorescence and luminescence Optically pumped atomic magnetometers are extensively studied for sensitive detection of magnetic fields in biomagnetics [1,2], fundamental science [3] and geophysical [4] applications. Synchronous pumping of atoms using modulated light increases the dynamic range in magnetic field measurement from microguass level to above the earth field [5,6]. Recently, magnetic-field measurement using fluorescence from sodium is being explored with interest and practical applications in remote magnetometry [7]. Laboratory studies in sodium cells are used as simulation platforms for studying the performance in remote earth field measurement [8,9]. Several sky experiments are conducted using back-scattered fluorescence from the mesosphere generated by resonant excitation of sodium D2 line with a modulated laser beam [10-13]. In this case, the earth field is measured by remotely detecting the magnetic resonance produced at the Larmor precession frequency, ΩL of sodium atoms in the mesosphere. The origin of this resonance is explained by the well-known Bell-Bloom scheme [14]. Currently, sensitivity reported in the sky experiments is very low (with highest sensitivity reported as 28 nT/√Hz [11])

compared to the sensitivity achieved in laboratory based remote sodium cell magnetometer (i.e. 150 pT/√Hz achieved at D1 line [8]). The sensitivity in sky experiment is primarily limited by the poor / of the resonance signal, and the photon shot-noise associated with the weak return fluorescence. A method using an additional repump light has been proposed to pump atoms back to the target state for increasing the amplitude of resonance [11]. However, the presence of repump also causes linewidth broadening and light shift, which compromises the sensitivity [15]. Polarization modulation with alternate circular polarizations was employed in sky experiment to increase the return fluorescence by confining atoms to strong cyclic transitions [12]. This technique did not provide any apparent improvement in the magnetometer performance. Thus, new techniques need to be explored for improving the performance in remote magnetometry experiments to sub-nanotesla level, so that planetary science studies could be performed using mesospheric magnetic fields. In this paper, we demonstrate a new technique, suitable for performing remote magnetometry using synchronous modulation of two laser fields, which are two-photon resonant with the sodium hyperfine ground states. Two-photon resonance with continuous laser fields has been widely studied for coherent population trapping (CPT), particularly for developing miniaturized CPT based atomic clocks and magnetometers [16-18]. The CPT resonance is produced by dark superposition of magnetic sublevels in the hyperfine ground states of alkali atoms. In the present work, synchronous modulation of two-photon resonant CPT fields is used as a strategy for producing magnetic resonances in fluorescence from D1 line in a sodium cell. We call this as the synchronous CPT scheme. The origin of magnetic resonances produced by the synchronous CPT scheme, is explained using Λ-systems formed in the sodium D1 manifold. To study the performance of synchronous CPT scheme for remote magnetometry, we measured the resonance signal at ΩL by applying a magnetic field perpendicular to the light propagation direction. In order to find the optimal duty cycle of light modulation for attaining high performance, amplitudes and linewidths of the resonance are measured as a function of the duty cycle, by keeping the peak intensity in CPT fields constant. We observed high amplitude in ΩL resonance at longer duty cycles

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our experiment. e (589.756 nm)ption spectroscoing SAS peaks, tD1 line. For impr beam is moduodulator (AOM)tic modulator (Ected light from Aer frequency. Thentical AOM (AO(QUBIG, Model: tor and amplifiquencies ±1.77quency separatioratio is approximy-Perot interferoeter is expandenfiguration (len. Experiments orr neon buffer a neutral dendjusted to circulwrapped with tgnetic field prcell is heated to 9atoms/cm3. The rmal insulationch is then instal

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The laser wave) and is monitopy (SAS) in a bthe laser is tuneplementing the ulated by a low-) followed by EOM). The ampAOM2 is frequehis frequency shiOM1) in the beamPM-Na23_1.7K3er combination71 GHz matchinon in sodium atomately set to 2:1ometer (Thorlabed from 2 mm nses L2 and L3), are conductedgas. The laser nsity (ND) filterlar ( ) polariztwisted nichromoduced by app92°C to yield a lcell is kept insidn in order to mlled at the cente

