principles of operation of the rubidium vapor magnetometer

Principles of Operation of the Rubidium Vapor Magnetometer

Arnold L. Bloom

This paper discusses some of the basic problems involved in designing and using a magnetometer em-ploying optical pumping. Particular attention is given to magnetometers of the self-oscillating type;i.e., those that are analogous to masers in that the resonant properties of the spin system itself are used to

sustain continuous oscillation at the resonant frequency. Among the topics treated are amplitudevariations with orientation, sensitivity, behavior in extremely weak magnetic fields, and response torapid field changes.

One of the most important of the practical applica-tions of optical pumping has been to the precise meas-urement of weak magnetic fields. To this end, severalmagnetometer systems have been developed usingeither alkali metal vapor or triplet metastable heliumas the rf resonant element. A number of these devicesare currently in use for measurement of the geomagneticfield at or near the surface of the earth, and severalrubidium vapor magnetometers have been flown inspace vehicles. One of these latter instruments suc-cessfully measured the interplanetary field out to adistance of 10 earth's radii. This paper discusses thetheoretical basis of these Rb space magnetometers,although emphasis is also placed on those problemsthat arise in operation at the surface magnetic field ofabout 0.5 gauss. Much of the theory developed hereapplies to metastable helium magnetometers as well. *

1. Fundamentals

The basic theory around which all these instrumentsare designed was presented in earlier papers by Deh-melt, ' and by the author and W. E. Bell. 2 All of thesesystems share the following apparatus in common:A light source producing an intense collimated beam ofresonance radiation, 3 a circular polarizer, an absorption

The author is with Spectra-Physics, Inc., Mountain View,California.

This work was supported in part by the Office of Naval Re-search. The work described in Section V of this paper was sup-ported by the Air Force Special Weapons Center, Kirtland AirForce Base, New Mexico, and carried out at Instrument Division,Varian Associates, Palo Alto, California.

Received July 1961.

* For a more detailed comparison of these two types, see P. L.Bender, Compt.-rend de 9 Colloq. Ampere, Librairie Payot,Geneva, 1960.

cell containing the vapor to be optically pumped, aradio-frequency coil to produce resonance in thepumped vapor, and a photocell to monitor the trans-mission of the light. Also under certain circumstancesit may be necessary to use a filter capable of eliminatingsome of the fine structure components of the resonanceradiation prior to its entering the absorption cell. Adetailed discussion of the conditions under which such afilter must be used will not be undertaken here, exceptto point out that it depends on the pressure of thebuffer gas, if any, that is used to reduce the rate ofcollisions of the atomic vapor with the walls. Therubidium magnetometers described here normallyemploy a fairly high pressure buffer gas (3 cm Hg orhigher) of neon and a filter is needed to pass the reso-nance radiation at X 7948 and reject X 7800. An inter-ference filter has been developed for this purpose* whichtransmits approximately 80% of the X 7948 radiationfor rays whose deviation from the perpendicular is asgreat as 150.

The change in optical transmission of the spinsystem upon application of a resonance rf field has beendiscussed earlier" 2 and depends in detail on the direc-tion of the incident light beam relative to the constantmagnetic field. The behavior of the spin system canbe described by the three variables M, My, and M, ofBloch's equations for a spin system,4 and the signalpresent at the photocell is proportional to M0 , where nis the direction of the light beam relative to the magneticfield. More specifically, the types of signals that maybe observed may correspond either to Mz, giving rise toa secular change in light intensity, or to Mz or M,which manifests itself as a high frequency light modula-

* Manufactured by Spectrolab, Inc., Los Angeles, California.

January 1962 / Vol. 1, No. 1 / APPLIED OPTICS 61

tion synchronized with the driving rf field. These twotypes of signals can be readily separated in the elec-tronics following the photocell by virtue of theirdifferences in frequency, and make possible a varietyof systems in which the photocell signals can be em-ployed to give information as to the value of the reso-nant frequency and hence the magnetic field.

