Hindawi Publishing CorporationThe Scientific World JournalVolume 2013 Article ID 858379 8 pageshttpdxdoiorg1011552013858379

Research ArticleHigh Sensitivity Optically Pumped Quantum Magnetometer

Valentina Tiporlini and Kamal Alameh

Electron Science Research Institute Edith Cowan University 270 Joondalup Drive Joondalup WA 6027 Australia

Correspondence should be addressed to Valentina Tiporlini vtiporl0ourecueduau

Received 12 April 2013 Accepted 2 May 2013

Academic Editors C Chen D Dong M Jiang and L-C Wang

Copyright copy 2013 V Tiporlini and K Alameh This is an open access article distributed under the Creative Commons AttributionLicense which permits unrestricted use distribution and reproduction in any medium provided the original work is properlycited

Quantummagnetometers based on optical pumping can achieve sensitivity as high as what SQUID-based devices can attain In thispaper we discuss the principle of operation and the optimal design of an optically pumped quantum magnetometer The ultimateintrinsic sensitivity is calculated showing that optimal performance of the magnetometer is attained with an optical pump powerof 20120583W and an operation temperature of 48∘C Results show that the ultimate intrinsic sensitivity of the quantummagnetometerthat can be achieved is 327 fTHz12 over a bandwidth of 26Hz and that this sensitivity drops to 130 pTHz12 in the presence ofenvironmental noise The quantum magnetometer is shown to be capable of detecting a sinusoidal magnetic field of amplitude aslow as 15 pT oscillating at 25Hz

1 Introduction

Optically pumped quantum magnetometers are based onthe use of the atomic-spin-dependent optical properties ofa medium The general principle of operation of opticallypumped quantum magnetometers is described in detail in[1] A circularly polarized laser light transmitted througha glass cell containing a vapor of alkali atoms (eg Cs)resonates when its frequency equals the first absorption lineof the alkali atoms thus creating a spin alignment thatprecesses with a frequency proportional to the modulus ofan externally applied magnetic field 119861

0(Larmor frequency

119908119871= 120574|119861

0|) If this precession is coherently driven by

an rf magnetic field 119861rf (oscillating at frequency 119908rf) theabsorption coefficient of the alkali medium changes thusmodulating the transmitted optical intensity By applying avery small oscillating magnetic field and maintaining thedriving rfmagnetic field resonant with the Larmor frequencythat is 119908rf = 119908119871 the very small oscillating magnetic fieldcan be determined Several optical magnetometers have beendeveloped demonstrating sensitivities as high as those ofsuperconducting quantum interference device- (SQUID-)based magnetometers However SQUID-based magnetome-tersmust be operated at very low temperatures thus requiringexpensive cooling mechanisms On the other hand opticalmagnetometers not only work at room temperature but also

have the potential of miniaturization making them morepractical for many applications [2 3]

The basic operation mode of optical magnetometersinvolves the following mechanisms Coherent PopulationTrapping (CPT) Nonlinear-Magneto Optical Rotation(NMOR) Spin-Exchange Relaxation Free (SERF) regimeand Mx magnetometer The CPT method is an all-opticaltechnique based on the use of two light sources (probe andpump) with orthogonal polarizations that create a couplingbetween two Zeeman sublevels located in different hyperfinestates When the modulation of the probe light is in reso-nance with the Zeeman splitting frequency ground sublevelsa decrement in the light intensity can be observed CPT-based magnetometers work in a scalar modeThe applicationof CPT-based magnetometers to cardiosignal detection hasbeen demonstrated showing a sensitivity of 1 pTHz12 in anunshielded environment [4]

The NMOR technique is based on the linear magnetooptical (Faraday) rotation principle When the light modifiesthe properties of the medium a nonlinear magneto opticalrotation occurs This happens when the light frequency isresonant with the atomic transitions of the medium thusallowing the optical absorption to take place The dynamicrange of an NMOR-based magnetometer is limited by thewidth of the resonance and the sensitivity that can be

2 The Scientific World Journal

obtained is around 015 pTHz12 [5] which is adequate forgeomagnetic measurements The magnetometers operatingin the SERF regime are also based on NMOR principleHowever such magnetometers have limited sensitivities dueto depolarization caused by various atoms interaction typesThe dominant type of these interactions is the spin-exchangecollisions that can change the hyperfine state of the atomswhile preserving the total angularmomentumof the collidingatom pair This results in a decoherent precession of theatom ensemble in the presence of a magnetic field whichmakes the measurement of the Larmor frequency difficultHowever decoherence due to spin-exchange collisions canbe completely eliminated if the spin-exchange collisionsoccur faster than the precession frequency of the atomsThis kind of optical magnetometers can reach a sensitivityof 054 fTHz12 [6] The Mx magnetometers are so calledbecause an rf oscillating magnetic field is supplied to theatoms to modulate the 119909-component of the magnetizationvector inside the vapor cell The phase difference betweenthe driving rf signal and the probe light transmitted throughthe vapor cell gives a direct measurement of the Larmorfrequency This kind of magnetometer is vastly used in mag-netocardiography and it can reach sensitivity of 99 fTHz12[7] Optical magnetometers based on CPT and SERF regimeoperate in zero-magnetic-fieldconditions while the othersrequire a weak magnetic field to induce Zeeman splittingBetween all the operation modes of optical magnetometersthe Mx configuration and SERF regime can achieve thehighest sensitivity An attractive feature of magnetometersworking in the SERF regime is that they do not need an rfmagnetic field or magnetic coils in the proximity of the vaporcell which could create crosstalk problems in array configu-rations On the other hand the SERF regime requires highertemperature to attain high sensitivity and only works in veryweakmagnetic fields because the frequency of collisionsmustbe higher than the Larmor frequency This makes the SERFregime much more susceptible to environmental noise

In this paper we describe the principle of operation of anMx-configuration-based optically pumped quantum magne-tometer and demonstrate experimentally the dependence ofits sensitivity and bandwidth upon the light power and thealkali vapor temperatureThepaper is organized as follows InSection 2 we explain the principle of operation of an opticalMx magnetometer In Section 3 the experimental setup isdescribed Finally in Section 4 we present and discuss theobtained experimental results

2 Atomic Mx Magnetometer

The generic configuration of an optical Mx magnetometer isshown in Figure 1 The core of the system is a glass cell filledwith the vapor of one of the alkali metals that have only oneelectron in their outermost shell Generally cesium is usedbecause it possesses only one stable isotope 133Cs with anuclear spin 119868 = 72

When a uniform dc external magnetic field is appliedeach hyperfine level of cesium atoms splits into 2119865+1Zeemansublevels as displayed in Figure 2 The light source is used

Uniform magnetic field z

x

Vapour cell

rf magnetic field

Light source

y

Figure 1The generic configuration of an opticalMxmagnetometerThe vapor cell contains alkali atoms such as Cs atoms

F = 4

F = 4

F = 3

F = 3

mF = minus4 minus3 minus2 minus1 0 +1 +2 +3 +4

Finestructure structure

Hyperfine Zeemansplitting

Opticalpumping

Dark states

120590+

62P12

62S12

Ground state

Excited state

D1120582 = 894nm

Figure 2 Fine hyperfine structures and Zeeman splitting of thecesium D1 line with the optical pumping process and the dark stateshighlighted

both for pumping theCs atoms to excited states and as a probesignal that senses an rf oscillating magnetic field modulatingthe absorption coefficient of the Cs atoms Photons havinga wavelength equal to the first absorption line of the alkaliatoms are absorbed by the cesium atoms thus moving themto the excited state Figure 2 shows the optical pumping overthe 119865 = 4 rarr 119865 = 3 transition of the cesium D1 absorptionline using right circularly polarized light which results inphotonrsquos angular momentum equal to +1 A Cs atom in thelower state with a quantum number 119898

119865is allowed to move

only to the upper level with 1198981015840119865

= 119898119865+ 1 because of

total angular momentum conservation A Cs atom that is inthe excited state can decay via one of three possible decaychannels and it spontaneously emits a photon that has equalprobability to be sent in any direction not necessary thedirection of light beamTherefore there is a finite probabilityfor the atom to decay into a level with a larger 119898

119865value

thus if the pumping process is repeated several times theatom moves to the two outermost states (119898

119865= 3 and 4) and

eventually can no longer be optically pumped because thereis not a corresponding state in the excited level available fortransition [8] Since these atoms do not absorb light they arecalled dark states

The Cs atoms in the dark states precess around the mag-netic field axis at the Larmor frequency that is proportional tothe field magnitude119908

119871= 120574|1198610| where 120574 is the gyromagnetic

constant that for cesium is 2120587 sdot 35HznT During this timethe atom spin accumulates an increasing phase angle

The Scientific World Journal 3

Waveform generator

LIA

rf driver

InRef

Out

Stabilized laser source

Optical Fiber

3D Helmholtzcoils system

rf coils

CollimatorQuarter-wave

plateCaesium

vapour cell

z

y

x

B

B

rf

(a)

Electromagnet system

Cesium vapor cell

Polarizationoptics

Photodetector

Waveformgenerator

Lock-in amplifier

Light sourceLaser

stabilization

(b)

Figure 3 (a) Block diagram and (b) photo of the experimental setup for demonstrating the concept of the optical Mx magnetometer

The spin state of an atom can be changed to an absorbing(nondark) state through the absorption of resonant radiofrequency radiation A change in the spin orientation causesa Cs atom to come out of the dark state into an absorbingstate Amplitude modulation of the transmitted light canbe achieved when a large fraction of the atoms precesscoherently in phase [9] To maintain this coherence andsynchronize the precession of atomic spins the rf drivingmagnetic field must be resonant with the Larmor frequencythat is 119908rf = 119908119871 The ensemble average of the magneticmoments associatedwith the spins can be treated as a classicalmagnetization vector 119872 The precession of 119872 around thetotal (dc and ac) magnetic field (119861tot = 1199111198610 + 119909119861rf cos (119908rf119905))is given by the Bloch equations [10]

(

119909

119910

119911

) = (

119872119909

119872119910

119872119911

)times(

120574119861rf cos119908rf1199050

1205741198610

)minus(

Γ2119872119909

Γ2119872119910

Γ1119872119911

) (1)

where Γ1and Γ

2are the longitudinal and the transverse

relaxation time respectively The calculated in-phase andquadrature amplitudes and the phase shift of light power withrespect to the driving rf magnetic field 119861rf are given by

119875ip (120575) = minus1198750 sin (2120579)Ωrf120575

Ω2rfΓ2Γ1 + Γ2

2

+ 1205752 (2)

119875qu (120575) = minus1198750 sin (2120579)ΩrfΓ2

Ω2rfΓ2Γ1 + Γ2

2

+ 1205752 (3)

120601 = arctan Γ2120575 (4)

where Ωrf = 120574 sdot 119908rf is the Rabi frequency 120575 = 119908rf minus 119908119871 is thefrequency detuning from the Larmor frequency and 120579 is theangle between the laser beam and 119861

0

Several important parameters can affect the magnetome-ter sensitivity namely the laser power the laser beam profilethe rf field power the cell size the buffer-gas pressure andthe density of Cs atoms (which depends on the temperature)Typically the magnetometer spatial resolution depends on

the cell dimensions In this paper we focus the investigationon the effects of optical power intensity and vapor celltemperature variations on the sensitivity and bandwidth ofthe optical Mx magnetometer

3 Experimental Setup

The Mx magnetometer used in the experiment is shown inFigures 3(a) and 3(b) The core of the instrument is a quartz-made cylindrical cell containing Cesium vapor Also Neon at34 Torr andArgon at 6 Torr are added to theCs vapor in orderto reduce atom collisions The cell diameter and length are21mm and 75mm respectively yielding a spatial resolutionof about 53mm In the experiments the gas pressure insidethe cell was increased by increasing the temperature usinghot water flowing into a silicon pipe wrapped around the cellThe vapor cell was placed in the center of an electromagnetthat generates a dc magnetic field in order to cancel thegeomagnetic field and supply a uniformmagnetization alongthe appropriate direction inside the vapor cell The usedelectromagnet consists of two parts (i) a 3D DC coilsof dimension 580mm times 530mm times 640mm providing amagnetic field with a uniformity better than 1 in the centralregion and (ii) an additional pair of coils that generate a small-magnitude rf magnetic field along the 119909-axis Each coil pairof the electromagnet was independently driven by a digitalpower supply to cancel the geomagnetic field along the 119909-and y-directions and generate a uniformmagnetic field alongthe 119911 axis The intensity of the magnetic field at the centerof the electromagnet was 13 120583T as measured by a three-axissmart digital magnetometer Honeywell HMR2300 The ACcoils were driven by a waveform generator (Agilent model33250A) to produce an rf magnetic field of intensity 200 nToscillating at 455 kHz along the x-axis