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by considering which case the n to its originam correspond toand a positive fg=2→Fe=2 tranatically tuned tonsible for produposition of groufrequency diffee sideband is chng ∆ ( Δcular Λ-system, gram [19,20]. Syg the light fieldso-photon resonawith frequencynents of modulin Figures 2(aes with Ω , 2Ωhe conventionalated light field ion. In this ca

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magnetic field dlight fields consal polarizatioo light fields gefirst-order sidebnsition, and to the Fg=1→Fe=2ucing a dark sund state subleverence, bethanged such tha) matches wii.e. Δ 0, Ωynchronous CPTs (i.e. carrier anance (i.e. Δ 0)y Ω . In thislated CPT fieldsa-c), and resona and 3Ω . Figurl Bell-Bloom sctuned to resoase, Λ-systems

e energy level dpresence of a mrequencies (a,b) 0med in the Bell-Bγ is the gyromain (c,d). The Zee

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direction as the sist and coon [19]. The twenerated by theband. The carriethe positive 2 transition. Eachstate corresponvels. CPT resontween the carrat two-photon (oith the resonant , 2Ω , 3ΩT scheme is impnd positive sideb) and by modulas case, differens form the samances will occurre 2(d) shows acheme, which unance with theare formed b

diagram showingmagnetic field. Λ-0 and ±2ΩL; (c) ±Bloom scheme. Hagnetic ratio. Aeman shifts in the

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g possible Λ--systems with ±ΩL and ±3ΩL,Here ΩL= γB is All possible Λ-e excited state

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eliberately modequency (i.e. Ωw-pass filteringdeband after thngitudinal field re created due tof dips satisfying transverse magesonances [Fig. reated due to nehown in Fig. 2(ps to seven in tn the populationublevels and thevolved in the coNext, we meynchronous CPTept on two-phoequency Ωm cesonances are aHz to 200 kHz),eld By = 85.7 mGmodulated light ystems [shown elds. Figure 4a (roduced at Ωm =ystems formed bormation of 3ΩLsed to exactly es=0) between thmagnetic field canetween ΩL and 3f this ratio with ansverse field Bym =120 kHz (2ΩLσ) excitations [ssible in the exnderstand the o

Fig. 3. CPT sp∆ between the CPTBz = 18 mG, Bx = 8.5

the Fg=2 grounfrequency, Ωe synchronous ced by the Bell-d state through rast of resonanows the observeng ∆ in the presve / , the

ulating the lase200 ≫g. The total ine EOM is set to(B=Bz), CPT reso Λ1-Λ3 systems conditions ∆=0 gnetic field (Bx a3 (dashed blueew Λ7-Λ10 system(b & c)]. This inthe spectrum. Thn distribution ae coupling strenrresponding Λ-seasure magneticT scheme. In thioton resonance corresponding acquired by sca, for a fixed higG (ΩL=60 kHz) has dominant in Fig. 2(c)] al(blue curve) sho=60 kHz (ΩL) anby strong (σ±, π)L resonance is ustablish the twohe two laser fn also be determ3ΩL resonances, light ellipticity y is expected to pL) due to Λ-systeshown in Figs. 2xperimental Figorigin of magne

pectrum plotted T fields for Bz= 15 mG, By = 8.8 mG

nd state. Resona matches wCPT scheme, -Bloom scheme.spontaneous ence produced bed CPT spectrumsence of a fixed resonances ar

er fields with a ≫ Ω ) and by acqntensity in theo 5.2 W/m2. In onances [Fig. 3 [shown in Fig. 2and ±2ΩL. In adand By) is appliee curve)] at ∆=±ms formed by (ncreases the totahe contrast of a among the groungths of σ+, σ- system [19]. c resonances pris experiment, t(i.e. ∆=0) andto the Larmonning Ωm over gher applied tra[Fig. 4a]. At 50first-harmonicsong with the uows strong magnd Ωm=180 kHz) excitations [shunique to this apo-photon resonafields. Directionmined by using thand pre-calibraand polarizatioproduce a very wems formed by w2(a), 2(b)]. Thisg. 4a (blue cuetic resonances