It is well known that all magnetometers employing aLarmor resonance have a resonant frequency directlyproportional to the applied magnetic field, independentof the angle made by the apparatus relative to thedirection of the field. However, the signal amplitudemay be a function of this relative orientation. In all ofthe presently developed optically pumped magnetom-eters, circularly polarized radiation is employed bothas the pumping agent and as the detecting agent.From the symmetry properties under rotation inherentin circular polarization the following angular de-pendence applies: (1) The secular pumping processvaries as cosO; (2) detection of the secular light modula-tion M varies as coso; (3) generation of free spinprecession varies as sinG; and (4) detection of theLarmor frequency modulation M., or My varies as sin,where 0 is the angle between the polar vector definedby the polarized light and the magnetic field Ho. Thetypes of angular dependence that may be observed inthe magnetometer, as a system, may therefore dependon sin2 0, cos20, or sinG, coso, depending on what com-binations of pumping and detecting mechanisms areused. Now, for space exploration purposes, one has toassume that the light beam vector may have an equalprobability of being in any position relative to themagnetic field. If the signal S is defined as S = whenthe instrument is in its most favorable orientation, thenwe can calculate the probability (dP/dS)AS that thesignal will have an amplitude between S and S + AS.It is calculated from the following:

the instrument having a relatively unfavorable orienta-tion and weak signal. Until recently, no practical

2

C,,a

01-oa

0.5S

1.0

Fig. 1. Differential probability of obtaining a signal of amplitudeS. Curve A: S = cos'o and S = sinO coso. Curve B: S = sin'o.

instruments had been suggested that might have aresponse given by curve B. However, the recent ob-servation of optically driven spin precession,5 which hasa sin2G dependence, makes such a magnetometerfeasible6 and suggests a close examination of the be-havior and requirements of such magnetometers.This is not attempted in this paper.

11. Possible Systems

Three types of systems have been developed intopractical magnetometers.

The first of these7 is shown in Fig. 2, and employs the

dP(o)/do = sin@,

dP _ dP(o)/dodS dS(O)/do

right-hand side is solved in terms of S. The

dP 1

dS 2/S

for S cos2 0 or S = sinG cosG;

dP 1

dS 2V(1- S)

for S sin2 0.

These results are plotted in Fig. 1. All of thedevices discussed here follow curve A and due allowancemust therefore be made for the high probability of

QUNY LARMRFREQUENCY FREQUENCY COUNTER OSCILLATOR FREQUENCY

CONTROL SIGNAL

Fig. 2. Block diagram of magnetometer employing M signaland phase detector to stabilize a local oscillator at the Larmor fre-quency. Minor variations of this scheme may employ magneticfield sweep, low-frequency offset oscillators, or servo loops re-sponsive only within a certain range of frequencies.

62 APPLIED OPTICS / Vol. 1, No. 1 / January 1962

then

and theresult is

DIRECTION OF MAGNETIC FIELD OR

VAPORRESONANCE

M, signal. A small frequency modulation is applied tothe local rf oscillator to sweep the rf back and forththrough resonance. The photocell signal then hasstrong components at even harmonics of the modula-tion frequency if the sweep is centered about theresonance. Any deviation gives rise to a fundamentalcomponent which is phase detected and used to servothe tracking rf oscillator. The angular dependence ofthe signal varies as cos20. This type of system does notplace severe restrictions on the performance of thephotocell or its amplifier, and it employs a type ofelectronic detection system that is well known in theart of magnetic resonance. It has been widely em-ployed to demonstrate the operation, in principle, ofoptically pumped magnetometers. However, for air-borne and space applications, where power and weightrequirements are at a premium, this type of systemdoes not possess the advantages of extreme simplicityand wide dynamic range that are characterized by thenext two systems to be described. Accordingly allof our present work in Rb vapor magnetometers isconcentrated on these two latter types of systems.The remainder of this paper will be concerned primarilywith them.

The next system to be described will be designated asthe "single cell self-oscillator" and is shown in Fig. 3.

DIRECTION OF +900 PHASE SH I FT,MAGNETIC FIELDS rRF FIELD TO LIGHT

/ MODULATIONINTERFERENCE RUIU

FI TVERR PHOTOCELL

RUBIDIUMLIFIERLAM I

CIRCULAR IPOLARIZER

ISHIFTIOU TPUTSIGNAL

Fig. 3. Self-oscillator type of magnetometer employing a single

absorption cell.

