Table Of ContentA microfabricated optically-pumped magnetic gradiometer
D. Sheng,1,2,a) A. R. Perry,1,2 S. P. Krzyzewski,1,2 S. Geller,1 J. Kitching,1 and S. Knappe1,2
1)Time and Frequency Division, National Institute of Standards and Technology, 325 Broadway, Boulder,
Colorado 80305, USA
2)University of Colorado, Boulder, Colorado 80309, USA
(Dated: 13 January 2017)
Wereportonthedevelopmentofamicrofabricatedatomicmagneticgradiometerbasedonopticalspectroscopy
of alkali atoms in the vapor phase. The gradiometer, which operates in the spin-exchange relaxation free
regime, has a length of 60 mm and cross sectional diameter of 12 mm, and consists of two chip-scale atomic
7 magnetometers which are interrogated by a common laser light. The sensor can measure differences in
1 magnetic fields, over a 20 mm baseline, of 10 fT/Hz1/2 at frequencies above 20 Hz. The maximum rejection
0 of magnetic field noise is 1000 at 10 Hz. By use of a set of compensation coils wrapped around the sensor,
2 we also measure the sensor sensitivity at several external bias field strengths up to 150 mG. This device is
n useful for applications that require both sensitive gradient field information and high common-mode noise
a cancellation.
J
2
1 Optically-pumped magnetometers operate with a net (a) 20 mm 1
spin polarization, and the spin undergoes Larmor pre- 3 4
] cession in an external magnetic field1. This spin rota- 2
t
e tion modifies the light-atom interaction, and a magnetic
d field dependent signal appears in either the absorption
- or phase shift of a probe beam2. Two main research 60 mm 5
s
n directions in this field have been to improve the sen- (b)
i sor sensitivity on the one hand and the size, weight, Sensing Reference TIA TIA
cs. power consumption and spatial resolution on the other λC/e4ll Cell Polarizer iRLno-epcfh koa-uisnte iLnRo-pechfk a-inisne
i hand. Subfemtotesla magnetic field sensitivity has been
s PID PID
achieved in the spin-exchange relaxation free (SERF)
y Adder
h regime3,4, andwithradio-frequency5, andscalar6 atomic Adder DAQ
p magnetometers. Micrometer and nanometer scale spa-
[ tialresolutionshavealsobeenrealizedinsystemssuchas FIG. 1. (Color online) (a) Photograph of the magnetic gra-
Bose-Einstein condensates7,8 and nitrogen-vacancy cen- diometer. 1. Kapton flexible coil, 2. optical bench, 3. PCB,
1
ters9, respectively. The combination of these two re- 4. CAT5e cable, 5. optical fibers. (b) Plot of the optical
v
paths inside the sensor and electrical signal processes (heat-
6 searchdirectionshasledtocompactcavity-assistedtable-
ingbeamsnotshown). TIA:trans-impedanceamplifier,PID:
3 top experiments6,10–13 and highly sensitive miniaturized
proportional-integral-derivative controller.
2 devices14. These devices, making use of millimeter-scale
3 cells, are small, power efficient, and broadly useful in
0
sensing applications that require portability or battery
.
1 operations. They are also useful for biomagnetic imag- high magnetic field sensitivity can result from a combi-
0 ing, where the target distance is on the millimeter to nationoftheSERFmechanism18,19 andazerofieldlevel
7 centimeter scale. Such applications include human mag- crossing resonance20. We build the gradiometer by plac-
1
netoencephalography15 andmagnetocardiography16. For ing two such cells on the same optical bench separated
:
v bettertargetfieldspatialinformationandcommonnoise by 20 mm as shown in Fig. 1(a). This geometry allows
i cancellationintheseapplications,itrequiresgradiometer bothcellstosharethesamelasersource. Asaresult,the
X
sensors. Here we report on the development of a minia- optical noise is largely common to both magnetometers.