as a function of d8 mG, Bx = By=0 (G (dashed blue lin

ance occurs whwith Ω and 2Ωa 3Ω resonan. Loss of atoms emission can aly the Bell-Bloom as a function applied magnere produced b

high modulatioquiring them wie carrier and ththe presence of(solid red curve2(a)], with centeddition to Bz, whed, additional CP±ΩL and ±3ΩL a(σ±, π) excitatioal number of CPCPT dip depenund state Zeemand π-transitioroduced using ththe CPT fields ad modulated wior frequency Ωa wide range (4ansverse magne% duty cycle, ths, which form unmodulated CPgnetic resonancz (3ΩL) due tohown in Fig. 2(cpproach. It can bance condition (in of the externhe amplitude ratating the variatioon angle [21]. Thweak resonanceweak (σ+, σ+) or (s resonance is nurve). To furthproduced by th

difference detunin(solid red line) anne).

en Ω . nce to lso om of tic by

on ith the f a e)] ers en PT are ns PT nds an ns the are ith ΩL. 40 tic he Λ-PT ces Λ-c)]. be i.e. nal tio on he at (σ-not her the

synchrobased ohyperfifurthermotion(blue cu3ΩL. Unresonan

Wthe lighfor Ωmaroundthis casΩm =3ΩresonanΩL resoby the in the B2(d). Oin the resonanshown

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Fiamplituboth plparame

onous CPT schon the density mine states (i.e. Fr simplified ourn, and the spatiurve) shows calnlike the experimnce at Ωm = 2ΩL i

When a differenceht fields, two-phm=ΩL±∆ and Ωmd Ωm=ΩL and Ωm=se, a two-photonΩL by the two lignce is observedonance can still bformation of ΩLBell-Bloom scheOur theoretical cexperiment (Finces at Ωm= 12in Fig. 2d for ∆=

nally, we demontometry applicaced by the syncmentally measudots) of ΩL resonak intensity in Crements. A tranield, is applied ad the Larmor freed using an LPFs lowered from 5

ig. 4. (a) Exptic resonances aeters used in theansit decay rate τ

ig. 5. (a) Experimude and FWHMlots show linear feters are same as

heme, we devematrix equationFg=1, Fg=2 and Fr model by negial distribution lculated magnetment [Fig. 4a (blis observed usin

e detuning ∆=10hoton resonancem=3ΩL±∆, thus,=3ΩL resonancesn resonance conght fields with ∆d in Fig. 4(a,b) fobe seen for ∆=1L resonance dueeme [9] througcalculations (Figig. 4a). The the20 kHz (2ΩL) f=10 kHz case.

nstrate an atomation, based onchronous CPT ured peak amplitnance at differenCPT fields is keptnsverse field Byand the modulatquency ΩL=180 F with cut-off fr50%, the amplit

perimentally andas a function of Ωe simulations: Rab=10-5 Γ, where Γ

mentally and (b)of Ωm=ΩL (180 kfittings to the lines in Fig. 4(b).

eloped a theorns by considerinFe=2) in Na D1 lglecting the effeof light intensittic resonances alue curve)], a weng the theoretica

0 kHz is introdue conditions are , forming news (Figs. 4a, 4b: rendition cannot b∆=10 kHz. Henceor ∆=10 kHz ca0 kHz. This can e to single-photogh Λ12-system, s. 4b) show simieoretical plot shformed through

mic magnetometen the ΩL resonscheme. Figuretudes (red dotsnt duty cycles ot constant at 5.2y = 257 mG, cotion frequency ΩkHz. The resonrequency 1 kHztude of ΩL reson

d (b) theoreticaΩm for two differbi frequencies Ωcis the spontaneou

) theoretically mkHz) resonance. ewidth data. Othe

retical model ng only three line [22]. We ect of atomic ty. Figure 4b at Ωm = ΩL and eak magnetic al model.

uced between also satisfied w resonances ed curves). In be satisfied at e, no Ωm =3ΩL ase. However, be explained on resonance shown in Fig. ilar results as hows a weak h Λ11-system,

er for remote nance signal e 5(a) shows s) and widths of CPT pulses. W/m2 for all omparable to Ωm is scanned ance signal is . As the duty nance initially

ally obtainedrent ∆ values.c=2Ωs = 0.03 Γus decay rate.

