Appl Phys B (2010) 100: 717–724DOI 10.1007/s00340-010-4084-9

Noise reduction in optically pumped magnetometer assemblies

V. Schultze · R. IJsselsteijn · H.-G. Meyer

Received: 30 November 2009 / Revised version: 6 April 2010 / Published online: 30 May 2010© Springer-Verlag 2010

Abstract In most magnetic field measurement configura-tions the resolution of optically pumped magnetometers islimited by the shot noise of the pump light. However, inpractice this noise limit is overwhelmed by other sources.One of them is the conversion of the pump laser’s frequencymodulation (FM) noise to amplitude modulation (AM) noisedue to the absorption in the magnetometer’s alkali vapourcell. This extra noise can be nearly completely cancelledby the illumination of an additional cell with the same laserlight and the subtraction of its photo current from that of themeasurement cell. The correlation of the photo signals ofdifferent cells is just slightly decreased by the applied mea-surement and rf fields B0 and B1, respectively. As a result,in real magnetic field measurements using the photo-currentsubtraction, a noise-limited magnetic field resolution of justtwice the shot-noise limit can be achieved. This is exper-imentally shown for the most thrifty setup with two cells;one time using the second cell just for the photo-currentsubtraction, the other time also serving for magnetic fieldmeasurements, forming a gradiometer with the first cell. Yet,the photo-current subtraction method is most appealing formagnetometer arrays, where the photo signal of just one ad-ditional vapour cell can be used for the noise reduction ofthe complete array.

1 Introduction

The most prominent figure of merit for magnetic field sen-sors is their noise-limited magnetic field sensitivity. It de-

V. Schultze (�) · R. IJsselsteijn · H.-G. MeyerInstitute of Photonic Technology (IPHT), Albert-Einstein-Str. 9,07745 Jena, Germanye-mail: volkmar.schultze@ipht-jena.de

notes the smallest magnetic field, the sensor is able to de-tect. For high-resolution magnetometers two problems areconnected with the denotation of this sensitivity. The firstone is its determination, the second one the utilisation inreal measurement circumstances. Both tasks depend on thephysical principle and the realisation possibilities of the sen-sor type. Looking at the two magnetic field sensor typeswith the highest sensitivities available today, SQUIDs (Su-perconducting QUantum Interference Devices) and OPMs(Optically Pumped Magnetometers), this gets obvious. Thedetermination of the intrinsic noise limitations of the mag-netic field sensitivity requires the absence of external noisesources. For SQUIDs this results in shielding the sensorfrom the external magnetic field with all its disturbances.The lower the sensor’s intrinsic noise, the better this shield-ing needs to be. To get benefit from ultra-low noise marginsof good SQUIDs, large shielding chambers are set up, wherethe SQUIDs can be characterised, but which are also usedfor measurements like biomagnetic diagnosis [1].

However, optical magnetometers can only be operated inzero magnetic field when they use the Coherent PopulationTrapping (CPT) method [2] or work in the Spin-ExchangeRelaxation-Free (SERF) regime [3]. Other working princi-ples, like the Bell–Bloom magnetometer [4], the applica-tion of Non-Linear Magneto-Optical Rotation (NMOR) [5]or the Mx method [6–8] ( which we have used), require amagnetic field for their operation. Therefore, the determina-tion of the intrinsic magnetic field resolution is impaired bythe noise contribution of that magnetic field, be it the nat-ural environmental field or an artificial one, produced insidea magnetic shielding. For the determination of the noise-limited magnetic field resolution Bn, the way out usuallygone in the OPM community, is to calculate it from other

718 V. Schultze et al.

measurable OPM parameters, which are not affected by themagnetic field. This can be done via the relation

Bn = 1

γ

Γ

S/N

/√�f , (1)

where γ is the gyromagnetic ratio and �f the measurementbandwidth [9]. Γ is the resonance line halfwidth of the op-tical magnetometer and S/N denotes the signal-to-noise ra-tio, i.e. the amount, the signal amplitude arises above therms noise level measured in the same frequency band.