An external-cavity semiconductor laser (made by Uni-quanta Technology Beijing China) was used as light sourcefor both pumping and probing The laser wavelength wastuned to 894 nm which is equal the cesium D1 absorptionline 119865 = 4 rarr 119865 = 3 transition and stabilized usingsaturation spectroscopy in an auxiliary cell The frequencystabilized light was coupled into a single-mode polarization

4 The Scientific World Journal

maintaining optical fiber of 5 120583mcore diameter and deliveredto the vapor cell which was placed inside the electromagnetAt the cell location the light was collimated providingan output beam diameter of 16mm and right circularlypolarized using a half-wave plate an optical polarizer and aquarter-wave plate The laser beam was transmitted throughthe vapor cell at an angle of 45 degrees with respect to boththe 119911- and the 119909-axesThe output light beamwas focused intoa photodiode (PED801 from UniQuanta Technology) whichwas placed outside the electromagnet in order to reducethe magnetic interference produced by the transimpedanceamplifier of the photodiode package A spectrum analyzer(Agilent model E4407B) was used to measure the powerspectral density of the photodiode output in order to calculatethe signal-to-noise ratio and hence the intrinsic and actualsensitivity of the optical Mx magnetometer Finally a lock-in amplifier (Stanford Research Systems model SR530) wasused to measure the phase shift between the photocurrentdetected by the photodiode with respect to the oscillatingrf magnetic field and the in-phase component and thequadrature component Note that by sweeping the frequencyof the rf magnetic field along the Larmor frequency thehalf width at half maximum (HWHM) of the in-phase thequadrature and the phase signals could be measured

It is important tomention that all the experimental resultsreported below were performed in laboratory environmentwithout any magnetic shield The uniform magnetic fieldalong the 119911-axis was 13 120583T corresponding of a Larmorfrequency of 455 kHz It is also important to note thatwhen the measurements were carried out with differentuniform dc magnetic field intensities the performances ofthe magnetometer were not affected The intensity of the rfmagnetic field was 200 nT In the experiments the optical Mxmagnetometer was operated in free-running mode withoutthe use of a feedback loop between the lock-in amplifier andthe signal generator to lock the rf frequency to the Larmorfrequency Particularly the dependence of the sensitivityand the bandwidth of the optical Mx magnetometer on celltemperature and optical power was investigated for differentinput optical power levels over a cell temperature range of23∘C to 55∘C

4 Results and Discussion

41 Sensitivity The sensitivity of the optical Mxmagnetome-ter is defined as the smallest change in magnetic field thatcan be detected by the magnetometer The sensitivity can becalculated using the Cramer-Rao equation [11]

120588 =4radic3radic119891bw120574SNR

(5)

where 119891bw is the bandwidth 120574 is the gyromagnetic constantand SNR is the signal-to-noise ratio of the magnetometer Allthe following results refer to a 1Hz bandwidth

The SNR can be calculated from the measured powerspectral density (PSD) of the photodiode output as illus-trated in Figure 4 Since the magnetometer was operated

0 50 100minus50minus100

Relative frequency (Hz)

10minus4

10minus6PSD

(Vrm

sH

z12

)

SNintr SNact

Figure 4 Power spectral density of the photodiode output normal-ized to the resonance frequency The spectrum was measured ina 1Hz bandwidth The signal was recorded with optical power of20 120583Wand cell temperature of 50∘CThe intrinsic and actual signal-to-noise ratios are highlighted

in a magnetically-unshielded environment all the measure-ments were dominated by the magnetic field noise

The intrinsic signal-to-noise ratio was calculated with thenoise being the intrinsic rms noise of the magnetometermeasured over 100Hz from the resonance frequency Theactual signal-to-noise ratio was calculated by taking intoaccount the sidebands induced by the 50Hz magnetic noiseproduced by power lines Figure 5 shows the intrinsic SNR (a)and the intrinsic sensitivity (b) of the magnetometer versusthe cell temperature for different input optical power levels

The intrinsic SNR and hence the intrinsic sensitivitycurve exhibits a similar trend for all input optical powerlevels namely the SNR increases with increasing temper-ature reaching a maximum value around 50∘C before itstarts to decrease Moreover increasing the input opticalpower increases the intrinsic SNR and hence the intrinsicsensitivity In fact when the temperature increases the gaspressure inside the vapor cell increases resulting in a highernumber of atoms interacting with the light and coherentlyprecessing around the magnetic field at the Larmor fre-quency Furthermore increasing the input optical powerresults in a greater number of atoms being optically pumpedHowever when the gas pressure is too high the collisions ofatoms with each other or with the walls of the cell lead tophase incoherence during precession thus reducing the SNRperformance of the magnetometer The best performance ofthe magnetometer was obtained with an input optical powerof 20120583W and a cell temperature of 50∘C The measuredintrinsic SNR was 5000 and the intrinsic sensitivity was63 fTHz12 measured in a 1Hz bandwidth

To obtain the actual SNR and the actual sensitivity of themagnetometer the SNRwas calculated by taking into accountthe external magnetic noise Obviously the actual sensitivityis strongly dependent on the location of the magnetometerAll the experiments reported in this paper were performedin the laboratory environment without any magnetic shieldThis resulted in a very poor actual signal-to-noise ratioand hence a very low actual sensitivity Figures 6(a) and

The Scientific World Journal 5

30 40 50

SNR

LP = 10120583WLP = 15120583WLP = 20120583W

103

Temperature (∘C)

(a)

30 40 50

LP = 10120583WLP = 15120583WLP = 20120583W

Sens

itivi

ty (p

TH

z12

)

100

10minus1

Temperature (∘C)

(b)

Figure 5 (a) Intrinsic signal-to-noise ratio (SNR) and (b) intrinsic sensitivity measured in a 1Hz bandwidth versus cell temperature for inputoptical power of 10120583W 15120583W and 20120583W

30 40 50

SNR

LP = 10120583WLP = 15120583WLP = 20120583W

101

Temperature (∘C)

(a)

30 40 50

LP = 10120583WLP = 15120583WLP = 20120583W

Sens

itivi

ty (p

TH

z12

)

102

Temperature (∘C)

(b)

Figure 6 (a) Actual signal-to-noise ratio (SNR) and (b) actual sensitivity versus cell temperature measured in a 1Hz bandwidth for an inputoptical light power of 10 120583W 15120583W and 20 120583W

6 The Scientific World Journal

6(b) show the actual SNR and the actual sensitivity of themagnetometer respectively Also noticed in this case thatthe actual SNR increases (and hence the actual sensitivity isenhanced) with increasing the input optical power Howeverthe actual SNRdecreaseswith increasing the cell temperaturemainly because of the higher phase incoherence that reducesthe output signal level With an input optical power of 20 120583Wand a cell temperature of 50∘C the actual SNR dropped to116 and the actual sensitivity was 27 pTHz12 measured ina 1Hz bandwidth The best actual sensitivity was obtainedwith an input optical power of 20120583W at room temperature(23∘C)The corresponding actual SNRwas 145 and the actualsensitivity was 21 pTHz12 measured in a 1Hz bandwidth

42 Bandwidth Another important feature of a magnetome-ter is its bandwidth that is how fast the magnetometerresponds to changes in the magnetic field The bandwidth119891bw of the magnetometer can be calculated as [12]

119891bw =120587

2Δ] (6)

where Δ] is the half width at half maximum (HWHM) band-width of the phase signal measured in hertz as illustrated inFigure 7(c)

Figures 7(a) and 7(b) show respectively the in-phaseand quadrature components of the lock-in amplifier outputversus the normalized frequency predicted by (2) and (3)Figure 7(c) shows the phase shift between the photodiodeoutput and the driving rf magnetic field 119861rf predictedby (4) All signals in Figures 7(a)ndash7(c) were measuredin a magnetically unshielded environment by continuouslysweeping the driving rf frequency along the resonancefrequency over a 6-second time range It is important tonote that the magnetically induced 50Hz interference signalwas suppressed by a notch filter It is obvious from Figures7(a)ndash7(c) that the HWHM bandwidths of both the in-phasesignal Δ]

119883 and the quadrature signal Δ]

119884 are equal and

smaller than the HWHM bandwidth Δ] of the phase-shiftsignal This agrees with the theoretical prediction using (2)ndash(4) In fact the phase shift is the only signal that is notdependent on the rfmagnetic fieldTherefore for the accurateevaluation of the bandwidth of the magnetometer 119891bw itis important to use into (6) the HWHM bandwidth Δ]measured from the phase shift rather than the HWHMbandwidths Δ]

119883and Δ]

119884 measured from the in-phase and

quadrature components respectivelyFigure 8 shows the magnetometer bandwidth versus cell

temperature for input optical power levels of 10120583W 15 120583Wand 20120583W The bandwidth exhibits a similar trend for allinput optical power levels initially decreasingwith increasingthe cell temperature until reaching itsminimumaround45∘CSubsequently the bandwidth increaseswith increasing the celltemperatureThe bandwidth depends on the transverse relax-ation time Γ

2 as evident from (4) and (6) An increase in the

cell temperature increases the vapor pressure which resultsin a larger number of atoms interacting with the light leadingto a longer relaxation time (smaller bandwidth) However athigh temperature the number of collisions between atoms or

0 2 4 6

0

1

2

In-p

hase

com

pone

nt(m

V)

Normalized frequency (Hz)minus6 minus4 minus2

minus2

minus1

0

Max

ΔX

(a)

minus6 minus4 minus2 0 2 4 6

0

2

4

Qua

drat

ure c

ompo

nent

(mV

)

Normalized frequency (Hz)

MaxHalf max

ΔY

(b)

minus6 minus4 minus2 0 2 4 6minus200

minus150

minus100

minus50

0

Phas

e shi

ft (d

eg)

Normalized frequency (Hz)

Δ

minus45∘

minus90∘

(c)

Figure 7 Measured in-phase component (a) quadrature com-ponent (b) and phase shift (c) between the photo diode outputand the driving rf magnetic field All signals were measured in amagnetically unshielded environment by continuously sweeping thedriving rf frequency along the resonance frequency over a 6-secondtime range It is important to note that the magnetically induced50Hz interference signal was suppressed by a notch filter The inputoptical power was 20120583W and the vapor cell temperature 48∘C TheHWHM bandwidth is highlighted for each measured output signal

with the walls of the cell increases significantly leading to ashorter relaxation time and hence a larger bandwidth Thisexplains the existence of a critical temperature (around 45∘)at which the intrinsic bandwidth is minimum

In the experiments the measured maximum bandwidthwas 175Hz obtained at room temperature (23∘C) with aninput optical power of 10120583W (blue curve in Figure 8) whilethe minimum bandwidth was 25Hz obtained with an inputoptical power of 20120583Wat a temperature of 45∘C (black curvein Figure 8)

43 Low-Amplitude Magnetic Field Measurement The ulti-mate intrinsic sensitivity of the magnetometer can be calcu-lated using (5) The best performance of the magnetometerwas obtained for an input optical power of 20120583W at celltemperature of 48∘C the ultimate intrinsic sensitivity was327 fTHz12 over a bandwidth of 26Hz However the exter-nalmagnetic noise generated by power lines and surroundingequipment caused the actual ultimate sensitivity of the

The Scientific World Journal 7

25 30 35 40 45 50 5520

40

60

80

100

120

140

160

180

(Hz)

LP = 10120583WLP = 15120583WLP = 20120583W

Temperature (∘C)

Figure 8 Intrinsic bandwidth versus cell temperature for an inputoptical light power of 10 120583W 15120583W and 20 120583W

