-
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:
[email protected]
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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chtem
hasplenge
lose to 35%), wroducing high rensitivity of 37chieved using
tensitivity can bechnique used inobserved using determining
tddition to its strell-Bloom schemtomic density bservations. Figure
1 rrangement. A ith a narrow lin
f 2W, is used in oa D1 resonanceaturation absorpeference cell.
Usiansition in Na Dcheme, the lasercousto-optic moGHz)
electro-optrst-order diffracHz from the lasesing another ideetup.
The EOM (F signal generatdebands at freround state freqdeband power
rscanning Fabryser beam diamlescopic lens come broadening.ontaining
10 Toontrolled using olarization is adate. The cell is he residual
magurrent. The Na cf about 1.6×109 ahamber for thermperature,
whi
Fig. 1. Diagraalf-wave plate; plitter; BS, beam nses; BF,
band-penerator.
which could be return fluoresce7 pT/√Hz in mthe ΩL resonae
further improvn our experimenthe synchronouthe orientationrength.
This resome [8,9,14]. Theomatrix analysishows the
sfrequency-doubewidth (< 1 MH
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
am showing theλ/4, quarter-wasplitter; D, beampass filter; PMT,
p
favorable in skyence. We show magnetic field nce signal at ved
by modifyinnt. An additional us CPT scheme, wn of external monance
has no coretical results ais to verify ochematic of tbled Raman
fibHz) and a maxim
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
experimental aave plate; PBS, m dump; M, mirrophotomultiplier
t
y experiments fthat a maximumeasurement 25% duty cycng the
modulatioresonance at 3Ωwhich can be usmagnetic fieldcounterpart in
thare obtained usinour experimentthe experimenter amplifier lasmum
output pow
elength is tuned tored by utilizinbuffer-gas-free Ned to Fg=
2→Fe =synchronous CP-frequency (MHa high-frequenplitude-modulatency
shifted by 8ift is compensatm path of the SA3) is driven by an to
create opticng the hyperfinom. The carrier1, measured usinb,
SA210-5B). Thto 8 mm usingto prevent trand using a Na cbeam
intensity r, and the beazation using a λ/me wires to cancplied DC
heatinlow vapor denside a non-magnemaintain a stear of a
two-layer
arrangement. λ/2polarizer beamor; L1-L4, convextube; FG,
function
for um is cle. on ΩL ed in the ng tal tal ser wer
to ng Na =2 PT Hz) ncy ted 80 ed AS an cal ne to ng he g a sit
cell is am λ/4 cel ng ity tic dy ed
mu-memagnetmounteutilizeddirectioexperimPMT,
pultra-naaroundlight frousing a Figphotonmagnet
drawn axis, in additiosystemcarrier the Fgautomaresponsuperpwhen
positivedetunina particthe diagkeepingon twofields wcomponshown
matchewith thmodulatransiti
2,mxn Figsystemstwo-phand (d)the Larsystemsare neg
-
-
-
-
Λ7π
etal enclosure wtic field is furtheed inside the md in our
experimon in synchronmental measureplaced perpendiarrow band-pad
589.45 nm is kom fluorescenca low-pass filter (gure 2 (a-c) shn
resonant lighttic field applied
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
g. 2. Na D1 lines formed in the hoton resonant fr) Λ-systems
formrmor frequency, s are not shown glected.
-2 -1 0 1
-2 -1 0 1
ΩL
ΩL
(a)
∆hfs
Ωc
Λ1 Λ2
σ+
-2 -1 0 1
-2 -1 0 1
(c)
ΩL
Λ8 Λ97σ-π
with a shieldiner cancelled usinmu-metal encloment to apply a
cnous CPT schemements by collecicular to the lighass filter with
kept before the ce. Magnetic res(LPF). hows possible t fields in Na
Din an arbitrary
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
Fe= 21 2 me -
2 mg
Fg= 2
Fg= 1Ωs
Λ3 Λ
σ+
Fe= 2 2 me
2 mg
Fg= 2
Fg= 1
2ΩL
Λ10
σ+
ng factor of ∼1ng three-axis Heosure. These coconstant field
Byme. We have pcting fluorescenht propagation bandwidth 1 nPMT to
removesonance signals Λ-systems formD1 line in the pdirection. The
Λ
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
-2 -1 0 1
-2 -1 0 1
(b)
Λ4 Λ6Λ5σ
σ-
-2 -1 0 1
-2 -1 0 1
(d)
Ω
Λ
σ+ σπ
ΩL
Λ11
102. Residual elmholtz coils oils are also y along the
y-performed all nce light on a direction. An nm centered e
background are detected med by two-presence of a Λ-systems are
quantization omponents in wo legs of Λ-e EOM i.e. a er is tuned
to sideband is h Λ-system is nding to the nance occurs rier and the
or difference) t frequency of as shown in plemented by band)
exactly ating the CPT nt frequency me Λ-systems r when Ω a
comparison uses a single e Fg=2→Fe=2 by magnetic
g possible Λ--systems with ±ΩL and ±3ΩL,Here ΩL= γB is All
possible Λ-e excited state
2
2
σ-
1 2
1 2
L
Λ12
σ-
-
suthCocathrescdifie
defrelowsidlonarof a
trecr[shdiponsuinvsykefreRekHfiemsyfieprsyFous∆=mbeof traΩm,
σvisun
∆B
ublevels within he modulation ompared to thannot be produche
other groundeduce the contrcheme. Figure 3 shofference detunineld.
To impro
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
Finmagnetproducexperim(blue dThe peameasurearth
fiaroundacquirecycle is
ngnd FimagnetParameand tra
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.
measured peakBlack lines iner simulations
-
inThcythhig[Farfluintis Th
of cuwiansethin fasshmar6anoshseis
mre41ra37litdusyduasexexcumrefie
mtfa
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
ve). uty in ers 0% ich urn ak ses cle. M)
ack ree de ted T is ed g a (a) in ed Fig. the (b) he cle e is
ity y of les to ted 0% he ger e is re, ky the ple ΩL PT tly
such thsidebanexperimtherefothe flucimprovsensitivphotonIn
schemeremoteresonanBloomtwo reproducsignificmeasuraveragepulse
dremotesodiumAcEPSCoR#NNX1Di
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[11] F. Hic
[12] F. Hic
[13] T. [14] W.[15] Z. Y[16] J. V[17] V.
Kit[18] J. K[19] L. M
(20[20] Z. W
41[21] R. [22] S.
nal,ins ahe
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,
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onance is produsence of a highone in a weaklyed sensitivity δBe
ambient maging environmennetometer to subted sensitivity. have
developepossibility for iasurement. Thissingle-photon rmote
magnetomatoms in both gΩL resonance. es the sensiter duty cycles
thd sensitivity of 4ng from 35% to y experiments eear future. ent:
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, and R. Tripathi, aomic Density Matr
uced by the twhly suppressed y shielded envirB may have
beegnetic field. Went will further b-picotesla level,ed a new
synchimproving the s technique usesresonance usedmetry. We
showground states cThe proposedtivity in mahan previously 1 pT/√Hz
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