For measurements in the Mx mode, another good observ-able is the steepness dPqu/df of the quadrature componentPqu at the centre of the resonance line. Then Bn can be de-termined by

Bn = 1

γ

N

dPqu/df

/√�f . (2)

Obviously, the ultimately achievable intrinsic magnetic fieldresolution is limited by the noise level N . Here a fundamen-tal limit is set by the spin projection noise, arising from arandom imbalance between the number of atoms with pos-itive and negative spin projection along the probe direc-tion [10]. Going beyond this limit is only possible with socalled squeezed spin states [11]. However, in most practi-cal magnetic field measurement setups like we use, eventhe spin projection noise is overwhelmed by another noisesource; the photon shot noise Nsn of the pumping light [12].It is determined by the dc component of the photo currentIdc by

Nsn = √2eIdc�f · G, (3)

where G is the transimpedance amplification factor of themeasured photo current.

Alexandrov et al. proved the validity of expression (2)experimentally with a special OPM, using two different ru-bidium isotopes in one single magnetometer cell [13].

It is usual to give the noise-limited sensitivity of an OPMdetermined in the way sketched above. Values in the order of10 fT/

√Hz are common. However, strictly speaking this is

just the shot-noise limited sensitivity which can be reachedwith the used vapour cell, when no other noise sources dete-riorate this value. In practice they do, however, often endingup with a magnetic field resolution of about 1 pT/

√Hz for

the whole magnetometer. Such additional noise sources willhave some technical origin in the remaining magnetometersetup (“internal sources”), but of course also come from themagnetic field itself (“external sources”). The latter can beconfined in a gradiometer setup, where the difference of themagnetic field at two different locations is measured.

For the internal noise sources other solutions have to befound. Coming from the concept of using two magnetome-ter cells, we here present a new method to suppress other

additional noise sources in the magnetometer setup too. So,the aim of this paper is to approach the shot-noise limit ofthe OPM field sensitivity also in real experiments.

2 Experimental setup

The vapour cells we use in our investigations are two glass-blown caesium-filled cells with paraffin-coated walls, pro-duced at the University of Fribourg in Switzerland. The pro-duction process and the general parameters of such cells aredescribed in the recent paper [14]. In the following, our twocells will be labelled as #1 and #2, respectively.

The characterisation system uses the Mx mode, in whichthe measurement magnetic field B0 is oriented at 45◦ withrespect to the pumping light beam direction [6–8]. Thepumping light is coming from a distributed feedback (DFB)laser diode system (Toptica DL 100) with its frequency sta-bilised to the F = 4 → F = 3 transition of the Doppler-freeD1 line of caesium using compact saturation spectroscopywith an additional Cs vapour cell. The laser beam inten-sity can be tuned by a combination of a computer-controlledmotor-driven rotatable polariser and a second non-rotatableone. A few percent of the beam are picked off to measurethe resulting intensity; the remaining part is attenuated bya neutral density filter. The linearly polarised beam is nowdirected into a magnetically shielding barrel, where the cen-tral parts of the OPM are mounted (Fig. 1). The mount-ings are made of plastic material in order not to produceany magnetic or electric disturbances in the vicinity of thevapour cells. First, the beam is split into two parallel onesto realise simultaneous operation of two vapour cells. Each

Fig. 1 Shielding barrel with two-cell measurement setup

Noise reduction in optically pumped magnetometer assemblies 719

Fig. 2 Noise characteristics inside the shielding barrel

beam passes a quarter-wave plate to create circular polarisedlight before entering the cells. The beams coming out of thecells are collimated onto two photodiodes. For the radio-frequency B1 field, small pairs of rectangular coils in aHelmholtz-like configuration are mounted around the cells.

The barrel consists of three concentric μ-metal cylinderswith three dismountable lids on each side. The available in-ner space is 1 m in diameter and 1 m long. Inside the barrel,for the B0-field a three-axes Helmholtz coil system with ad-ditional correction coils is mounted.1 Each of the two coilpairs producing the magnetic field of one direction is sup-plied by a separate current source (Kepco ABC 60). In thisway, homogeneous fields up to Earth’s field magnitude aswell as ascertained field gradients can be tuned. The field di-rection, magnitude and gradient can be computer-controlledvaried in a whole spatial quadrant. The achieved homogene-ity in a central cube of 10 cm side length, using equal cur-rents in the coils belonging together, has distortions of lessthan 2 × 10−3. Purposely originated linear field gradientshave the same accuracy.