0 01 02 03 04 05150

155

160

165

170

175

180

185

Mag

netic

fiel

d (p

T)

Time (s)

Figure 9Measured 15 pTpeak oscillating field at frequency of 25Hzfiltered with a low-pass filter with cutoff frequency of 50Hz

magnetometer to drop to 130 pTHz12 over a bandwidth of26Hz

The magnetometer in its optimal configuration (inputoptical power of 20120583W at cell temperature of 48∘C) wasthen used to measure an applied small-signal sinusoidalmagnetic field of amplitude 15 pT oscillating at 25Hz whichwas generated by a test coil placed at a distance of 6 cmfrom the vapor cell For this measurement the uniformdc magnetic field was 13120583T corresponding to a Larmorfrequency of 455 kHz The frequency of the rf magnetic fieldwas then set at 455 kHz resulting in a phase shift of minus90degrees between the photodiode output and the driving rfsignal as predicted by (4) and verified experimentally bythe result shown in Figure 7(c) When another 25Hz small-amplitude magnetic field was applied in addition to the dcand rf magnetic fields the Larmor frequency changed andnomore resonance occurred causing the phase shift betweenthe photodiode output and the driving rf signal to oscillatearound minus90 degrees at 25Hz This enabled the measurementof the new Larmor frequency and hence the calculation of

the magnitude of the 25Hz small-amplitude magnetic fieldwhich is proportional to the new Larmor frequency

Figure 9 shows the magnetic field calculated from themeasurement of the Larmor frequency after a 25Hz 15 pTmagnetic field was applied A lowpass filter of a cutoff fre-quency of 50Hz was used after the lock-in amplifier in orderto remove the power line noise (at 50Hz and its harmonics) aswell as all high frequencies noise It is obvious from Figure 9that the small-signal 25Hz magnetic field could be recovered(peak-to-peak magnitude is around 33 pT) demonstratingthe capability of the optical Mx magnetometer to measureultra-low-amplitude magnetic fields

5 Conclusion

An optically pumped quantum magnetometer on Mx con-figuration has been developed and its capability to measureultra-low-amplitude magnetic fields has been experimentallydemonstrated A high intrinsic sensitivity of 63 fTHz12measured in a 1Hz bandwidth has been achieved with aninput optical power of 20120583W at a vapor cell temperature of50∘C Experimental results have shown that the environmen-tal noise can significantly drop the magnetometer sensitivityby several orders of magnitude to as low as 27 pTHz12 Ahigh actual sensitivity of 21 pTHz12 has been attained withan input optical power of 20120583W at room temperature Themeasured bandwidth of the magnetometer has been shownto vary between 100Hz at room temperature and 25Hz at45∘C Experimental results have also shown that the ultimatebest intrinsic sensitivity (327 fTHz12) calculated over themeasured bandwidth (26Hz) can be attained with an inputoptical power of 20 120583W at a vapor cell temperature of 48∘Cand that the environmental noise reduces this sensitivityto 130 pTHz12 Finally the ability of the magnetometer todetect a 25Hz sinusoidal magnetic field of amplitude as lowas 15 pT has experimentally been demonstrated

References

[1] D Budker and M Romalis ldquoOptical magnetometryrdquo NaturePhysics vol 3 no 4 pp 227ndash234 2007

[2] V Shah S Knappe P D D Schwindt and J Kitching ldquoSub-picotesla atomic magnetometry with a microfabricated vapourcellrdquo Nature Photonics vol 1 no 11 pp 649ndash652 2007

[3] L A Liew S Knappe J Moreland H Robinson L Hollbergand J Kitching ldquoMicrofabricated alkali atom vapor cellsrdquoApplied Physics Letters vol 84 no 14 pp 2694ndash2696 2004

[4] J Belfi G Bevilacqua V Biancalana S Cartaleva Y DanchevaandLMoi ldquoCesiumcoherent population trappingmagnetome-ter for cardiosignal detection in an unshielded environmentrdquoJournal of the Optical Society of America B vol 24 no 9 pp2357ndash2362 2007

[5] P D D Schwindt L Hollberg and J Kitching ldquoSelf-oscillatingrubidiummagnetometer using nonlinearmagneto-optical rota-tionrdquo Review of Scientific Instruments vol 76 no 12 Article ID126103 pp 1ndash4 2005

[6] I K Kominis T W Kornack J C Allred and M V RomalisldquoA subfemtotesla multichannel atomic magnetometerrdquo Naturevol 422 no 6932 pp 596ndash599 2003

8 The Scientific World Journal

[7] G Bison R Wynands and A Weis ldquoA laser-pumped mag-netometer for the mapping of human cardiomagnetic fieldsrdquoApplied Physics B vol 76 no 3 pp 325ndash328 2003

[8] D Budker D F Kimball and D P DeMille Atomic Physics AnExplorationThrough Problems and Solutions Oxford UniversityPress New York NY USA 2004

[9] W E Bell and A L Bloom ldquoOptically driven spin precessionrdquoPhysical Review Letters vol 6 no 6 pp 280ndash281 1961

[10] F Bloch ldquoNuclear inductionrdquo Physical Review vol 70 no 7-8pp 460ndash474 1946

[11] D C Rife andR R Boorstyn ldquoSingle tone parameter estimationfrom discrete-time observationsrdquo IEEE Transactions on Infor-mation Theory vol 20 no 5 pp 591ndash598 1974

[12] G Bison R Wynands and A Weis ldquoOptimization and perfor-mance of an optical cardiomagnetometerrdquo Journal of the OpticalSociety of America B vol 22 no 1 pp 77ndash87 2005

The Scientific World Journal 3

Waveform generator

LIA

rf driver

InRef

Out

Stabilized laser source

Optical Fiber

3D Helmholtzcoils system

rf coils

CollimatorQuarter-wave

plateCaesium

vapour cell

z

y

x

B

B

rf

(a)

Electromagnet system

Cesium vapor cell

Polarizationoptics

Photodetector

Waveformgenerator

Lock-in amplifier

Light sourceLaser

stabilization

(b)

Figure 3 (a) Block diagram and (b) photo of the experimental setup for demonstrating the concept of the optical Mx magnetometer

The spin state of an atom can be changed to an absorbing(nondark) state through the absorption of resonant radiofrequency radiation A change in the spin orientation causesa Cs atom to come out of the dark state into an absorbingstate Amplitude modulation of the transmitted light canbe achieved when a large fraction of the atoms precesscoherently in phase [9] To maintain this coherence andsynchronize the precession of atomic spins the rf drivingmagnetic field must be resonant with the Larmor frequencythat is 119908rf = 119908119871 The ensemble average of the magneticmoments associatedwith the spins can be treated as a classicalmagnetization vector 119872 The precession of 119872 around thetotal (dc and ac) magnetic field (119861tot = 1199111198610 + 119909119861rf cos (119908rf119905))is given by the Bloch equations [10]

(

119909

119910

119911

) = (

119872119909

119872119910

119872119911

)times(

120574119861rf cos119908rf1199050

1205741198610

)minus(

Γ2119872119909

Γ2119872119910

Γ1119872119911

) (1)

where Γ1and Γ

2are the longitudinal and the transverse

relaxation time respectively The calculated in-phase andquadrature amplitudes and the phase shift of light power withrespect to the driving rf magnetic field 119861rf are given by

119875ip (120575) = minus1198750 sin (2120579)Ωrf120575

Ω2rfΓ2Γ1 + Γ2

2

+ 1205752 (2)

119875qu (120575) = minus1198750 sin (2120579)ΩrfΓ2

Ω2rfΓ2Γ1 + Γ2

2

+ 1205752 (3)

120601 = arctan Γ2120575 (4)

where Ωrf = 120574 sdot 119908rf is the Rabi frequency 120575 = 119908rf minus 119908119871 is thefrequency detuning from the Larmor frequency and 120579 is theangle between the laser beam and 119861

0

Several important parameters can affect the magnetome-ter sensitivity namely the laser power the laser beam profilethe rf field power the cell size the buffer-gas pressure andthe density of Cs atoms (which depends on the temperature)Typically the magnetometer spatial resolution depends on

the cell dimensions In this paper we focus the investigationon the effects of optical power intensity and vapor celltemperature variations on the sensitivity and bandwidth ofthe optical Mx magnetometer

3 Experimental Setup

The Mx magnetometer used in the experiment is shown inFigures 3(a) and 3(b) The core of the instrument is a quartz-made cylindrical cell containing Cesium vapor Also Neon at34 Torr andArgon at 6 Torr are added to theCs vapor in orderto reduce atom collisions The cell diameter and length are21mm and 75mm respectively yielding a spatial resolutionof about 53mm In the experiments the gas pressure insidethe cell was increased by increasing the temperature usinghot water flowing into a silicon pipe wrapped around the cellThe vapor cell was placed in the center of an electromagnetthat generates a dc magnetic field in order to cancel thegeomagnetic field and supply a uniformmagnetization alongthe appropriate direction inside the vapor cell The usedelectromagnet consists of two parts (i) a 3D DC coilsof dimension 580mm times 530mm times 640mm providing amagnetic field with a uniformity better than 1 in the centralregion and (ii) an additional pair of coils that generate a small-magnitude rf magnetic field along the 119909-axis Each coil pairof the electromagnet was independently driven by a digitalpower supply to cancel the geomagnetic field along the 119909-and y-directions and generate a uniformmagnetic field alongthe 119911 axis The intensity of the magnetic field at the centerof the electromagnet was 13 120583T as measured by a three-axissmart digital magnetometer Honeywell HMR2300 The ACcoils were driven by a waveform generator (Agilent model33250A) to produce an rf magnetic field of intensity 200 nToscillating at 455 kHz along the x-axis

An external-cavity semiconductor laser (made by Uni-quanta Technology Beijing China) was used as light sourcefor both pumping and probing The laser wavelength wastuned to 894 nm which is equal the cesium D1 absorptionline 119865 = 4 rarr 119865 = 3 transition and stabilized usingsaturation spectroscopy in an auxiliary cell The frequencystabilized light was coupled into a single-mode polarization

4 The Scientific World Journal

maintaining optical fiber of 5 120583mcore diameter and deliveredto the vapor cell which was placed inside the electromagnetAt the cell location the light was collimated providingan output beam diameter of 16mm and right circularlypolarized using a half-wave plate an optical polarizer and aquarter-wave plate The laser beam was transmitted throughthe vapor cell at an angle of 45 degrees with respect to boththe 119911- and the 119909-axesThe output light beamwas focused intoa photodiode (PED801 from UniQuanta Technology) whichwas placed outside the electromagnet in order to reducethe magnetic interference produced by the transimpedanceamplifier of the photodiode package A spectrum analyzer(Agilent model E4407B) was used to measure the powerspectral density of the photodiode output in order to calculatethe signal-to-noise ratio and hence the intrinsic and actualsensitivity of the optical Mx magnetometer Finally a lock-in amplifier (Stanford Research Systems model SR530) wasused to measure the phase shift between the photocurrentdetected by the photodiode with respect to the oscillatingrf magnetic field and the in-phase component and thequadrature component Note that by sweeping the frequencyof the rf magnetic field along the Larmor frequency thehalf width at half maximum (HWHM) of the in-phase thequadrature and the phase signals could be measured

It is important tomention that all the experimental resultsreported below were performed in laboratory environmentwithout any magnetic shield The uniform magnetic fieldalong the 119911-axis was 13 120583T corresponding of a Larmorfrequency of 455 kHz It is also important to note thatwhen the measurements were carried out with differentuniform dc magnetic field intensities the performances ofthe magnetometer were not affected The intensity of the rfmagnetic field was 200 nT In the experiments the optical Mxmagnetometer was operated in free-running mode withoutthe use of a feedback loop between the lock-in amplifier andthe signal generator to lock the rf frequency to the Larmorfrequency Particularly the dependence of the sensitivityand the bandwidth of the optical Mx magnetometer on celltemperature and optical power was investigated for differentinput optical power levels over a cell temperature range of23∘C to 55∘C

4 Results and Discussion

41 Sensitivity The sensitivity of the optical Mxmagnetome-ter is defined as the smallest change in magnetic field thatcan be detected by the magnetometer The sensitivity can becalculated using the Cramer-Rao equation [11]