Here the photocell observes the signal corresponding toMz, which is at the driving radio frequency, and whosephase relative to the driving rf field varies near reso-nance in much the same way as the phase of the circu-lating current in a tuned resonant circuit. The photo-cell signal is fed back through suitable amplifiers andphase shifters to the rf coil and maintains a closed loopthrough which information can be transmitted onlywithin the resonance line width. This system willoscillate spontaneously at the resonant frequency if the

U) .

>0. 0~ ~~~~~=.

0 10 20 30 40 50 60 70 80 90e DEGREES

Fig. 4. Signal amplitude or signal-to-noise ratio of the sf-oscillator as a function of 0. These curves differ from the simplesino coso dependence in that they include the effect of variationof the perpendicular component of the rf field. K = yHa( T1T2)'1

where 2H0 is the peak value of the alternating rf field along thecoil axis.

gain of the loop is unity and the sum of all phase shiftsin the loop is zero. In order to reduce the number ofaxes of symmetry to a minimum, the rf coil is woundcoaxial with the light beam so that only the one angle0 suffices to describe all variations in performance suchas are shown in Fig. 4. (If the rf coil axis were per-pendicular to the light beam, then the phase shift wouldvary with rotation of the instrument about the lightbeam axis.) The component of rf field Hi perpendic-ular to Ho defines the x-direction, and correspondinglythe alternating signal observed by the photocell alwayscorresponds to Ma, rather than to M, or some linearcombination. Bloch's equations predict a 90° phaseshift between Hi and M. at exact resonance, and this isthe reason for the 900 phase shifter.

The system just described has the following disadvan-tage: In the angular dependence of the signal as givenby sinG cosO or in Fig. 4, the change in sign whichoccurs at 0 = 900 must be taken literally. It corre-sponds to the fact that if the instrument is properlyphased for 0 < 0 < 900, then it is wrongly phased for900 < 0 < 180°. An engineering solution to thisproblem has been obtained by including, in the feed-back loop, a "signal searcher" which periodicallyinterchanges the connections of the rf coil until oscilla-tion is established. However, a much more elegantsolution is that of the third system to be described,shown in Fig. 5, which will be designated as the "two-cell self-oscillator system." This system consists oftwo identical optical systems in which one photocelloutput is used to drive the rf coil of the complementaryabsorption cell. It may be described most simply bysaying that each optical system acts as a 900 phaseshifter for the other. Here the sum of the phase shiftsof the entire feedback loop can be made zero without


Fig. 5. Self-oscillator employing two absorption cells. If thetwo optical systems are placed back-to-back, as shown, then thetwo circular polarizers should be of the same sense (e.g., right-handed) to preserve symmetry upon 1800 rotation.

insertion of electronic phase shifters and the device hascomplete symmetry for 1800 rotations, so that it willoscillate spontaneously in all directions except 0 = 0or 90°.

Both of the above types of instruments have beenflown in space vehicles.

Ill. Theoretical Sensitivity

For our purposes we are concerned with two aspectsof sensitivity: (a) the smallest absolute value ofthe field that can be measured by the apparatus (im-portant for interplanetary field measurements) and (b)the smallest increment in magnetic field, at some rea-sonable ambient level, which can be measured.

The smallest absolute value of field that can bemeasured by any Larmor resonance apparatus isroughly equal to the rf resonance line width expressedin magnetic field units, since at smaller values theresponse is no longer that of a resonant system. Thispoint is elaborated on in Section IV, where the prob-lems involved in reaching the limit are defined moreprecisely. The total line width r of the resonance isgiven in general by

r = r + rt

where r represents the effect of absorption of resonanceradiation and t, due to thermal relaxation, is theminimum line width that is obtainable in the limit ofzero light intensity (and therefore in the limit of zerosignal-to-noise ratio!). For the alkali vapors, rt hasbeen found' to be of the order of 0.03 cps. For Rb87,which has as high a g-factor as can be found in any ofthe alkali isotopes, the gyromagnetic ratio is 700 kc/sper gauss so that the above number corresponds to aminimum magnetic field of less than 10-7 gauss. Asa practical matter, however, including line broadeningfrom the light, the minimum measurable field appears

to be about 2.0 X 0-5 gauss. Metastable helium,whose gyromagnetic ratio is 2.8 Mc/s per gauss, ap-pears to have a minimum line width of about 103 cpscorresponding to 40 X 0-5 gauss.