For the investigation of the noise-limited magnetic fieldresolution of the OPMs, the noise of the field inside the bar-rel is of major importance. To measure not only the noiseof the artificially generated magnetic field B0, but also ofthe residual field, the measurements were performed within-house produced SQUIDs (which do not need magneticfields for operation) [15]. Figure 2 shows the noise spec-tra, recorded in various experimental conditions. Withoutapplied magnetic field the spectrum just reflects the noiseof the used SQUID (white noise floor of 18 fT/

√Hz, ad-

ditional 1/f -noise at low frequencies). Thus the noise in-side the shielding will be below these margins. The addi-

1The shielding barrel together with the Helmholtz coil system, takingthe shielding material in the vicinity into account, were delivered bySekels GmbH, Germany (www.sekels.de).

tional noise contributions at several ten Hertz are due to vi-brations, which cause slight movements of the cryostat withthe SQUIDs with respect to the barrel, which has a residualfield of about 8 nT in the centre (SQUIDs measure such ori-entation distortions, because they are vectorial sensors—incontrast to OPM, which are scalar ones). Switching on themagnetic field produced with the Helmholtz coils resultedin a strong increase of the noise inside the barrel. This, how-ever, could be suppressed down to the measurable values ofthe field-free conditions, using self-made LC filters betweenthe current sources and the coils.

Outside the shielding chamber the modulated photodi-ode signal is amplified by transimpedance amplifiers (FemtoDLPCA-200) and read out with lock-in amplifiers (SignalRecovery 7280 DSP). With a frequency sweep of the B1-field across the Larmor frequency νL = γB0, where γ =3.5 kHz/µT is the gyromagnetic ratio of Cs, the resonancecurves of the magnetometer cells can be recorded. Two-channel function generators (Tektronix AFG 3102) are usedto supply both the reference of the lock-in amplifier as wellas the frequency of the B1 field. Its amplitude is tuned byvariable amplifiers (Stanford Research Systems SIM 983).

The characterisation system is completely computer-controlled. It allows for the variation of magnitude and di-rection of the magnetic field B0, the magnitude, the directionand the frequency of the radio-frequency field B1 as well asthe laser intensity. From the dependencies of the in-phaseand quadrature components Pin and Pqu on the detuningδ = ω − ωL of the actual B1 field driving frequency ω fromthe Larmor frequency ωL, their amplitudes and widths aswell as the steepness of the quadrature component are auto-matically extracted. The measured curves can be fitted verynicely with the formulas for Pin and Pqu given in [9]. The re-sulting relaxation rates of the spin polarisation, extrapolatedto zero laser power, are Γ0/2π = 5 Hz for cell #1 and 12 Hzfor cell #2, respectively. Furthermore, using formulae (2)and (3) and the measured conversion factor dPqu/df , theshot-noise limited magnetic field resolution results, givingoptimum sensitivities of cell #1 and #2 of Bn = 24 fT/

√Hz

and 57 fT/√

Hz, respectively. All these data correspond tothe ones specified in Fribourg for our two cells.

3 Noise investigation

3.1 Conventional magnetometer configuration

Corresponding to the discussion in Sect. 1, such noise datacould by far not be reached in a real noise measurement.Instead, values of up to Bn = 1 pT/

√Hz emerged. In the

following we started to analyse the effects, which contributeto this noise in a way described by Groeger et al. in [16]. Inorder to avoid redundancy, only results obtained with cell #1will be presented.

720 V. Schultze et al.

Fig. 3 Spectrum and signal-to-noise ratios S/N of the photo-currentnoise In around the Larmor frequency. Nsn, Nint and Next denote thenoise levels determined by the shot noise, the internal OPM noise andthe external noise sources, respectively

The magnetic field information is transferred to the Lar-mor frequency by the sinusoidal modulation of the light dueto the precessing spins of the Cs-atoms. Figure 3 shows aspectrum of the photodiode current around the Larmor fre-quency νL. At νL a “pedestal” is superimposed, which isdue to low frequency fluctuations of the magnetic field orany other external sources. One prominent such disturbanceis the 50 Hz line frequency, which is shown as a sidebandof the Larmor frequency. Most interesting, however, is theinternal noise level Nint, which is distinctly above the shotnoise Nsn. This noise only appears with the Cs cell in thelight path. Without cell no increase in the noise level aboveNsn is observed.