120588 =4radic3radic119891bw120574SNR

(5)

where 119891bw is the bandwidth 120574 is the gyromagnetic constantand SNR is the signal-to-noise ratio of the magnetometer Allthe following results refer to a 1Hz bandwidth

The SNR can be calculated from the measured powerspectral density (PSD) of the photodiode output as illus-trated in Figure 4 Since the magnetometer was operated

0 50 100minus50minus100

Relative frequency (Hz)

10minus4

10minus6PSD

(Vrm

sH

z12

)

SNintr SNact

Figure 4 Power spectral density of the photodiode output normal-ized to the resonance frequency The spectrum was measured ina 1Hz bandwidth The signal was recorded with optical power of20 120583Wand cell temperature of 50∘CThe intrinsic and actual signal-to-noise ratios are highlighted

in a magnetically-unshielded environment all the measure-ments were dominated by the magnetic field noise

The intrinsic signal-to-noise ratio was calculated with thenoise being the intrinsic rms noise of the magnetometermeasured over 100Hz from the resonance frequency Theactual signal-to-noise ratio was calculated by taking intoaccount the sidebands induced by the 50Hz magnetic noiseproduced by power lines Figure 5 shows the intrinsic SNR (a)and the intrinsic sensitivity (b) of the magnetometer versusthe cell temperature for different input optical power levels

The intrinsic SNR and hence the intrinsic sensitivitycurve exhibits a similar trend for all input optical powerlevels namely the SNR increases with increasing temper-ature reaching a maximum value around 50∘C before itstarts to decrease Moreover increasing the input opticalpower increases the intrinsic SNR and hence the intrinsicsensitivity In fact when the temperature increases the gaspressure inside the vapor cell increases resulting in a highernumber of atoms interacting with the light and coherentlyprecessing around the magnetic field at the Larmor fre-quency Furthermore increasing the input optical powerresults in a greater number of atoms being optically pumpedHowever when the gas pressure is too high the collisions ofatoms with each other or with the walls of the cell lead tophase incoherence during precession thus reducing the SNRperformance of the magnetometer The best performance ofthe magnetometer was obtained with an input optical powerof 20120583W and a cell temperature of 50∘C The measuredintrinsic SNR was 5000 and the intrinsic sensitivity was63 fTHz12 measured in a 1Hz bandwidth

To obtain the actual SNR and the actual sensitivity of themagnetometer the SNRwas calculated by taking into accountthe external magnetic noise Obviously the actual sensitivityis strongly dependent on the location of the magnetometerAll the experiments reported in this paper were performedin the laboratory environment without any magnetic shieldThis resulted in a very poor actual signal-to-noise ratioand hence a very low actual sensitivity Figures 6(a) and

The Scientific World Journal 5

30 40 50

SNR

LP = 10120583WLP = 15120583WLP = 20120583W

103

Temperature (∘C)

(a)

30 40 50

LP = 10120583WLP = 15120583WLP = 20120583W

Sens

itivi

ty (p

TH

z12

)

100

10minus1

Temperature (∘C)

(b)

Figure 5 (a) Intrinsic signal-to-noise ratio (SNR) and (b) intrinsic sensitivity measured in a 1Hz bandwidth versus cell temperature for inputoptical power of 10120583W 15120583W and 20120583W

30 40 50

SNR

LP = 10120583WLP = 15120583WLP = 20120583W

101

Temperature (∘C)

(a)

30 40 50

LP = 10120583WLP = 15120583WLP = 20120583W

Sens

itivi

ty (p

TH

z12

)

102

Temperature (∘C)

(b)

Figure 6 (a) Actual signal-to-noise ratio (SNR) and (b) actual sensitivity versus cell temperature measured in a 1Hz bandwidth for an inputoptical light power of 10 120583W 15120583W and 20 120583W

6 The Scientific World Journal

6(b) show the actual SNR and the actual sensitivity of themagnetometer respectively Also noticed in this case thatthe actual SNR increases (and hence the actual sensitivity isenhanced) with increasing the input optical power Howeverthe actual SNRdecreaseswith increasing the cell temperaturemainly because of the higher phase incoherence that reducesthe output signal level With an input optical power of 20 120583Wand a cell temperature of 50∘C the actual SNR dropped to116 and the actual sensitivity was 27 pTHz12 measured ina 1Hz bandwidth The best actual sensitivity was obtainedwith an input optical power of 20120583W at room temperature(23∘C)The corresponding actual SNRwas 145 and the actualsensitivity was 21 pTHz12 measured in a 1Hz bandwidth

42 Bandwidth Another important feature of a magnetome-ter is its bandwidth that is how fast the magnetometerresponds to changes in the magnetic field The bandwidth119891bw of the magnetometer can be calculated as [12]

119891bw =120587

2Δ] (6)

where Δ] is the half width at half maximum (HWHM) band-width of the phase signal measured in hertz as illustrated inFigure 7(c)

Figures 7(a) and 7(b) show respectively the in-phaseand quadrature components of the lock-in amplifier outputversus the normalized frequency predicted by (2) and (3)Figure 7(c) shows the phase shift between the photodiodeoutput and the driving rf magnetic field 119861rf predictedby (4) All signals in Figures 7(a)ndash7(c) were measuredin a magnetically unshielded environment by continuouslysweeping the driving rf frequency along the resonancefrequency over a 6-second time range It is important tonote that the magnetically induced 50Hz interference signalwas suppressed by a notch filter It is obvious from Figures7(a)ndash7(c) that the HWHM bandwidths of both the in-phasesignal Δ]

119883 and the quadrature signal Δ]

119884 are equal and

smaller than the HWHM bandwidth Δ] of the phase-shiftsignal This agrees with the theoretical prediction using (2)ndash(4) In fact the phase shift is the only signal that is notdependent on the rfmagnetic fieldTherefore for the accurateevaluation of the bandwidth of the magnetometer 119891bw itis important to use into (6) the HWHM bandwidth Δ]measured from the phase shift rather than the HWHMbandwidths Δ]

119883and Δ]

119884 measured from the in-phase and

quadrature components respectivelyFigure 8 shows the magnetometer bandwidth versus cell

temperature for input optical power levels of 10120583W 15 120583Wand 20120583W The bandwidth exhibits a similar trend for allinput optical power levels initially decreasingwith increasingthe cell temperature until reaching itsminimumaround45∘CSubsequently the bandwidth increaseswith increasing the celltemperatureThe bandwidth depends on the transverse relax-ation time Γ

2 as evident from (4) and (6) An increase in the

cell temperature increases the vapor pressure which resultsin a larger number of atoms interacting with the light leadingto a longer relaxation time (smaller bandwidth) However athigh temperature the number of collisions between atoms or

0 2 4 6

0

1

2

In-p

hase

com

pone

nt(m

V)

Normalized frequency (Hz)minus6 minus4 minus2

minus2

minus1

0

Max

ΔX

(a)

minus6 minus4 minus2 0 2 4 6

0

2

4

Qua

drat

ure c

ompo

nent

(mV

)

Normalized frequency (Hz)

MaxHalf max

ΔY

(b)

minus6 minus4 minus2 0 2 4 6minus200

minus150

minus100

minus50

0

Phas

e shi

ft (d

eg)

Normalized frequency (Hz)

Δ

minus45∘

minus90∘

(c)

Figure 7 Measured in-phase component (a) quadrature com-ponent (b) and phase shift (c) between the photo diode outputand the driving rf magnetic field All signals were measured in amagnetically unshielded environment by continuously sweeping thedriving rf frequency along the resonance frequency over a 6-secondtime range It is important to note that the magnetically induced50Hz interference signal was suppressed by a notch filter The inputoptical power was 20120583W and the vapor cell temperature 48∘C TheHWHM bandwidth is highlighted for each measured output signal

with the walls of the cell increases significantly leading to ashorter relaxation time and hence a larger bandwidth Thisexplains the existence of a critical temperature (around 45∘)at which the intrinsic bandwidth is minimum

In the experiments the measured maximum bandwidthwas 175Hz obtained at room temperature (23∘C) with aninput optical power of 10120583W (blue curve in Figure 8) whilethe minimum bandwidth was 25Hz obtained with an inputoptical power of 20120583Wat a temperature of 45∘C (black curvein Figure 8)

43 Low-Amplitude Magnetic Field Measurement The ulti-mate intrinsic sensitivity of the magnetometer can be calcu-lated using (5) The best performance of the magnetometerwas obtained for an input optical power of 20120583W at celltemperature of 48∘C the ultimate intrinsic sensitivity was327 fTHz12 over a bandwidth of 26Hz However the exter-nalmagnetic noise generated by power lines and surroundingequipment caused the actual ultimate sensitivity of the

The Scientific World Journal 7

25 30 35 40 45 50 5520

40

60

80

100

120

140

160

180

(Hz)

LP = 10120583WLP = 15120583WLP = 20120583W

Temperature (∘C)

Figure 8 Intrinsic bandwidth versus cell temperature for an inputoptical light power of 10 120583W 15120583W and 20 120583W

0 01 02 03 04 05150

155

160

165

170

175

180

185

Mag

netic

fiel

d (p

T)

Time (s)

Figure 9Measured 15 pTpeak oscillating field at frequency of 25Hzfiltered with a low-pass filter with cutoff frequency of 50Hz

magnetometer to drop to 130 pTHz12 over a bandwidth of26Hz

The magnetometer in its optimal configuration (inputoptical power of 20120583W at cell temperature of 48∘C) wasthen used to measure an applied small-signal sinusoidalmagnetic field of amplitude 15 pT oscillating at 25Hz whichwas generated by a test coil placed at a distance of 6 cmfrom the vapor cell For this measurement the uniformdc magnetic field was 13120583T corresponding to a Larmorfrequency of 455 kHz The frequency of the rf magnetic fieldwas then set at 455 kHz resulting in a phase shift of minus90degrees between the photodiode output and the driving rfsignal as predicted by (4) and verified experimentally bythe result shown in Figure 7(c) When another 25Hz small-amplitude magnetic field was applied in addition to the dcand rf magnetic fields the Larmor frequency changed andnomore resonance occurred causing the phase shift betweenthe photodiode output and the driving rf signal to oscillatearound minus90 degrees at 25Hz This enabled the measurementof the new Larmor frequency and hence the calculation of

the magnitude of the 25Hz small-amplitude magnetic fieldwhich is proportional to the new Larmor frequency

Figure 9 shows the magnetic field calculated from themeasurement of the Larmor frequency after a 25Hz 15 pTmagnetic field was applied A lowpass filter of a cutoff fre-quency of 50Hz was used after the lock-in amplifier in orderto remove the power line noise (at 50Hz and its harmonics) aswell as all high frequencies noise It is obvious from Figure 9that the small-signal 25Hz magnetic field could be recovered(peak-to-peak magnitude is around 33 pT) demonstratingthe capability of the optical Mx magnetometer to measureultra-low-amplitude magnetic fields

5 Conclusion

An optically pumped quantum magnetometer on Mx con-figuration has been developed and its capability to measureultra-low-amplitude magnetic fields has been experimentallydemonstrated A high intrinsic sensitivity of 63 fTHz12measured in a 1Hz bandwidth has been achieved with aninput optical power of 20120583W at a vapor cell temperature of50∘C Experimental results have shown that the environmen-tal noise can significantly drop the magnetometer sensitivityby several orders of magnitude to as low as 27 pTHz12 Ahigh actual sensitivity of 21 pTHz12 has been attained withan input optical power of 20120583W at room temperature Themeasured bandwidth of the magnetometer has been shownto vary between 100Hz at room temperature and 25Hz at45∘C Experimental results have also shown that the ultimatebest intrinsic sensitivity (327 fTHz12) calculated over themeasured bandwidth (26Hz) can be attained with an inputoptical power of 20 120583W at a vapor cell temperature of 48∘Cand that the environmental noise reduces this sensitivityto 130 pTHz12 Finally the ability of the magnetometer todetect a 25Hz sinusoidal magnetic field of amplitude as lowas 15 pT has experimentally been demonstrated