r
a turizedmagneticgradiometerbasedonchip-scaleatomic Comparedtoothergradiometers,whichusetwoseparate
magnetometers. magnetometer devices21 or a single large cell22, the sen-
NIST chip-scale magnetometers14,17 use microfabri- sor in this paper maintains both a high common-mode
catedvaporcells,andoperatewithasinglelaserbeamfor rejection ratio (CMRR) and a small cell size.
both pumping and probing the atomic polarization. The The optical bench is a cylinder with a length of 60
mm and a diameter of 12 mm, fabricated using high-
resolution stereolithography. The bench is fabricated in
twohalvesseparatedbyaplaneinthecylinderaxis. One
a)Current Address: Department of Precision Machinery and Pre- halfcontainsthephotodetectors,whiletheotherhalfcon-
cision Instrumentation, University of Science and Technology of tains all the optics. The cells are located 4 mm and
China,Hefei230027,China 24 mm from the end of the sensor, respectively, which
2
allows the sensing cell to be placed in close proximity to attached, T (T ) is the cell (environment) temperature,
c e
the magnetic field source. and σ is the Stefan-Boltzmann constant. At T =20 ◦C,
e
There are three separate optical beams inside the sen- Eq. (1) predicts that it takes 115 mW power to heat the
sor. One beam at 795 nm is used for the optical pump- cellto150◦C.Experimentallyaheatbeampowerof150
ing,whichissplitintotwobeams,oneforeachcell. Two mW was required to reach the same temperature, which
separate beams at 1550 nm are used for independently confirmsthattheheatlossofoursensorisdominatedby
heating the cells23. Fig. 1(b) shows the pumping beam theblack-bodyradiationofthecell. Eq.(1)alsopredicts
paths inside the sensor. This pumping beam is gener- that, forfixedheatingpower, T changesby7.5◦Cwhen
c
ated by a distributed feedback diode laser, and sent to T changes by 20 ◦C. We confirmed this dependence by
e
the bench through a 6 m long polarization maintaining adding an oven around the sensor and monitoring the
fiber. A 0.2 mm thick polarizer at the end of the fiber change in beam transmission. Since the SERF regime
cleans up the beam polarization. The diverging beam covers a broad temperature range, a change in T results
c
goesthroughalensanti-reflectioncoatedforwavelengths mainly in a change of the pumping beam transmission
from700nmto1600nm,andtheoutputcollimatedbeam on a long time scale. This effect can be diminished by
diameter is about 2 mm. A dichroic mirror is placed stabilizing the cell temperature through monitoring the
next to the reference cell, acting as a 50/50 beam split- dclevelofthephotodiodeoutputandfeedingbacktothe
ter for the pumping beam, and a reflector for the refer- heater power.
ence cell heating beam. A gold coated mirror under the A SERF magnetometer requires not only a high cell
sensingcellreflectsbothitspumpingandheatingbeams. temperature for a large atomic density, but also a low
Thinquarter-waveplatescircularlypolarizethepumping magneticfieldenvironment. Inthiscase, astableatomic
beams, which are detected after the cells by two silicon polarization P = 2(cid:104)S (cid:105) builds up, where S is the elec-
p p
photodiode chips with an active area of 3.5 mm2. The tronspinalongthepumpingbeamdirection. Amagnetic
photodiode chips are attached to a printed circuit board field modulation of frequency ω, which is much larger
(PCB), using conductive glue for the cathodes and wire than the Zeeman frequency and optical pumping rate,
bonding for the anodes. A printed Kapton flexible coil perpendicular to the pumping beam direction results in
system is wrapped around the optical bench. This flex modulated polarization components at harmonics of ω,
coilsystemprovidestwopairsofcircularHelmholtzcoils with the first harmonic component as20,25,
for magnetic fields in the main sensitive direction along
γ B R sinωt
the cylinder axis of the sensor, and two pairs of saddle P(ω)= e t,0 p ×