This extra noise was expected to be due to the conversionof frequency modulation (FM) noise of the laser source toamplitude modulation (AM) noise. Such conversion is pro-duced, when the light intensity is discriminated by the pas-sage through a resonant absorptive medium, in our case thecaesium vapour of our cells [17, 18]. To prove this expla-nation we slowly scanned the laser frequency across partof the Cs-D1 absorption line. The resulting photo-currentnoise in dependence on this detuning is shown in Fig. 4, to-gether with the D1 absorption of the reference cell, whichis normally used for the laser frequency stabilisation (seeSect. 2). Clearly, because of the laser frequency noise, aphoto-current noise arises, which follows the derivative ofthe absorption curve. Additionally, obviously because of theamount of laser frequency noise, the photo-current noisedoes not reach zero at the maximum of the absorption. Thisresult coincides with the investigations of this FM to AMnoise conversion process in [19].

Now, after knowing the origin of the extra noise, ways forits cancellation have to be looked for. An easy one would bethe choice of another laser system with less frequency noise.

Fig. 4 Transitions 6S1/2 F4 → 6P1/2 F3 and 6S1/2 F4 → 6P1/2 F4of the D1 absorption line and photo-current noise In, both in de-pendence on the detuning from the optimum absorption wave lengthλ = 894.6 nm. The photo-current noises of the two photo diodes (PD)after Cs cells #1 and #2 as well as of the subtracted photo currents(PD1–PD2) are shown

However, compared to such devices like the external cav-ity laser, the DFB laser does not suffer from mode-hoppingand the necessity of frequent retuning, what are strong argu-ments for its use in magnetometer applications. Another wayout might be a stabilisation of the laser frequency. However,as the aforementioned experiments show, such active stabil-isation itself needs permanent frequency modulation.

For these reasons we looked for another solution to can-cel the noise produced by the laser FM to AM noise conver-sion. The next chapter will report about our correspondingexperimental configuration and the achieved results, also incomparison to the usual setup.

3.2 New configuration using subtracted photo currents

The basic idea of our noise diminution is to pump two nom-inally identical Cs vapour cells with the same laser light andto subtract the photo currents of the two photodiodes. Due tothe same absorption process in the two vapour cells, corre-lated amplitude fluctuations and therefore a noise reductionshould be expected.

For atomic clocks and magnetometers, using coherentpopulation trapping (CPT) resonance, two connatural ideashave been published already [20, 21]. Both use two beams,coming from the same laser source, but with different po-larisation. After subtraction of the photodiode currents thesignal is left unchanged, but the noise originated in the cellis cancelled. In contrast, in our setup we use separate cellswhich receive equal laser light. This offers a good potentialfor multi-channel measurements.

In Fig. 5 various measurement setups are sketched, whichare used (or are feasible to use) for the investigation of the

Noise reduction in optically pumped magnetometer assemblies 721

Fig. 5 Sketch of various setups for the measurement of magnetic fieldswith two channels M1 and M2 and magnetic field gradient G: (a) usualsetup; (b) with subtracted photo currents and artificial magnetic fieldgradient �B0; (c) with an additional Cs cell just for photo-current sub-traction

noise properties and for the application in magnetic fieldmeasurements. Our investigations started with the config-uration highlighted in grey in Fig. 5c, where one cell (the“measurement cell”) is used for the magnetic field measure-ment M1 and one additional vapour cell (the “subtraction

Fig. 6 Various parameters of the measurement cell #1 in dependenceon the dc photo current Idc: The measurement cell’s own photo-currentnoise In(PD1) and the noise of the subtracted photo current In(PD1−PD2),both related to shot-noise limit Isn, the correlation between the twophoto currents, and the shot-noise limited magnetic field resolutionBn,sn, taken at optimum B1 field

cell”) exclusively for the photo-current subtraction. The re-sult is shown in the In (PD1-PD2) curve in Fig. 4. As canbe seen, the idea works well and the extra noise in the ab-sorption range is completely cancelled. As a consequence,we have the same noise floor for the whole frequency range,which, however, is