References

[1] D Budker and M Romalis ldquoOptical magnetometryrdquo NaturePhysics vol 3 no 4 pp 227ndash234 2007

[2] V Shah S Knappe P D D Schwindt and J Kitching ldquoSub-picotesla atomic magnetometry with a microfabricated vapourcellrdquo Nature Photonics vol 1 no 11 pp 649ndash652 2007

[3] L A Liew S Knappe J Moreland H Robinson L Hollbergand J Kitching ldquoMicrofabricated alkali atom vapor cellsrdquoApplied Physics Letters vol 84 no 14 pp 2694ndash2696 2004

[4] J Belfi G Bevilacqua V Biancalana S Cartaleva Y DanchevaandLMoi ldquoCesiumcoherent population trappingmagnetome-ter for cardiosignal detection in an unshielded environmentrdquoJournal of the Optical Society of America B vol 24 no 9 pp2357ndash2362 2007

[5] P D D Schwindt L Hollberg and J Kitching ldquoSelf-oscillatingrubidiummagnetometer using nonlinearmagneto-optical rota-tionrdquo Review of Scientific Instruments vol 76 no 12 Article ID126103 pp 1ndash4 2005

[6] I K Kominis T W Kornack J C Allred and M V RomalisldquoA subfemtotesla multichannel atomic magnetometerrdquo Naturevol 422 no 6932 pp 596ndash599 2003

8 The Scientific World Journal

[7] G Bison R Wynands and A Weis ldquoA laser-pumped mag-netometer for the mapping of human cardiomagnetic fieldsrdquoApplied Physics B vol 76 no 3 pp 325ndash328 2003

[8] D Budker D F Kimball and D P DeMille Atomic Physics AnExplorationThrough Problems and Solutions Oxford UniversityPress New York NY USA 2004

[9] W E Bell and A L Bloom ldquoOptically driven spin precessionrdquoPhysical Review Letters vol 6 no 6 pp 280ndash281 1961

[10] F Bloch ldquoNuclear inductionrdquo Physical Review vol 70 no 7-8pp 460ndash474 1946

[11] D C Rife andR R Boorstyn ldquoSingle tone parameter estimationfrom discrete-time observationsrdquo IEEE Transactions on Infor-mation Theory vol 20 no 5 pp 591ndash598 1974

[12] G Bison R Wynands and A Weis ldquoOptimization and perfor-mance of an optical cardiomagnetometerrdquo Journal of the OpticalSociety of America B vol 22 no 1 pp 77ndash87 2005

4 The Scientific World Journal

maintaining optical fiber of 5 120583mcore diameter and deliveredto the vapor cell which was placed inside the electromagnetAt the cell location the light was collimated providingan output beam diameter of 16mm and right circularlypolarized using a half-wave plate an optical polarizer and aquarter-wave plate The laser beam was transmitted throughthe vapor cell at an angle of 45 degrees with respect to boththe 119911- and the 119909-axesThe output light beamwas focused intoa photodiode (PED801 from UniQuanta Technology) whichwas placed outside the electromagnet in order to reducethe magnetic interference produced by the transimpedanceamplifier of the photodiode package A spectrum analyzer(Agilent model E4407B) was used to measure the powerspectral density of the photodiode output in order to calculatethe signal-to-noise ratio and hence the intrinsic and actualsensitivity of the optical Mx magnetometer Finally a lock-in amplifier (Stanford Research Systems model SR530) wasused to measure the phase shift between the photocurrentdetected by the photodiode with respect to the oscillatingrf magnetic field and the in-phase component and thequadrature component Note that by sweeping the frequencyof the rf magnetic field along the Larmor frequency thehalf width at half maximum (HWHM) of the in-phase thequadrature and the phase signals could be measured

It is important tomention that all the experimental resultsreported below were performed in laboratory environmentwithout any magnetic shield The uniform magnetic fieldalong the 119911-axis was 13 120583T corresponding of a Larmorfrequency of 455 kHz It is also important to note thatwhen the measurements were carried out with differentuniform dc magnetic field intensities the performances ofthe magnetometer were not affected The intensity of the rfmagnetic field was 200 nT In the experiments the optical Mxmagnetometer was operated in free-running mode withoutthe use of a feedback loop between the lock-in amplifier andthe signal generator to lock the rf frequency to the Larmorfrequency Particularly the dependence of the sensitivityand the bandwidth of the optical Mx magnetometer on celltemperature and optical power was investigated for differentinput optical power levels over a cell temperature range of23∘C to 55∘C

4 Results and Discussion

41 Sensitivity The sensitivity of the optical Mxmagnetome-ter is defined as the smallest change in magnetic field thatcan be detected by the magnetometer The sensitivity can becalculated using the Cramer-Rao equation [11]

120588 =4radic3radic119891bw120574SNR

(5)

where 119891bw is the bandwidth 120574 is the gyromagnetic constantand SNR is the signal-to-noise ratio of the magnetometer Allthe following results refer to a 1Hz bandwidth

The SNR can be calculated from the measured powerspectral density (PSD) of the photodiode output as illus-trated in Figure 4 Since the magnetometer was operated

0 50 100minus50minus100

Relative frequency (Hz)

10minus4

10minus6PSD

(Vrm

sH

z12

)

SNintr SNact

Figure 4 Power spectral density of the photodiode output normal-ized to the resonance frequency The spectrum was measured ina 1Hz bandwidth The signal was recorded with optical power of20 120583Wand cell temperature of 50∘CThe intrinsic and actual signal-to-noise ratios are highlighted

in a magnetically-unshielded environment all the measure-ments were dominated by the magnetic field noise

The intrinsic signal-to-noise ratio was calculated with thenoise being the intrinsic rms noise of the magnetometermeasured over 100Hz from the resonance frequency Theactual signal-to-noise ratio was calculated by taking intoaccount the sidebands induced by the 50Hz magnetic noiseproduced by power lines Figure 5 shows the intrinsic SNR (a)and the intrinsic sensitivity (b) of the magnetometer versusthe cell temperature for different input optical power levels

The intrinsic SNR and hence the intrinsic sensitivitycurve exhibits a similar trend for all input optical powerlevels namely the SNR increases with increasing temper-ature reaching a maximum value around 50∘C before itstarts to decrease Moreover increasing the input opticalpower increases the intrinsic SNR and hence the intrinsicsensitivity In fact when the temperature increases the gaspressure inside the vapor cell increases resulting in a highernumber of atoms interacting with the light and coherentlyprecessing around the magnetic field at the Larmor fre-quency Furthermore increasing the input optical powerresults in a greater number of atoms being optically pumpedHowever when the gas pressure is too high the collisions ofatoms with each other or with the walls of the cell lead tophase incoherence during precession thus reducing the SNRperformance of the magnetometer The best performance ofthe magnetometer was obtained with an input optical powerof 20120583W and a cell temperature of 50∘C The measuredintrinsic SNR was 5000 and the intrinsic sensitivity was63 fTHz12 measured in a 1Hz bandwidth

To obtain the actual SNR and the actual sensitivity of themagnetometer the SNRwas calculated by taking into accountthe external magnetic noise Obviously the actual sensitivityis strongly dependent on the location of the magnetometerAll the experiments reported in this paper were performedin the laboratory environment without any magnetic shieldThis resulted in a very poor actual signal-to-noise ratioand hence a very low actual sensitivity Figures 6(a) and

The Scientific World Journal 5

30 40 50

SNR

LP = 10120583WLP = 15120583WLP = 20120583W

103

Temperature (∘C)

(a)

30 40 50

LP = 10120583WLP = 15120583WLP = 20120583W

Sens

itivi

ty (p

TH

z12

)

100

10minus1

Temperature (∘C)

(b)

Figure 5 (a) Intrinsic signal-to-noise ratio (SNR) and (b) intrinsic sensitivity measured in a 1Hz bandwidth versus cell temperature for inputoptical power of 10120583W 15120583W and 20120583W

30 40 50

SNR

LP = 10120583WLP = 15120583WLP = 20120583W

101

Temperature (∘C)

(a)

30 40 50

LP = 10120583WLP = 15120583WLP = 20120583W

Sens

itivi

ty (p

TH

z12

)

102

Temperature (∘C)

(b)

Figure 6 (a) Actual signal-to-noise ratio (SNR) and (b) actual sensitivity versus cell temperature measured in a 1Hz bandwidth for an inputoptical light power of 10 120583W 15120583W and 20 120583W

6 The Scientific World Journal

6(b) show the actual SNR and the actual sensitivity of themagnetometer respectively Also noticed in this case thatthe actual SNR increases (and hence the actual sensitivity isenhanced) with increasing the input optical power Howeverthe actual SNRdecreaseswith increasing the cell temperaturemainly because of the higher phase incoherence that reducesthe output signal level With an input optical power of 20 120583Wand a cell temperature of 50∘C the actual SNR dropped to116 and the actual sensitivity was 27 pTHz12 measured ina 1Hz bandwidth The best actual sensitivity was obtainedwith an input optical power of 20120583W at room temperature(23∘C)The corresponding actual SNRwas 145 and the actualsensitivity was 21 pTHz12 measured in a 1Hz bandwidth

42 Bandwidth Another important feature of a magnetome-ter is its bandwidth that is how fast the magnetometerresponds to changes in the magnetic field The bandwidth119891bw of the magnetometer can be calculated as [12]

119891bw =120587

2Δ] (6)

where Δ] is the half width at half maximum (HWHM) band-width of the phase signal measured in hertz as illustrated inFigure 7(c)

Figures 7(a) and 7(b) show respectively the in-phaseand quadrature components of the lock-in amplifier outputversus the normalized frequency predicted by (2) and (3)Figure 7(c) shows the phase shift between the photodiodeoutput and the driving rf magnetic field 119861rf predictedby (4) All signals in Figures 7(a)ndash7(c) were measuredin a magnetically unshielded environment by continuouslysweeping the driving rf frequency along the resonancefrequency over a 6-second time range It is important tonote that the magnetically induced 50Hz interference signalwas suppressed by a notch filter It is obvious from Figures7(a)ndash7(c) that the HWHM bandwidths of both the in-phasesignal Δ]

119883 and the quadrature signal Δ]

119884 are equal and

smaller than the HWHM bandwidth Δ] of the phase-shiftsignal This agrees with the theoretical prediction using (2)ndash(4) In fact the phase shift is the only signal that is notdependent on the rfmagnetic fieldTherefore for the accurateevaluation of the bandwidth of the magnetometer 119891bw itis important to use into (6) the HWHM bandwidth Δ]measured from the phase shift rather than the HWHMbandwidths Δ]

119883and Δ]

119884 measured from the in-phase and

quadrature components respectivelyFigure 8 shows the magnetometer bandwidth versus cell

temperature for input optical power levels of 10120583W 15 120583Wand 20120583W The bandwidth exhibits a similar trend for allinput optical power levels initially decreasingwith increasingthe cell temperature until reaching itsminimumaround45∘CSubsequently the bandwidth increaseswith increasing the celltemperatureThe bandwidth depends on the transverse relax-ation time Γ

2 as evident from (4) and (6) An increase in the

cell temperature increases the vapor pressure which resultsin a larger number of atoms interacting with the light leadingto a longer relaxation time (smaller bandwidth) However athigh temperature the number of collisions between atoms or

0 2 4 6

0

1

2

In-p

hase

com

pone

nt(m

V)

Normalized frequency (Hz)minus6 minus4 minus2

minus2

minus1

0

Max

ΔX

(a)

minus6 minus4 minus2 0 2 4 6

0

2

4

Qua

drat

ure c

ompo

nent

(mV

)

Normalized frequency (Hz)

MaxHalf max

ΔY

(b)

minus6 minus4 minus2 0 2 4 6minus200

minus150

minus100

minus50

0

Phas

e shi

ft (d

eg)

Normalized frequency (Hz)

Δ

minus45∘

minus90∘

(c)