The sensitivity of the instrument for small incre-ments of field depends in part upon line width, and inpart upon actual signal-to-noise ratio for the resonancesignal itself. Because of the success of theoreticalsignal-to-noise calculations in nuclear and electronspin resonance, it is attractive to attempt the same sortof calculation for an optically pumped system. Un-fortunately, the problem in this case is made difficultby the large number of variables whose effect on per-formance is difficult to assess experimentally, much lesstheoretically, and because comparison with a standardis not available. For a given configuration we mightproceed as follows. If we start with the assumptionthat the light source is perfectly incoherent, and thatthe photocell has unity quantum efficiency and zerodark current, then the noise current N is given by

N = (2e2nB)1/2

where e is the electronic charge, n is the number ofphotons per second, and B is the effective bandwidth;in this case B = . Since r is proportional to n, wehave

N (rrr)l/2.

The relative signal current, S is calculated in formula(1Oa) of I and can be written as

S c rr2/r.

The sensitivity of the instrument for small changes infield in its optimum orientation is then given by

S rr3/2

Nr (rr + rt)5

2.

This has a maximum at r, = /2rt, suggesting operationwith narrow lines and weak light. In practice, how-ever, other sources of noise are also present and it isusually found desirable to operate with the highestpossible light intensity consistent with other require-ments. Typical operating conditions, for moderatelystrong magnetic fields and illumination, are approx-imately as follows: Average photocurrent, about 1.0X 10-4 amp; noise, N = 1.65 X 0-9 amp; signal,about 1% of average photocurrent or about 1.0 X 10-6amp; line width at this light intensity, about 100 cps.The minimum detectable change in frequency, Nr/S,is then about 0.025 cps corresponding to a field changeof 3 X 10-8 gauss for Rb8 7. This is comparable toexperimentally determined results and suggests thatphotoelectron shot noise is indeed the limiting factorfor this particular configuration. At lower light inten-sities, dark-current or amplifier noise seems to pre-dominate. This might be avoided by increasing the


diameter of the optical system from the present 5cm, while maintaining good optical geometry sothat the size and brightness of the image on the photo-cell is comparable to that now available. An increasein diameter, however, is incompatible with size andweight limitations for space applications.

IV. Perturbations from the Larmor ResonanceCondition

Up to now, we have specified that the oscillationfrequency of either of the two self-oscillating magne-tometers is actually the Larmor (angular) frequencyso = yHo. However, we must be concerned about thepossibility of deviations from this condition, for tworeasons. First, we demand that the magnetometermeasure field increments much smaller than the reso-nance line width. Since the usual first-order perturba-tion theory leading to a description of resonance effectsis good only to within orders of magnitude of the linewidth, it is therefore apparent that we must look forhigher order effects. Second, operation of the magne-tometer in extremely weak fields may bring us close tothe condition where the spin system is no longerrecognizable as a resonance system, and in that case wemust be concerned as to exactly how far we can pushthe operation of the system toward zero magnetic field.We shall consider the effect of variations of phase in thefeedback loop, and then go on to effects intrinsic to thespin system that have not been discussed so far.

Phase Relationships

In the vicinity of resonance, the amplitude of thereceived signal M_ is approximately constant (it ismaximum by definition), but the phase varies asctn-' (T2zcA), where 1/7rT2 is the line width (in or-dinary frequency units) and Awc is the deviation fromresonance.* It is clear from this that even with thenarrowest lines that are conveniently available, say 15to 100 cps, the phase of the feedback loop and of thereceived signal M., must be held constant within 0.10or better if the magnetometer is to retain its potentialsensitivity. Most of the problems that are experiencedin practice, in maintaining correct phase relationships,are electronic ones that will not be of concern here.We will mention one additional problem-that of effectsof misorientation of the mean axis of the rf coil. If thecoil axis is not exactly parallel to that of the light beam,then the coaxial symmetry which was discussed earlieris partially destroyed and orientation effects can showup in the form of spurious phase shifts. The maximumpossible shifts are shown in Fig. 6. The figure showsthat serious effects occur only when 0 is small; however,

* From this point on, the mathematical notation is identical tothat employed in I except that Si, S2 are replaced by the moreconventional symbols T, and 7'2. T, T2 are relaxation timesincluding lifetime-shortening effects of the light.

under such conditions even a small misorientation anglecan give rise to a large error. Special care is thereforerequired in winding the rf coil about the absorption celland maintaining it rigid with respect to the externalsupports, also in maintaining an optical system withwell-defined axis of symmetry despite the broadness ofthe source.