√2 higher than before because of the

quadratic addition of the shot noise of both photodiodes.Because the photo-current subtraction is the basis of the

desired noise reduction, it was investigated more in detail.Figure 6 shows the dependence of the photo-current noiseon the dc photo-current of the measurement cell with andwithout subtraction of the photo current of the subtractioncell. The photo-current noise is related to the shot noise ofthe measurement cell, calculated with formula (3). A strongincrease of the photo-current noise of the stand-alone mea-surement cell can be seen. With the photo-current subtrac-tion in the range between Idc = (1 . . .100) µA this noiseis decreased to the ultimate limit of

√2 times the shot

noise. Only outside this range, there are slight increases; forsmaller photo currents due to the photo detectors’ dark cur-rent noise and for higher currents due to the technical lasernoise [16]. The latter normally also should be cancelled bythe photo-current subtraction, however, we tuned the twophoto currents for optimum noise cancellation in the rangearound Idc = 10 µA. This balancing was slightly different(about 10%) from a pure dc current tuning.

Figure 6 also shows the correlation of the two photo cur-rents. It follows pretty well the course of the single cell’sextra noise. Clearly, the more the laser’s FM noise is con-verted to AM noise by the absorption in the alkali vapour,the more this noise rises above the shot noise, and the betterit can be cancelled by the photo-current subtraction. Whenthe extra noise dominates, the correlation is nearly equal to

722 V. Schultze et al.

Fig. 7 Photo-current noise I n after the measurement cell (PD1)and the subtraction cell (PD2) and of the subtracted photo currents(PD1–PD2) in comparison to the shot-noise limit Isn (top) and cor-relation of the two photo currents with and without fields (bottom)

100% and the noise cancellation works very well. Further-more, the region with the strongest noise increase due to thelight absorption in the alkali vapour coincides with the bestintrinsic magnetometer sensitivity. This is revealed by thedependence of the calculated shot-noise limited magneticfield resolution of the measurement cell on the dc photo cur-rent at the optimum B1 field of 3 nT. Each of the curvesin Fig. 6 shows an optimum for a dc photo current Idc ofabout 7 µA. Therefore, all the following measurements wereperformed with a laser power corresponding to that photocurrent.

The measurements of the photo-current behaviour asshown in Fig. 6 have been performed without magnetic fieldB0. From now on B0 ≈ 5 µT is applied in the shielding barrel(with B1 field at optimum of 3 nT), which yields a Larmorfrequency νL of about 17.45 kHz. Figure 7 (top) shows thephoto-current noise of the two cells and of the subtractedcurrent around νL. First, one can see that the separate sig-nals of the two cells have the same baseline value; a result

Fig. 8 Magnetic field noise of the magnetometer signal M1 in con-ventional measurement configuration (direct photo current) and withsubtracted photo current

of the photo-current balancing. For the measurement cellthe Larmor frequency and the sidebands of 50 and 150 Hzpower line and harmonics are superimposed. The subtrac-tion cell’s signal just shows a signal at the Larmor frequency.That there is one at all reflects a crosstalk from the measure-ment cell of about 3%, originated by the B1 field. The noisereduction by the photo-current subtraction again is promi-nent, also bringing the magnetic field low frequency noise(visible as the broad pedestal under the Larmor frequencypeak) to visibility. The noise floor of the subtracted photocurrent is a factor of about 1.5 higher than before, however.This increase is existing also for frequencies far away fromthe Larmor frequency. It emerges only, when the B1 fieldfrequency is matched to the Larmor frequency. Obviously,because of the additional information in the measurementcell’s photo current, the correlation between the two photocurrents is reduced. This can be seen in Fig. 7 (bottom). Be-sides the prominent correlation reduction around the Lar-mor frequency νL and at the power line frequencies (thecounter-acting 100% correlation directly at νL is due to theaforementioned cross talk) this overall impairment is visi-ble. Therefore, all in all with this magnetometer setup usinga second cell just for photo-current subtraction, the photo-current noise is reduced to twice the shot-noise limit of asingle cell.