Figure 7 Measured in-phase component (a) quadrature com-ponent (b) and phase shift (c) between the photo diode outputand the driving rf magnetic field All signals were measured in amagnetically unshielded environment by continuously sweeping thedriving rf frequency along the resonance frequency over a 6-secondtime range It is important to note that the magnetically induced50Hz interference signal was suppressed by a notch filter The inputoptical power was 20120583W and the vapor cell temperature 48∘C TheHWHM bandwidth is highlighted for each measured output signal

with the walls of the cell increases significantly leading to ashorter relaxation time and hence a larger bandwidth Thisexplains the existence of a critical temperature (around 45∘)at which the intrinsic bandwidth is minimum

In the experiments the measured maximum bandwidthwas 175Hz obtained at room temperature (23∘C) with aninput optical power of 10120583W (blue curve in Figure 8) whilethe minimum bandwidth was 25Hz obtained with an inputoptical power of 20120583Wat a temperature of 45∘C (black curvein Figure 8)

43 Low-Amplitude Magnetic Field Measurement The ulti-mate intrinsic sensitivity of the magnetometer can be calcu-lated using (5) The best performance of the magnetometerwas obtained for an input optical power of 20120583W at celltemperature of 48∘C the ultimate intrinsic sensitivity was327 fTHz12 over a bandwidth of 26Hz However the exter-nalmagnetic noise generated by power lines and surroundingequipment caused the actual ultimate sensitivity of the

The Scientific World Journal 7

25 30 35 40 45 50 5520

40

60

80

100

120

140

160

180

(Hz)

LP = 10120583WLP = 15120583WLP = 20120583W

Temperature (∘C)

Figure 8 Intrinsic bandwidth versus cell temperature for an inputoptical light power of 10 120583W 15120583W and 20 120583W

0 01 02 03 04 05150

155

160

165

170

175

180

185

Mag

netic

fiel

d (p

T)

Time (s)

Figure 9Measured 15 pTpeak oscillating field at frequency of 25Hzfiltered with a low-pass filter with cutoff frequency of 50Hz

magnetometer to drop to 130 pTHz12 over a bandwidth of26Hz

The magnetometer in its optimal configuration (inputoptical power of 20120583W at cell temperature of 48∘C) wasthen used to measure an applied small-signal sinusoidalmagnetic field of amplitude 15 pT oscillating at 25Hz whichwas generated by a test coil placed at a distance of 6 cmfrom the vapor cell For this measurement the uniformdc magnetic field was 13120583T corresponding to a Larmorfrequency of 455 kHz The frequency of the rf magnetic fieldwas then set at 455 kHz resulting in a phase shift of minus90degrees between the photodiode output and the driving rfsignal as predicted by (4) and verified experimentally bythe result shown in Figure 7(c) When another 25Hz small-amplitude magnetic field was applied in addition to the dcand rf magnetic fields the Larmor frequency changed andnomore resonance occurred causing the phase shift betweenthe photodiode output and the driving rf signal to oscillatearound minus90 degrees at 25Hz This enabled the measurementof the new Larmor frequency and hence the calculation of

the magnitude of the 25Hz small-amplitude magnetic fieldwhich is proportional to the new Larmor frequency

Figure 9 shows the magnetic field calculated from themeasurement of the Larmor frequency after a 25Hz 15 pTmagnetic field was applied A lowpass filter of a cutoff fre-quency of 50Hz was used after the lock-in amplifier in orderto remove the power line noise (at 50Hz and its harmonics) aswell as all high frequencies noise It is obvious from Figure 9that the small-signal 25Hz magnetic field could be recovered(peak-to-peak magnitude is around 33 pT) demonstratingthe capability of the optical Mx magnetometer to measureultra-low-amplitude magnetic fields

5 Conclusion

An optically pumped quantum magnetometer on Mx con-figuration has been developed and its capability to measureultra-low-amplitude magnetic fields has been experimentallydemonstrated A high intrinsic sensitivity of 63 fTHz12measured in a 1Hz bandwidth has been achieved with aninput optical power of 20120583W at a vapor cell temperature of50∘C Experimental results have shown that the environmen-tal noise can significantly drop the magnetometer sensitivityby several orders of magnitude to as low as 27 pTHz12 Ahigh actual sensitivity of 21 pTHz12 has been attained withan input optical power of 20120583W at room temperature Themeasured bandwidth of the magnetometer has been shownto vary between 100Hz at room temperature and 25Hz at45∘C Experimental results have also shown that the ultimatebest intrinsic sensitivity (327 fTHz12) calculated over themeasured bandwidth (26Hz) can be attained with an inputoptical power of 20 120583W at a vapor cell temperature of 48∘Cand that the environmental noise reduces this sensitivityto 130 pTHz12 Finally the ability of the magnetometer todetect a 25Hz sinusoidal magnetic field of amplitude as lowas 15 pT has experimentally been demonstrated

References

[1] D Budker and M Romalis ldquoOptical magnetometryrdquo NaturePhysics vol 3 no 4 pp 227ndash234 2007

[2] V Shah S Knappe P D D Schwindt and J Kitching ldquoSub-picotesla atomic magnetometry with a microfabricated vapourcellrdquo Nature Photonics vol 1 no 11 pp 649ndash652 2007

[3] L A Liew S Knappe J Moreland H Robinson L Hollbergand J Kitching ldquoMicrofabricated alkali atom vapor cellsrdquoApplied Physics Letters vol 84 no 14 pp 2694ndash2696 2004

[4] J Belfi G Bevilacqua V Biancalana S Cartaleva Y DanchevaandLMoi ldquoCesiumcoherent population trappingmagnetome-ter for cardiosignal detection in an unshielded environmentrdquoJournal of the Optical Society of America B vol 24 no 9 pp2357ndash2362 2007

[5] P D D Schwindt L Hollberg and J Kitching ldquoSelf-oscillatingrubidiummagnetometer using nonlinearmagneto-optical rota-tionrdquo Review of Scientific Instruments vol 76 no 12 Article ID126103 pp 1ndash4 2005

[6] I K Kominis T W Kornack J C Allred and M V RomalisldquoA subfemtotesla multichannel atomic magnetometerrdquo Naturevol 422 no 6932 pp 596ndash599 2003

8 The Scientific World Journal

[7] G Bison R Wynands and A Weis ldquoA laser-pumped mag-netometer for the mapping of human cardiomagnetic fieldsrdquoApplied Physics B vol 76 no 3 pp 325ndash328 2003

[8] D Budker D F Kimball and D P DeMille Atomic Physics AnExplorationThrough Problems and Solutions Oxford UniversityPress New York NY USA 2004

[9] W E Bell and A L Bloom ldquoOptically driven spin precessionrdquoPhysical Review Letters vol 6 no 6 pp 280ndash281 1961

[10] F Bloch ldquoNuclear inductionrdquo Physical Review vol 70 no 7-8pp 460ndash474 1946

[11] D C Rife andR R Boorstyn ldquoSingle tone parameter estimationfrom discrete-time observationsrdquo IEEE Transactions on Infor-mation Theory vol 20 no 5 pp 591ndash598 1974

[12] G Bison R Wynands and A Weis ldquoOptimization and perfor-mance of an optical cardiomagnetometerrdquo Journal of the OpticalSociety of America B vol 22 no 1 pp 77ndash87 2005

The Scientific World Journal 5

30 40 50

SNR

LP = 10120583WLP = 15120583WLP = 20120583W

103

Temperature (∘C)

(a)

30 40 50

LP = 10120583WLP = 15120583WLP = 20120583W

Sens

itivi

ty (p

TH

z12

)

100

10minus1

Temperature (∘C)

(b)

Figure 5 (a) Intrinsic signal-to-noise ratio (SNR) and (b) intrinsic sensitivity measured in a 1Hz bandwidth versus cell temperature for inputoptical power of 10120583W 15120583W and 20120583W

30 40 50

SNR

LP = 10120583WLP = 15120583WLP = 20120583W

101

Temperature (∘C)

(a)

30 40 50

LP = 10120583WLP = 15120583WLP = 20120583W

Sens

itivi

ty (p

TH

z12

)

102

Temperature (∘C)

(b)

Figure 6 (a) Actual signal-to-noise ratio (SNR) and (b) actual sensitivity versus cell temperature measured in a 1Hz bandwidth for an inputoptical light power of 10 120583W 15120583W and 20 120583W

6 The Scientific World Journal

6(b) show the actual SNR and the actual sensitivity of themagnetometer respectively Also noticed in this case thatthe actual SNR increases (and hence the actual sensitivity isenhanced) with increasing the input optical power Howeverthe actual SNRdecreaseswith increasing the cell temperaturemainly because of the higher phase incoherence that reducesthe output signal level With an input optical power of 20 120583Wand a cell temperature of 50∘C the actual SNR dropped to116 and the actual sensitivity was 27 pTHz12 measured ina 1Hz bandwidth The best actual sensitivity was obtainedwith an input optical power of 20120583W at room temperature(23∘C)The corresponding actual SNRwas 145 and the actualsensitivity was 21 pTHz12 measured in a 1Hz bandwidth

42 Bandwidth Another important feature of a magnetome-ter is its bandwidth that is how fast the magnetometerresponds to changes in the magnetic field The bandwidth119891bw of the magnetometer can be calculated as [12]

119891bw =120587

2Δ] (6)

where Δ] is the half width at half maximum (HWHM) band-width of the phase signal measured in hertz as illustrated inFigure 7(c)

Figures 7(a) and 7(b) show respectively the in-phaseand quadrature components of the lock-in amplifier outputversus the normalized frequency predicted by (2) and (3)Figure 7(c) shows the phase shift between the photodiodeoutput and the driving rf magnetic field 119861rf predictedby (4) All signals in Figures 7(a)ndash7(c) were measuredin a magnetically unshielded environment by continuouslysweeping the driving rf frequency along the resonancefrequency over a 6-second time range It is important tonote that the magnetically induced 50Hz interference signalwas suppressed by a notch filter It is obvious from Figures7(a)ndash7(c) that the HWHM bandwidths of both the in-phasesignal Δ]

119883 and the quadrature signal Δ]

119884 are equal and

smaller than the HWHM bandwidth Δ] of the phase-shiftsignal This agrees with the theoretical prediction using (2)ndash(4) In fact the phase shift is the only signal that is notdependent on the rfmagnetic fieldTherefore for the accurateevaluation of the bandwidth of the magnetometer 119891bw itis important to use into (6) the HWHM bandwidth Δ]measured from the phase shift rather than the HWHMbandwidths Δ]

119883and Δ]

119884 measured from the in-phase and

quadrature components respectivelyFigure 8 shows the magnetometer bandwidth versus cell

temperature for input optical power levels of 10120583W 15 120583Wand 20120583W The bandwidth exhibits a similar trend for allinput optical power levels initially decreasingwith increasingthe cell temperature until reaching itsminimumaround45∘CSubsequently the bandwidth increaseswith increasing the celltemperatureThe bandwidth depends on the transverse relax-ation time Γ

2 as evident from (4) and (6) An increase in the

cell temperature increases the vapor pressure which resultsin a larger number of atoms interacting with the light leadingto a longer relaxation time (smaller bandwidth) However athigh temperature the number of collisions between atoms or

0 2 4 6

0

1

2

In-p

hase

com

pone

nt(m

V)

Normalized frequency (Hz)minus6 minus4 minus2

minus2

minus1

0

Max

ΔX

(a)

minus6 minus4 minus2 0 2 4 6

0

2

4

Qua

drat

ure c

ompo

nent

(mV

)

Normalized frequency (Hz)

MaxHalf max

ΔY

(b)

minus6 minus4 minus2 0 2 4 6minus200

minus150

minus100

minus50

0

Phas

e shi

ft (d

eg)

Normalized frequency (Hz)

Δ

minus45∘

minus90∘

(c)

Figure 7 Measured in-phase component (a) quadrature com-ponent (b) and phase shift (c) between the photo diode outputand the driving rf magnetic field All signals were measured in amagnetically unshielded environment by continuously sweeping thedriving rf frequency along the resonance frequency over a 6-secondtime range It is important to note that the magnetically induced50Hz interference signal was suppressed by a notch filter The inputoptical power was 20120583W and the vapor cell temperature 48∘C TheHWHM bandwidth is highlighted for each measured output signal

with the walls of the cell increases significantly leading to ashorter relaxation time and hence a larger bandwidth Thisexplains the existence of a critical temperature (around 45∘)at which the intrinsic bandwidth is minimum