(R +R )2+(γ B )2
coils for common magnetic fields in the two perpendic- r p e t,0
ular directions. The flex coils are soldered to the PCB, J (γeBt,m)J (γeBt,m), (2)
so that all electrical controls exit the sensor through the 0 Q(P)ω 1 Q(P)ω
PCB. A 6 m long CAT5e cable transfers the electrical
whereJ isBesselfunctionofthefirstkind,γ istheelec-
signals to the control electronics. e
tron gyromagnetic ratio, Q(P) is the nuclear spin slow-
The chip-scale cells used in this sensor are made us-
downfactor,B andB aretheoffsetandmodulation
inganodicbondingbetweensiliconandPyrexglass. The t,0 t,m
fields in the transverse direction, respectively, R is the
cell’s outer size is 4×4×2.7 mm3 with an interior size of p
pumping rate, and R is the spin relaxation rate which
3×3×2mm3. Thecellswerefilledwithroughly1amgof r
is dominated by the spin-destruction relaxation rate in
N gas, and a droplet of 87Rb. If cells in a gradiometer
2 the SERF regime. Because the pumping beam absorp-
are filled with different gas pressures, Rb atoms experi-
tion is related to the atomic spin polarization, there are
ence different shifts of the optical absorption line. This
correspondingmodulationsofthebeamtransmissionI at
reduces the laser noise cancellation in the gradiometer,
harmonicsofω. ItsfirstharmoniccomponentI(ω)shows
becausethesamepumpingbeamfrequencynoisecoverts
asimilardispersiverelationwiththeoffsetfieldasP(ω).
todifferentamplitudenoiseofthetransmittedbeam. To
In the experiment, we use the reference output of a lock-
minimize this effect, we pick two cells which differ in the
in amplifier to provide the modulation field, which also
pressure shifts of the Rb D1 line by less than 0.3 GHz,
demodulatesthetransmittedbeamsignalatfrequencyω.
which corresponds to a N pressure difference less than
2 We pass the in-phase output signal to a PID controller,
0.04 amg. We attach pieces of 0.2 and 0.6 mm thick
feed back the PID output to the Helmholtz coils on the
color glass filter to the front and back of the cell to heat
sensor,andreadoutthefieldnoisefromthefeedbacksig-
uniformly the cells through the absorption of 1550 nm
nal. Theconversionfromafeedbacksignaltoamagnetic
light14.
fielddependsonthecoilfieldcalibrationonly. Therefore,
ThecellsweresuspendedonaKaptonwebinsideavac-
it is more robust to changes in sensor parameters than
uum package24 with dimensions of 8.5×8×5 mm3. The
in the case of open-loop operations14, which leads to a
heat loss of a vacuum-packed cell is dominated by the
better CMRR.
Stefan-Boltzmann law,
The gradiometer sensor was tested in a three-layer
P =Aσ(T4−T4), (1) magnetically-shielded room. The sensor works in a free-
c e
running mode, without optical power, wavelength, or
where A is the surface area of the cell with colored glass temperature control. Fig. 2(a) shows the sensor perfor-
3
(a) 1021/2Hz) ggrualadrioHmeeltmerhoalttzthceoiclesnytsetremofwaitthhrseied-edilmenegntshiosnoaflarbeoctuatn1-
1/2e (fT/Hz)102 oise (fT/cm/ malar.bgaeWnHdeweplimdatshhsolwotzfhi1cto5ei0lnsHoaizlso,enatgnhdtrhoceuogsnhenneascittloivtwehegpraoasudstipofiumltteertteowrtidhtihe-
nois 101ent n rection. Fig. 2(b) shows that, with a single integrator
101 adi in the PID controller, the sensor CMRR is about 500 at
gr
100 101 102 1 Hz, and larger than 100 at frequencies up to 50 Hz.
frequency (Hz) By adding a second integrator in the PID controller, we
104 (b) 1041/2z) achieve better noise cancellation in the feedback loop at
1/2noise (fT/Hz)110032 110032ent noise (fT/cm/H td1tChi0imMoeHmeRczeocR,tsoewtnrrsehostpefharonoberwtattenshoddfeawftboChiredeMstmthsReaCcrRgMoendneuRudtpcRicittniogfotrrene1ag.q0dru0aiIoe0tnnmoacrtet.yhtifeTisrsrehscrqiaeisunlseaeintst,hecttdeihheSseteoEnbgRteerhaasFert-
101100 101 101201gradi regime27.
frequency (Hz) The suppression of spin-exchange relaxation in the
SERF regime limits the sensor dynamic range to 10 nT.