All these features are reflected in the actual magneticfield noise measurements as shown in Fig. 8. Especiallyin the white noise region above 100 Hz, the noise reducesto 60 fT/

√Hz, what in fact is about two times the shot-

noise level. The photo-current subtraction is very attractivefor magnetic field measurements with more than one chan-nel. In this case, the photo-current of just one cell can beused for the subtraction of many measurement cells. For twomeasurement channels this setup is sketched in the complete

Noise reduction in optically pumped magnetometer assemblies 723

Fig. 5c with the ability to form a gradiometer G out of thetwo magnetometers M1 and M2. Because we only had twocaesium cells available, we could not perform this measure-ment, however. Instead, we used both cells at the same timefor magnetic field measurement and for photo-current sub-traction. Measurements with this setup (shown in Fig. 5b)were compared to the ones using the normal magnetic fieldand gradient measurement configuration of Fig. 5a.

The price of the combination of magnetic field measure-ment and photo-current subtraction with the same cells is anecessary artificial magnetic field gradient �B0, which hasto be introduced between the two magnetometer cells. Thisgradient is needed to assure an adequate distance betweenthe Larmor frequencies of the two cells. Because the sig-nals of both channels are incorporated in the same subtractedphoto current, just this separation guarantees the dedicatedoperation of each magnetometer electronics.

A small differential field is preferable, because the gradi-ent increases the line width of the magnetometer’s resonancecurve, thus reducing the conversion factor between magneticfield and measurement voltage. In our measurements weused a relatively large differential field of �B0 = 115 nT,corresponding to a frequency difference of 400 Hz. As aconsequence of the resulting conversion factor degradationfrom 72 to 50 mV/nT, the photo-current noise is now con-verted to about 90 fT/

√Hz in the magnetometer measure-

ment instead of 60 fT/√

Hz without gradient.In a gradiometer measurement, both magnetometers must

have the same conversion factor. Starting with open-loopmeasurements using the steep part of the quadrature sig-nal, tuning of the conversion factors means impairment ofthe better one. Therefore, we increased the B1 field strengthof cell #1 from 3 nT to 25 nT, ending up at the magneticfield resolution of cell #2. Taking its measured shot-noiselimited magnetic field noise and taking also the degradationdue to the magnetic field gradient into account, a shot-noiselimit of the magnetic field resolution of the two magnetome-ters of Bn = 160 fT/

√Hz comes out. In closed-loop oper-

ation the conversion factor can be tuned independently bythe feedback strength, leaving the noise-limited resolutionuntouched.

In Fig. 9 the measurements in the gradiometer config-uration are summarised. Within each operation mode (di-rect photo-current or subtracted photo current) the open-loop measurements are almost identical for the two magne-tometers (except, of course, when different magnetic fieldsexists at the two places of the cells, as for example around50 Hz), because the intrinsic noise of magnetometer #1 wastuned to the worse #2. For magnetometer and gradiometermeasurement we achieve the desired improvement by thephoto-current subtraction. For higher frequencies, where themeasurable magnetic field gradient is below the gradiometernoise, the gradiometer signal is larger by a factor of

√2 than

Fig. 9 Magnetic field noise of the two magnetometer signals M1 andM2 as well as the gradiometer G in conventional measurement con-figuration (direct photo current, cf. Fig. 5a) and with subtracted photocurrent (cf. Fig. 5b), all measured in open-loop configuration

the magnetometer values, because the two intrinsic noisesources add. For frequencies below several Hertz the gra-diometer reduces the magnetic field noise, because here ex-ternal magnetic field noise sources dominate.

4 Conclusion

The impairment of the intrinsic noise-limited magnetic fieldresolution of optically pumped magnetometers by the pump-ing laser source frequency noise, converted to amplitudenoise by the absorption in the magnetometer’s alkali vapour,can be reduced by a special measurement arrangement us-ing two such vapour cells. They are illuminated with lightcoming from one common pumping laser source. Due to thenearly complete correlation of these two beams (except forthe superimposed magnetic field informations, of course),in a subsequent subtraction of the two photo signals, this ex-tra noise can be mostly eliminated, leaving a noise floor ofonly two times the limit, given by the shot noise of a singlevapour cell.