In the experiments the measured maximum bandwidthwas 175Hz obtained at room temperature (23∘C) with aninput optical power of 10120583W (blue curve in Figure 8) whilethe minimum bandwidth was 25Hz obtained with an inputoptical power of 20120583Wat a temperature of 45∘C (black curvein Figure 8)

43 Low-Amplitude Magnetic Field Measurement The ulti-mate intrinsic sensitivity of the magnetometer can be calcu-lated using (5) The best performance of the magnetometerwas obtained for an input optical power of 20120583W at celltemperature of 48∘C the ultimate intrinsic sensitivity was327 fTHz12 over a bandwidth of 26Hz However the exter-nalmagnetic noise generated by power lines and surroundingequipment caused the actual ultimate sensitivity of the

The Scientific World Journal 7

25 30 35 40 45 50 5520

40

60

80

100

120

140

160

180

(Hz)

LP = 10120583WLP = 15120583WLP = 20120583W

Temperature (∘C)

Figure 8 Intrinsic bandwidth versus cell temperature for an inputoptical light power of 10 120583W 15120583W and 20 120583W

0 01 02 03 04 05150

155

160

165

170

175

180

185

Mag

netic

fiel

d (p

T)

Time (s)

Figure 9Measured 15 pTpeak oscillating field at frequency of 25Hzfiltered with a low-pass filter with cutoff frequency of 50Hz

magnetometer to drop to 130 pTHz12 over a bandwidth of26Hz

The magnetometer in its optimal configuration (inputoptical power of 20120583W at cell temperature of 48∘C) wasthen used to measure an applied small-signal sinusoidalmagnetic field of amplitude 15 pT oscillating at 25Hz whichwas generated by a test coil placed at a distance of 6 cmfrom the vapor cell For this measurement the uniformdc magnetic field was 13120583T corresponding to a Larmorfrequency of 455 kHz The frequency of the rf magnetic fieldwas then set at 455 kHz resulting in a phase shift of minus90degrees between the photodiode output and the driving rfsignal as predicted by (4) and verified experimentally bythe result shown in Figure 7(c) When another 25Hz small-amplitude magnetic field was applied in addition to the dcand rf magnetic fields the Larmor frequency changed andnomore resonance occurred causing the phase shift betweenthe photodiode output and the driving rf signal to oscillatearound minus90 degrees at 25Hz This enabled the measurementof the new Larmor frequency and hence the calculation of

the magnitude of the 25Hz small-amplitude magnetic fieldwhich is proportional to the new Larmor frequency

Figure 9 shows the magnetic field calculated from themeasurement of the Larmor frequency after a 25Hz 15 pTmagnetic field was applied A lowpass filter of a cutoff fre-quency of 50Hz was used after the lock-in amplifier in orderto remove the power line noise (at 50Hz and its harmonics) aswell as all high frequencies noise It is obvious from Figure 9that the small-signal 25Hz magnetic field could be recovered(peak-to-peak magnitude is around 33 pT) demonstratingthe capability of the optical Mx magnetometer to measureultra-low-amplitude magnetic fields

5 Conclusion

An optically pumped quantum magnetometer on Mx con-figuration has been developed and its capability to measureultra-low-amplitude magnetic fields has been experimentallydemonstrated A high intrinsic sensitivity of 63 fTHz12measured in a 1Hz bandwidth has been achieved with aninput optical power of 20120583W at a vapor cell temperature of50∘C Experimental results have shown that the environmen-tal noise can significantly drop the magnetometer sensitivityby several orders of magnitude to as low as 27 pTHz12 Ahigh actual sensitivity of 21 pTHz12 has been attained withan input optical power of 20120583W at room temperature Themeasured bandwidth of the magnetometer has been shownto vary between 100Hz at room temperature and 25Hz at45∘C Experimental results have also shown that the ultimatebest intrinsic sensitivity (327 fTHz12) calculated over themeasured bandwidth (26Hz) can be attained with an inputoptical power of 20 120583W at a vapor cell temperature of 48∘Cand that the environmental noise reduces this sensitivityto 130 pTHz12 Finally the ability of the magnetometer todetect a 25Hz sinusoidal magnetic field of amplitude as lowas 15 pT has experimentally been demonstrated

References

[1] D Budker and M Romalis ldquoOptical magnetometryrdquo NaturePhysics vol 3 no 4 pp 227ndash234 2007

[2] V Shah S Knappe P D D Schwindt and J Kitching ldquoSub-picotesla atomic magnetometry with a microfabricated vapourcellrdquo Nature Photonics vol 1 no 11 pp 649ndash652 2007

[3] L A Liew S Knappe J Moreland H Robinson L Hollbergand J Kitching ldquoMicrofabricated alkali atom vapor cellsrdquoApplied Physics Letters vol 84 no 14 pp 2694ndash2696 2004

[4] J Belfi G Bevilacqua V Biancalana S Cartaleva Y DanchevaandLMoi ldquoCesiumcoherent population trappingmagnetome-ter for cardiosignal detection in an unshielded environmentrdquoJournal of the Optical Society of America B vol 24 no 9 pp2357ndash2362 2007

[5] P D D Schwindt L Hollberg and J Kitching ldquoSelf-oscillatingrubidiummagnetometer using nonlinearmagneto-optical rota-tionrdquo Review of Scientific Instruments vol 76 no 12 Article ID126103 pp 1ndash4 2005

[6] I K Kominis T W Kornack J C Allred and M V RomalisldquoA subfemtotesla multichannel atomic magnetometerrdquo Naturevol 422 no 6932 pp 596ndash599 2003

8 The Scientific World Journal

[7] G Bison R Wynands and A Weis ldquoA laser-pumped mag-netometer for the mapping of human cardiomagnetic fieldsrdquoApplied Physics B vol 76 no 3 pp 325ndash328 2003

[8] D Budker D F Kimball and D P DeMille Atomic Physics AnExplorationThrough Problems and Solutions Oxford UniversityPress New York NY USA 2004

[9] W E Bell and A L Bloom ldquoOptically driven spin precessionrdquoPhysical Review Letters vol 6 no 6 pp 280ndash281 1961

[10] F Bloch ldquoNuclear inductionrdquo Physical Review vol 70 no 7-8pp 460ndash474 1946

[11] D C Rife andR R Boorstyn ldquoSingle tone parameter estimationfrom discrete-time observationsrdquo IEEE Transactions on Infor-mation Theory vol 20 no 5 pp 591ndash598 1974

[12] G Bison R Wynands and A Weis ldquoOptimization and perfor-mance of an optical cardiomagnetometerrdquo Journal of the OpticalSociety of America B vol 22 no 1 pp 77ndash87 2005

6 The Scientific World Journal

6(b) show the actual SNR and the actual sensitivity of themagnetometer respectively Also noticed in this case thatthe actual SNR increases (and hence the actual sensitivity isenhanced) with increasing the input optical power Howeverthe actual SNRdecreaseswith increasing the cell temperaturemainly because of the higher phase incoherence that reducesthe output signal level With an input optical power of 20 120583Wand a cell temperature of 50∘C the actual SNR dropped to116 and the actual sensitivity was 27 pTHz12 measured ina 1Hz bandwidth The best actual sensitivity was obtainedwith an input optical power of 20120583W at room temperature(23∘C)The corresponding actual SNRwas 145 and the actualsensitivity was 21 pTHz12 measured in a 1Hz bandwidth

42 Bandwidth Another important feature of a magnetome-ter is its bandwidth that is how fast the magnetometerresponds to changes in the magnetic field The bandwidth119891bw of the magnetometer can be calculated as [12]

119891bw =120587

2Δ] (6)

where Δ] is the half width at half maximum (HWHM) band-width of the phase signal measured in hertz as illustrated inFigure 7(c)

Figures 7(a) and 7(b) show respectively the in-phaseand quadrature components of the lock-in amplifier outputversus the normalized frequency predicted by (2) and (3)Figure 7(c) shows the phase shift between the photodiodeoutput and the driving rf magnetic field 119861rf predictedby (4) All signals in Figures 7(a)ndash7(c) were measuredin a magnetically unshielded environment by continuouslysweeping the driving rf frequency along the resonancefrequency over a 6-second time range It is important tonote that the magnetically induced 50Hz interference signalwas suppressed by a notch filter It is obvious from Figures7(a)ndash7(c) that the HWHM bandwidths of both the in-phasesignal Δ]

119883 and the quadrature signal Δ]

119884 are equal and

smaller than the HWHM bandwidth Δ] of the phase-shiftsignal This agrees with the theoretical prediction using (2)ndash(4) In fact the phase shift is the only signal that is notdependent on the rfmagnetic fieldTherefore for the accurateevaluation of the bandwidth of the magnetometer 119891bw itis important to use into (6) the HWHM bandwidth Δ]measured from the phase shift rather than the HWHMbandwidths Δ]

119883and Δ]

119884 measured from the in-phase and

quadrature components respectivelyFigure 8 shows the magnetometer bandwidth versus cell

temperature for input optical power levels of 10120583W 15 120583Wand 20120583W The bandwidth exhibits a similar trend for allinput optical power levels initially decreasingwith increasingthe cell temperature until reaching itsminimumaround45∘CSubsequently the bandwidth increaseswith increasing the celltemperatureThe bandwidth depends on the transverse relax-ation time Γ

2 as evident from (4) and (6) An increase in the

cell temperature increases the vapor pressure which resultsin a larger number of atoms interacting with the light leadingto a longer relaxation time (smaller bandwidth) However athigh temperature the number of collisions between atoms or

0 2 4 6

0

1

2

In-p

hase

com

pone

nt(m

V)

Normalized frequency (Hz)minus6 minus4 minus2

minus2

minus1

0

Max

ΔX

(a)

minus6 minus4 minus2 0 2 4 6

0

2

4

Qua

drat

ure c

ompo

nent

(mV

)

Normalized frequency (Hz)

MaxHalf max

ΔY

(b)

minus6 minus4 minus2 0 2 4 6minus200

minus150

minus100

minus50

0

Phas

e shi

ft (d

eg)

Normalized frequency (Hz)

Δ

minus45∘

minus90∘

(c)

Figure 7 Measured in-phase component (a) quadrature com-ponent (b) and phase shift (c) between the photo diode outputand the driving rf magnetic field All signals were measured in amagnetically unshielded environment by continuously sweeping thedriving rf frequency along the resonance frequency over a 6-secondtime range It is important to note that the magnetically induced50Hz interference signal was suppressed by a notch filter The inputoptical power was 20120583W and the vapor cell temperature 48∘C TheHWHM bandwidth is highlighted for each measured output signal

with the walls of the cell increases significantly leading to ashorter relaxation time and hence a larger bandwidth Thisexplains the existence of a critical temperature (around 45∘)at which the intrinsic bandwidth is minimum

In the experiments the measured maximum bandwidthwas 175Hz obtained at room temperature (23∘C) with aninput optical power of 10120583W (blue curve in Figure 8) whilethe minimum bandwidth was 25Hz obtained with an inputoptical power of 20120583Wat a temperature of 45∘C (black curvein Figure 8)

43 Low-Amplitude Magnetic Field Measurement The ulti-mate intrinsic sensitivity of the magnetometer can be calcu-lated using (5) The best performance of the magnetometerwas obtained for an input optical power of 20120583W at celltemperature of 48∘C the ultimate intrinsic sensitivity was327 fTHz12 over a bandwidth of 26Hz However the exter-nalmagnetic noise generated by power lines and surroundingequipment caused the actual ultimate sensitivity of the

The Scientific World Journal 7

25 30 35 40 45 50 5520

40

60

80

100

120

140

160

180

(Hz)

LP = 10120583WLP = 15120583WLP = 20120583W

Temperature (∘C)

Figure 8 Intrinsic bandwidth versus cell temperature for an inputoptical light power of 10 120583W 15120583W and 20 120583W

0 01 02 03 04 05150

155

160

165

170

175

180

185

Mag

netic

fiel

d (p

T)

Time (s)