FIG. 2. (Color online) (a) Plot of the magnetic field and Ifthebiasfieldisbeyondthisdynamicrangeatthetime
gradient field sensitivity of the sensor. The blue (magenta) of turning on the gradiometer, its control system is not
dashlinecorrespondstothereference(sensing)cellresult,the able to provide the correct feedback current to null the
black solid line is the noise of the difference between them.
offset field. A way around this problem is to add an
Thereddash-dotlineisthesubtractionofthelock-inampli-
additional compensation coil system and a sensor with
fier quadrature outputs. (b) Plot of the gradiometer CMRR
a larger dynamic range to first bring the bias field to
withdifferentPIDsettings. Theblue(magenta)dashlinecor-
within the dynamic range of atomic sensor28. To imple-
responds to the reference (sensing) cell result, the red dash-
ment this scheme in our gradiometer sensor while keep-
dot (black solid) line corresponds to the gradiometer result
using a single (double) integrator in the PID controller. ingthesensorsizeunchangedrequiresasecondsmalland
stable magnetic sensor. An example of such a sensor is
the Honeywell HMC1053 three-axis magnetoresistive de-
mance with 1.2 mW of power coupled into the pumping vice29. Wehavetestedthissensorinthepolarityswitch-
beam fiber, 150 mW of power coupled into each heat- ingmode,andconfirmedthatthereadoutisstablewithin
ing beam fiber, and 100 nT modulation field at 1.79 10 nT over 30 hours with a proper thermal isolation.
kHz. Each magnetometer has an open-loop bandwidth The compensation coils are also required to be small
of 130 Hz, and a magnetic field sensitivity better than to keep the whole system compact. We wrap a pair of
20 fT/Hz1/2 at frequencies above 10 Hz. An indepen- Helmholtzandanti-Helmholtzcoilsforeachcellonaslot-
denttable-topexperiment26 withsimilarcellsandbetter tedcylinderattachedtothesensoroutersurfaceascom-
control of the pumping-beam noise shows that it is pos- pensation coils. Compared to references which used a
sible to improve the single magnetometer sensitivity to large compensation coil system30,31, the small compen-
better than 10 fT/Hz1/2. The cross-talk effect of the sation coils compatible with our sensor could generate
Helmholtzcoilsofonecellontotheothercellislessthan significant field gradients. To test the limitation in this
4 %. We acquire the gradiometer results by subtracting small system, we use the 1 m size Helmholtz coil system
the two magnetometer results. The gradiometer sensi- mentionedpreviouslytogenerateanoffsetfield,andmea-
tivity is around 5 fT/cm/Hz1/2 at frequencies above 20 sure the gradiometer sensitivity after zeroing the offset
Hz. Thisagreeswiththephoton-noise-limitedsensitivity fieldusingthesensorcompensationcoils. Fig.3(a)shows
intheopen-loopoperation,whichwefindbysubtracting the result at a 50 mG bias field. The sensitivity of each
the lock-in amplifier quadrature outputs14. We also find magnetometer is dominated by the noise from the bias
that the gradiometer sensitivity degrades by less than field current source32. The gradiometer largely cancels