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creases, and mahereafter, the amycle ranging fromhe Bell-Bloom sgh amplitude ΩFig. 5(a)]. Long dre beneficial inuorescence fromtensity constantlowered propoherefore, the lin

f ΩL resonance urve]. Theoreticaith experimentaThe sensitivind the linewidthensitivity δB of th where ∆f is the gyromagneti√ by measust-Fourier-transhows the magnmodulation. The rround 45 pT/√a: red line). Sincoise decreases rhows the variaensitivity δB impdecreased frommaximum. For lemains constant 1 pT/√Hz (Figanging between 7 pT/√Hz is terature, highestuty cycle, empynchronous CPTuty cycles. Additssociated with xpected to give bxperiments [7]. urrent setup is sumodification of thesonance can beelds. This can b

Fig. 6. (a) Mmeasured at 35%the frequency ranfunction of the CPaverage sensitivit

aximizes near 35mplitude deceasm 30% to 10%. cheme [8], synΩL resonance at lduty cycle corresn sky experimm mesospheric st at 5.2 W/m2, thortionately withnewidth (i.e. full-

reduces linearlyal results shownal results shown ity of a magnetoth of resonancehe magnetomete ∆ / . /the FWHM of ΩLic ratio of sodiuring the noise isform (FFT) onnetic noise specroot-mean-squa within the frce the LPF is setrapidly for frequation in sensitiproves nearly bym 50% to 35%, lower duty cycwithout much vg. 6b: dashed li35% and 10%achieved for 2t sensitivity in skploying the BT scheme offers ionally, the darkreduced photbetter magneticBesides, the sub-optimal. It cahe modulation e maximized by be achieved by

agnetic field nois% duty cycle. Thnge 1Hz to 1 kHzPT pulse duty cycty from 35% to 1

5% duty cycle (Fses almost lineaUnlike ΩL resonnchronous CPTlonger duty cycsponds to long Cents for increasodium layer. The average intenh the lowering o-width at half-m

y with duty cycn in Figure 5(b) qin Figure 5(a). ometer depends e. The photon ser is given by / L resonance, γ = um atom, and n the ΩL resonan the oscilloscctrum using 35are of magnetic nfrequency ranget to a 1 kHz cut-uencies above 1ivity δB with y a factor of twowhere amplitudcles below 35%variation. An aveine) is achieved. A maximum s5% duty cycleky experiment isBell-Bloom schhigher sensitivitk ΩL resonance inton shot noisec field detectionsensitivity δB an be further imtechnique. Theequalizing the pconfiguring the

se spectrum in Ωe red line showsz. (b) Variation incle. The dashed b0% duty cycle.

Fig. 5a: red curvarly over the dunance produced T scheme delivecles closer to 50CPT pulses, whiasing the retuTo keep the pensity in CPT pulsof the duty cycmaximum, FWHM

cle [Fig. 5a: blaqualitatively agron the amplitushot-noise limit (1) 6.99812 Hz/nT/ is measurance signal usingcope. Figure 6(5% duty cycle noise is measure 1 Hz -1 kHz (F-off frequency, th1 kHz. Figure 6(duty cycles. Tho, as the duty cycde of resonance%, the sensitivierage sensitivity d for duty cyclsensitivity close . In the reports recorded at 20heme [11]. Thty at much longn sodium D1 linee, and thereforn sensitivity in smeasured in thmproved by simpe amplitude of power in the CPe EOM different

ΩL resonance signs the noise-floor n sensitivity δB asblue line shows th

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hat the ΩL resonds in the presment is also doore, the measurectuations in theving the shieldivity of the magnn shot-noise limitsummary, we e, showing the e earth field meance instead ofscheme for remesonant fields, ace a strong Ωcantly enhancerement at longee magnetic fieldduty cycle rangine magnetometrym D1 line in the ncknowledgemeR award #80N15AP84A . isclosures. The ences Bison, N. Castagnsprzak, H. SaudanKnappe, T. H. Sandahms, Appl. Phys. . Smiciklas, J. M. B

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