Figure 9Measured 15 pTpeak oscillating field at frequency of 25Hzfiltered with a low-pass filter with cutoff frequency of 50Hz

magnetometer to drop to 130 pTHz12 over a bandwidth of26Hz

The magnetometer in its optimal configuration (inputoptical power of 20120583W at cell temperature of 48∘C) wasthen used to measure an applied small-signal sinusoidalmagnetic field of amplitude 15 pT oscillating at 25Hz whichwas generated by a test coil placed at a distance of 6 cmfrom the vapor cell For this measurement the uniformdc magnetic field was 13120583T corresponding to a Larmorfrequency of 455 kHz The frequency of the rf magnetic fieldwas then set at 455 kHz resulting in a phase shift of minus90degrees between the photodiode output and the driving rfsignal as predicted by (4) and verified experimentally bythe result shown in Figure 7(c) When another 25Hz small-amplitude magnetic field was applied in addition to the dcand rf magnetic fields the Larmor frequency changed andnomore resonance occurred causing the phase shift betweenthe photodiode output and the driving rf signal to oscillatearound minus90 degrees at 25Hz This enabled the measurementof the new Larmor frequency and hence the calculation of

the magnitude of the 25Hz small-amplitude magnetic fieldwhich is proportional to the new Larmor frequency

Figure 9 shows the magnetic field calculated from themeasurement of the Larmor frequency after a 25Hz 15 pTmagnetic field was applied A lowpass filter of a cutoff fre-quency of 50Hz was used after the lock-in amplifier in orderto remove the power line noise (at 50Hz and its harmonics) aswell as all high frequencies noise It is obvious from Figure 9that the small-signal 25Hz magnetic field could be recovered(peak-to-peak magnitude is around 33 pT) demonstratingthe capability of the optical Mx magnetometer to measureultra-low-amplitude magnetic fields

5 Conclusion

An optically pumped quantum magnetometer on Mx con-figuration has been developed and its capability to measureultra-low-amplitude magnetic fields has been experimentallydemonstrated A high intrinsic sensitivity of 63 fTHz12measured in a 1Hz bandwidth has been achieved with aninput optical power of 20120583W at a vapor cell temperature of50∘C Experimental results have shown that the environmen-tal noise can significantly drop the magnetometer sensitivityby several orders of magnitude to as low as 27 pTHz12 Ahigh actual sensitivity of 21 pTHz12 has been attained withan input optical power of 20120583W at room temperature Themeasured bandwidth of the magnetometer has been shownto vary between 100Hz at room temperature and 25Hz at45∘C Experimental results have also shown that the ultimatebest intrinsic sensitivity (327 fTHz12) calculated over themeasured bandwidth (26Hz) can be attained with an inputoptical power of 20 120583W at a vapor cell temperature of 48∘Cand that the environmental noise reduces this sensitivityto 130 pTHz12 Finally the ability of the magnetometer todetect a 25Hz sinusoidal magnetic field of amplitude as lowas 15 pT has experimentally been demonstrated

References

[1] D Budker and M Romalis ldquoOptical magnetometryrdquo NaturePhysics vol 3 no 4 pp 227ndash234 2007

[2] V Shah S Knappe P D D Schwindt and J Kitching ldquoSub-picotesla atomic magnetometry with a microfabricated vapourcellrdquo Nature Photonics vol 1 no 11 pp 649ndash652 2007

[3] L A Liew S Knappe J Moreland H Robinson L Hollbergand J Kitching ldquoMicrofabricated alkali atom vapor cellsrdquoApplied Physics Letters vol 84 no 14 pp 2694ndash2696 2004

[4] J Belfi G Bevilacqua V Biancalana S Cartaleva Y DanchevaandLMoi ldquoCesiumcoherent population trappingmagnetome-ter for cardiosignal detection in an unshielded environmentrdquoJournal of the Optical Society of America B vol 24 no 9 pp2357ndash2362 2007

[5] P D D Schwindt L Hollberg and J Kitching ldquoSelf-oscillatingrubidiummagnetometer using nonlinearmagneto-optical rota-tionrdquo Review of Scientific Instruments vol 76 no 12 Article ID126103 pp 1ndash4 2005

[6] I K Kominis T W Kornack J C Allred and M V RomalisldquoA subfemtotesla multichannel atomic magnetometerrdquo Naturevol 422 no 6932 pp 596ndash599 2003

8 The Scientific World Journal

[7] G Bison R Wynands and A Weis ldquoA laser-pumped mag-netometer for the mapping of human cardiomagnetic fieldsrdquoApplied Physics B vol 76 no 3 pp 325ndash328 2003

[8] D Budker D F Kimball and D P DeMille Atomic Physics AnExplorationThrough Problems and Solutions Oxford UniversityPress New York NY USA 2004

[9] W E Bell and A L Bloom ldquoOptically driven spin precessionrdquoPhysical Review Letters vol 6 no 6 pp 280ndash281 1961

[10] F Bloch ldquoNuclear inductionrdquo Physical Review vol 70 no 7-8pp 460ndash474 1946

[11] D C Rife andR R Boorstyn ldquoSingle tone parameter estimationfrom discrete-time observationsrdquo IEEE Transactions on Infor-mation Theory vol 20 no 5 pp 591ndash598 1974

[12] G Bison R Wynands and A Weis ldquoOptimization and perfor-mance of an optical cardiomagnetometerrdquo Journal of the OpticalSociety of America B vol 22 no 1 pp 77ndash87 2005

The Scientific World Journal 7

25 30 35 40 45 50 5520

40

60

80

100

120

140

160

180

(Hz)

LP = 10120583WLP = 15120583WLP = 20120583W

Temperature (∘C)

Figure 8 Intrinsic bandwidth versus cell temperature for an inputoptical light power of 10 120583W 15120583W and 20 120583W

0 01 02 03 04 05150

155

160

165

170

175

180

185

Mag

netic

fiel

d (p

T)

Time (s)

Figure 9Measured 15 pTpeak oscillating field at frequency of 25Hzfiltered with a low-pass filter with cutoff frequency of 50Hz

magnetometer to drop to 130 pTHz12 over a bandwidth of26Hz

The magnetometer in its optimal configuration (inputoptical power of 20120583W at cell temperature of 48∘C) wasthen used to measure an applied small-signal sinusoidalmagnetic field of amplitude 15 pT oscillating at 25Hz whichwas generated by a test coil placed at a distance of 6 cmfrom the vapor cell For this measurement the uniformdc magnetic field was 13120583T corresponding to a Larmorfrequency of 455 kHz The frequency of the rf magnetic fieldwas then set at 455 kHz resulting in a phase shift of minus90degrees between the photodiode output and the driving rfsignal as predicted by (4) and verified experimentally bythe result shown in Figure 7(c) When another 25Hz small-amplitude magnetic field was applied in addition to the dcand rf magnetic fields the Larmor frequency changed andnomore resonance occurred causing the phase shift betweenthe photodiode output and the driving rf signal to oscillatearound minus90 degrees at 25Hz This enabled the measurementof the new Larmor frequency and hence the calculation of

the magnitude of the 25Hz small-amplitude magnetic fieldwhich is proportional to the new Larmor frequency

Figure 9 shows the magnetic field calculated from themeasurement of the Larmor frequency after a 25Hz 15 pTmagnetic field was applied A lowpass filter of a cutoff fre-quency of 50Hz was used after the lock-in amplifier in orderto remove the power line noise (at 50Hz and its harmonics) aswell as all high frequencies noise It is obvious from Figure 9that the small-signal 25Hz magnetic field could be recovered(peak-to-peak magnitude is around 33 pT) demonstratingthe capability of the optical Mx magnetometer to measureultra-low-amplitude magnetic fields

5 Conclusion

An optically pumped quantum magnetometer on Mx con-figuration has been developed and its capability to measureultra-low-amplitude magnetic fields has been experimentallydemonstrated A high intrinsic sensitivity of 63 fTHz12measured in a 1Hz bandwidth has been achieved with aninput optical power of 20120583W at a vapor cell temperature of50∘C Experimental results have shown that the environmen-tal noise can significantly drop the magnetometer sensitivityby several orders of magnitude to as low as 27 pTHz12 Ahigh actual sensitivity of 21 pTHz12 has been attained withan input optical power of 20120583W at room temperature Themeasured bandwidth of the magnetometer has been shownto vary between 100Hz at room temperature and 25Hz at45∘C Experimental results have also shown that the ultimatebest intrinsic sensitivity (327 fTHz12) calculated over themeasured bandwidth (26Hz) can be attained with an inputoptical power of 20 120583W at a vapor cell temperature of 48∘Cand that the environmental noise reduces this sensitivityto 130 pTHz12 Finally the ability of the magnetometer todetect a 25Hz sinusoidal magnetic field of amplitude as lowas 15 pT has experimentally been demonstrated

References

[1] D Budker and M Romalis ldquoOptical magnetometryrdquo NaturePhysics vol 3 no 4 pp 227ndash234 2007

[2] V Shah S Knappe P D D Schwindt and J Kitching ldquoSub-picotesla atomic magnetometry with a microfabricated vapourcellrdquo Nature Photonics vol 1 no 11 pp 649ndash652 2007

[3] L A Liew S Knappe J Moreland H Robinson L Hollbergand J Kitching ldquoMicrofabricated alkali atom vapor cellsrdquoApplied Physics Letters vol 84 no 14 pp 2694ndash2696 2004

[4] J Belfi G Bevilacqua V Biancalana S Cartaleva Y DanchevaandLMoi ldquoCesiumcoherent population trappingmagnetome-ter for cardiosignal detection in an unshielded environmentrdquoJournal of the Optical Society of America B vol 24 no 9 pp2357ndash2362 2007

[5] P D D Schwindt L Hollberg and J Kitching ldquoSelf-oscillatingrubidiummagnetometer using nonlinearmagneto-optical rota-tionrdquo Review of Scientific Instruments vol 76 no 12 Article ID126103 pp 1ndash4 2005

[6] I K Kominis T W Kornack J C Allred and M V RomalisldquoA subfemtotesla multichannel atomic magnetometerrdquo Naturevol 422 no 6932 pp 596ndash599 2003

8 The Scientific World Journal

[7] G Bison R Wynands and A Weis ldquoA laser-pumped mag-netometer for the mapping of human cardiomagnetic fieldsrdquoApplied Physics B vol 76 no 3 pp 325ndash328 2003

[8] D Budker D F Kimball and D P DeMille Atomic Physics AnExplorationThrough Problems and Solutions Oxford UniversityPress New York NY USA 2004

[9] W E Bell and A L Bloom ldquoOptically driven spin precessionrdquoPhysical Review Letters vol 6 no 6 pp 280ndash281 1961

[10] F Bloch ldquoNuclear inductionrdquo Physical Review vol 70 no 7-8pp 460ndash474 1946

[11] D C Rife andR R Boorstyn ldquoSingle tone parameter estimationfrom discrete-time observationsrdquo IEEE Transactions on Infor-mation Theory vol 20 no 5 pp 591ndash598 1974

[12] G Bison R Wynands and A Weis ldquoOptimization and perfor-mance of an optical cardiomagnetometerrdquo Journal of the OpticalSociety of America B vol 22 no 1 pp 77ndash87 2005

8 The Scientific World Journal

[7] G Bison R Wynands and A Weis ldquoA laser-pumped mag-netometer for the mapping of human cardiomagnetic fieldsrdquoApplied Physics B vol 76 no 3 pp 325ndash328 2003

[8] D Budker D F Kimball and D P DeMille Atomic Physics AnExplorationThrough Problems and Solutions Oxford UniversityPress New York NY USA 2004

[9] W E Bell and A L Bloom ldquoOptically driven spin precessionrdquoPhysical Review Letters vol 6 no 6 pp 280ndash281 1961

[10] F Bloch ldquoNuclear inductionrdquo Physical Review vol 70 no 7-8pp 460ndash474 1946

[11] D C Rife andR R Boorstyn ldquoSingle tone parameter estimationfrom discrete-time observationsrdquo IEEE Transactions on Infor-mation Theory vol 20 no 5 pp 591ndash598 1974

[12] G Bison R Wynands and A Weis ldquoOptimization and perfor-mance of an optical cardiomagnetometerrdquo Journal of the OpticalSociety of America B vol 22 no 1 pp 77ndash87 2005