10%,whenthepumpingbeamfrequencyistunedwithin this common noise, and its sensitivity is limited by the
a 5 GHz range. This makes it possible to run multiple field gradients. To compare the gradiometer sensitivity
gradiometers with different buffer-gas pressure shifts us- at different bias fields, we take the average gradiometer
ing a single pumping-beam source, as long as the two sensitivity from 90 Hz to 110 Hz, and plot the results in
cells inside each gradiometer have similar gas pressures. Fig.3(b). Thegradiometernoiselevelincreasesquadrat-
The common-mode noise rejection ratio is an impor- ically with the bias field strength, which agrees with the
tant parameter to characterize the gradiometer. A large expected scaling due to the gradient field33. With this
CMRR implies that the gradiometer could work in a scaling, the sensitivity of this gradiometer sensor is ex-
noisy environment, which relaxes the requirements on pected to be around 0.5 pT/cm/Hz1/2 at the earth field
the test room shielding factor or the instrument noise amplitude, comparable with several previous measure-
of nulling fields. To measure the CMRR, we place the ments using a larger system30,31. By adding more field
4
103 (a) 1031/2m/Hz) 23DI..KB.uKdokmerinains,dTM..WR.oKmoarlnisa,cNk,aJtu.rCe.PAhllyrse.d3,,a2n2d7M(2.0V07.)R.omalis,
1/2Hz) 102e (fT/c 4NHa.tBu.rDea4n2g2,,A5.96C.(2M0a0l3o)o.f, andM.V.Romalis,Appl.Phys.Lett.
noise (fT/102 101gradient nois 569SAD.7p.-,KpS1lh..5LeP1ne1hge1y,,0KsS.(..2LLL0ei.1t,St0N.a).u8.e9Dr,u,2Sr1a.4lJ,1.0Sa6neld(t2zM0e0r.,6OV)...ARloemma,liasn,dPhMy.sV.R.Revo.mLaeltist.,
101 25 50 75 100 125 150 110,160802(2013).
frequency (Hz) 7M.Vengalattore,J.Higbie,S.Leslie,J.Guzman,L.Sadler, and
75 D.Stamper-Kurn,Phys.Rev.Lett.98,200801(2007).
1/2z) (b) 8Y.Eto, H.Saito, andT.Hirano,Phys.Rev.Lett.112,185301
T/cm/H50 9(P2.0M14a)l.etinsky, S. Hong, M. S. Grinolds, B. Hausmann, M. D.
e (f Lukin,R.L.Walsworth,M.Loncar, andA.Yacoby,Nat.Nan-
nt nois25 10Sot.eLchi,nPol.oVgyac7h,a3sp2a0t(i,20D1.2)S.heng, N. Dural, and M. V. Romalis,
e
di Phys.Rev.A84,061403(2011).
a
gr 00 25 50 75 100 125 150 11K. Jensen, N. Leefer, A. Jarmola, Y. Dumeige, V. M. Acosta,
P. Kehayias, B. Patton, and D. Budker, Phys. Rev. Lett. 112,
bias magnetic field (mG)
160802(2014).
12H.Clevenson,M.E.Trusheim,C.Teale,T.Schr¨oder,D.Braje,
FIG.3. (Coloronline). (a)Plotofthemagneticfieldandgra-
andD.Englund,Nat.Phys.11,393(2015).
dient field sensitivity of the sensor at a bias field of 50 mG. 13G.Vasilakis,H.Shen,K.Jensen,M.Balabas,D.Salart,B.Chen,
The blue (magenta) dash line corresponds to the reference andE.S.Polzik,Nat.Phys.11,389(2015).
(sensing) cell result, and the black solid line is the difference 14R.Mhaskar,S.Knappe, andJ.Kitching,Appl.Phys.Lett.101,
of the two magnetometer results. (b) The averaged gradi- 241105(2012).
ent magnetic field sensitivity around 100 Hz at different bias 15T.Sander,J.Preusser,R.Mhaskar,J.Kitching,L.Trahms, and
fields. Black empty box (red solid line) is the experimental S.Knappe,Biomed.Opt.Express3,981(2012).
(fitting) result. 16S. Knappe, T. H. Sander, O. Kosch, F. Wiekhorst, J. Kitching,
andL.Trahms,Appl.Phys.Lett.97,133703(2010).