In this setup, the two vapour cells can be used at thesame time to form a magnetic field gradiometer. Becauseboth magnetometers, whose magnetic field measurementsignals will be subtracted later on, use the same photo sig-nal containing both Larmor frequencies, the price of thismethod is the necessity of an adequate magnetic field gradi-ent, which securely separates these two Larmor frequencies.Such a gradient may degrade the magnetic field resolutionof the magnetometers. For not too large gradients, the gainin noise-limited resolution will clearly overbalance this sac-rifice, however.

The gain of the subtracted photo currents is completelyunimpaired for pure magnetic field measurement, using the

724 V. Schultze et al.

second cell just for shot-noise approach. This gets most ap-pealing for the setup of optical magnetometer arrays. Herethe pumping laser light can be divided into many beams,pumping all vapour cells at once. One of the cells will not beused for magnetometer measurement, but only for the lasernoise conversion. The photodiode signal from this channelcan be subtracted from the photodiode signals from all otherones, enabling a magnetic field measurement resolution onlyscarcely above the shot-noise limit.

Acknowledgements We thank the group of Antoine Weis at the Uni-versity of Fribourg in Switzerland very much for their training, howto work with optically pumped magnetometers and how to set up agood characterisation system. Especially the manifold explanations byGeorg Bison, now at the University Jena, Germany, are thankfully ac-knowledged.

References

1. H. Koch, IEEE Trans. Appl. Supercond. 11, 49 (2001)2. R. Wynands, A. Nagel, Appl. Phys. B 68, 1 (1999)3. I.K. Kominis, T.W. Kornack, J.C. Allred, M.V. Romalis, Nature

422, 596 (2003)4. W.E. Bell, A.L. Bloom, Phys. Rev. Lett. 6, 280 (1961)5. D. Budker, W. Gawlik, D.F. Kimball, S.M. Rochester, V.V.

Yashchuk, A. Weis, Rev. Mod. Phys. 74, 1153 (2002)

6. A.L. Bloom, Appl. Opt. 1, 61 (1962)7. E.B. Alexandrov, M.V. Balabas, A.K. Vershovski, A.E. Ivanov,

N.N. Yakobson, V.L. Velichanskii, N.V. Senkov, Opt. Spectrosc.78, 292 (1995)

8. S. Groeger, G. Bison, J.-L. Schenker, R. Wynands, A. Weis, Eur.Phys. J. D 38, 239 (2006)

9. G. Bison, R. Wynands, A. Weis, J. Opt. Soc. Am. B 22, 77 (2005)10. D. Budker, M.V. Romalis, Nat. Phys. 3, 227 (2007)11. M. Auzinsh, D. Budker, D.F. Kimball, S.M. Rochester, J.E. Stal-

naker, A.O. Sushkov, V.V. Yashchuk, Phys. Rev. Lett. 96, 173002(2004)

12. J.L. Sorensen, B. Julsgaard, Ch. Schori, E.S. Polzik, Spectrochim.Acta B 58, 999 (2003)

13. E.B. Alexandrov, M.V. Balabas, A.K. Vershovski, A.S. Pazgalev,Tech. Phys. 49, 779 (2004)

14. N. Castagna, G. Bison, G. Domenico, A. Hofer, P. Knowles,C. Macchione, H. Saudan, A. Weis, Appl. Phys. B 96, 763 (2009)

15. A. Chwala, V. Schultze, R. Stolz, J. Ramos, R. IJsselsteijn, H.-G.Meyer, D. Kretzschmar, Physica C 354, 45 (2001)

16. S. Groeger, A.S. Pazgalev, A. Weis, Appl. Phys. B 80, 645 (2005)17. J.C. Camparo, J. Opt. Soc. Am. B 15, 1177 (1998)18. J. Kitching, H.G. Robinson, L. Hollberg, S. Knappe, R. Wynands,

J. Opt. Soc. Am. B 18, 1676 (2001)19. J.G. Coffer, M. Anderson, J.C. Camparo, Phys. Rev. A 65, 033807

(2002)20. M. Rosenbluth, V. Shah, S. Knappe, J. Kitching, Opt. Express 14,

6588 (2006)21. V. Gerginov, S. Knappe, V. Shah, L. Hollberg, J. Kitching, IEEE

Trans. Instrum. Meas. 57, 1357 (2008)