17P. D. Schwindt, S. Knappe, V. Shah, L. Hollberg, J. Kitching,
L.-A.Liew, andJ.Moreland,Appl.Phys.Lett.85,6409(2004).
gradientcancellationcoilstothesensor,itwouldbepos- 18W.HapperandH.Tang,Phys.Rev.Lett.31,273(1973).
sible to reduce the gradient field by another factor of 19J.C.Allred,R.N.Lyman,T.W.Kornack, andM.V.Romalis,
three, this would reduce the noise level at earth field to Phys.Rev.Lett.89,130801(2002).
be less than 100 fT/cm/Hz1/2, comparable to a recent 20C.Cohen-Tannoudji,J.Dupont-Roc,S.Haroche, andF.Lalo¨e,
Rev.Phys.Appl.5,95(1970).
result using a scalar gradiometer with a large compen- 21V.K.ShahandR.T.Wakai,Phys.Med.Bio.58,8153(2013).
sation coil system34. This could potentially lead to a 22C.Johnson,P.D.Schwindt, andM.Weisend,Appl.Phys.Lett.
compact biomagnetic imaging system in an unshielded 97,243703(2010).
environment. 23J. Preusser, S. Knappe, J. Kitching, and V. Gerginov, in 2009
IEEE International Frequency Control Symposium Joint with
Insummary, wehavedevelopedaminiaturizedatomic
the 22nd European Frequency and Time forum (IEEE, 2009)
magnetic gradiometer using vacuum-packaged chip-scale
pp.1180–1182.
cells. This gradiometer works with a single laser beam, 24S. Knappe, O. Alem, D. Sheng, and J. Kitching, in Journal of
andoperatesintheSERFregime. Itsheatingpowercon- Physics: Conference Series, Vol. 723 (IOP Publishing, 2016) p.
sumptionisdominatedbytheblack-bodyradiationfrom 012055.
25V.ShahandM.V.Romalis,Phys.Rev.A80,013416(2009).
the cells. This gradiometer shows a gradient field sensi-
26S. P. Krzyzewski, A. R. Perry, S. Geller, V. Gerginov, and S.
tivity of 5 fT/cm/Hz1/2 with a 20 mm baseline, and a Knappe,inpreparation.
maximum CMRR of 1000 within the sensor bandwidth. 27PreviouslyreportedCMRRofSERFgradiometersistypicallyin
By adding a set of coils around the sensor to cancel the therangeof10∼100.
28S.J.Seltzer,Ph.D.thesis,PrincetonUniversity(2008).
offset magnetic field, we test the sensor performance at
29Trade name is stated for technical clarity and does not imply
external bias fields up to 150 mG. We are working to
endorsementbyNIST.
improve the sensitivity of this system by one order of 30S. J. Seltzer and M. V. Romalis, Appl. Phys. Lett. 85, 4804
magnitude in an unshielded environment. This device is (2004).
useful for applications that require both sensitive gradi- 31J.Belfi,G.Bevilacqua,V.Biancalana,R.Cecchi,Y.Dancheva,
andL.Moi,Rev.Sci.Instrum.81,065103(2010).
ent field information and high CMRR.
32We use a Thorlabs LDC 205C current supply for the large
FundingfromNIHandNISTisacknowledged. Theau-
Helmholtz coil system, and a NIST home-built current source
thors thank Susan Schima for fabrication support. This for the small compensation coil system. The noise of Thorlabs
work is a contribution of NIST, an agency of U.S. Gov- currentsupplyisaboutoneorderofmagnitudehigherthanthat
ernment, and is not subject to copyright. oftheNISThome-builtcurrentsource.
33H.C.Torrey,Phys.Rev.104,563(1956).
1D. Budker and D. F. J. Kimball, Optical magnetometry (Cam- 34G. Bevilacqua, V. Biancalana, P. Chessa, and Y. Dancheva,
bridgeUniversityPress,2013). Appl.Phys.B122,1(2016).