Higher Order Terms in Bloch's Equations

In I there was developed a solution to the equationsof motion of a spin-l/ 2 optically pumped system basedon Bloch's equations. It was pointed out there that,although the equations held strictly only for spin-'/ 2particles, it was hoped that they might find more gen-eral application for the more complicated spin systemwhich actually represents a Rb atom. Experienceunder a wide variety of conditions has shown that theseequations do indeed give a quite accurate representationof the behavior of the signals, except for some specificinstances where the hyperfine coupling results in amultiplet structure. These situations are dealt withlater. We are concerned here with those deviationsfrom the normal resonance conditions that can bepredicted within the scope of Bloch's equations. Theseeffects are particularly important in very weak fields.

In I we developed a Fourier expansion of Bloch'sequations in terms of components at the drivingfrequency and its harmonics. The expansion is asgiven overleaf

80

0

60

PHASE 50SHIFT

DEGREES 40 -

30 lo

00 10 20 30 40 50 60 70 80 90

19 DEGREES

Fig. 6. Phase shift in the photocell signal as a function of orien-tation angle, 0, shown for three misorientation angles of the rf coilaxis relative to the optical axis.


Alz + iy = f Oe fl = -D.

Of the various coefficients, fl, f-i and m,(= m-1 *) areat the driving frequency itself and can therefore alltake part in the signal contained in the feedback loop.The other terms can be considered as perturbationscontributing to the final solution, and of these only theterms with n < 2 will be different from zero exceptunder the most extreme conditions. Solution of Eqs.(14a) and (14b) of I for a weak H1 field (m0 M Mo)gives the following for ilio,, the magnetic momentoscillating at the driving frequency. With the phasechosen by II = 2Hcos wt we have:

31'-o = Aix sing + (M,)i cos 0,

YizI1AJIY2 - 2 + ( + )2 + -2 + ( cO o Co

-yHMor 1n1t1T2 T2-2 + (W + U)2 T 2-2 + (o - )sin@t2

(M - 2yH IT1T2 WoMo'(coswt - coT2 sinwt)(1 + T 2,0

2 )(1 + T22CO02)

The M part of the equation consists of the usualresonance expression plus additional terms that takeinto account the fact that the alternating rf field reallycontains two frequencies, +w and -co, and each ofthese must act independently upon the spin system.The extra terms cannot be ignored in weak fields.They give rise to a deviation in the apparent Larmorfrequency, in that the frequency for which there is a900 phase shift is given by

C = (1/712)2 + Wo2] 12

The effect may be of importance even when the fielddiffers from zero by several line widths. It represents,however, a fixed correction that can be included if T2 isknown.

Simultaneous with the shift in phase relationships isa change in signal amplitude. The signal amplitudeat the frequency at which there is 900 phase shift isproportional to wo [(1/T2)2 + W02 ] '/2 if H, is held fixedand more nearly proportional to W0

2 if H < Ho. Itis apparent from this that one can get self-oscillation infields much smaller than a line width if signal-to-noiseis available; however, it is also clear that there will notbe much sensitivity for variations of the "true" Larmorfrequency in this case.

The effect of the (M,)1 term is to introduce additionalspurious phase and resonance amplitude information,which varies in a complicated way with and withfrequency. No detailed attempt has been made tostudy the effect of this perturbation analytically, exceptto note that it is small for magnetic fields greater thanabout one line width.

The effect of an rf field not exactly perpendicular toHo is to introduce, in the above equations, a correctionterm to Mo proportional to (1 + coo2T 2

2) -. However,it does not change the above results appreciably.

The Boch-Siegert effect is a well-known effectdepending upon higher order perturbation terms in-volving Hi. It can be obtained in the above formalismby including m2 and m- 2 in the closed solution for f-Iand gives an apparent decrease in resonant frequencygiven by

= yH 2 /4Ho.

Its effect can be maintained moderately small, althoughperhaps not negligible, by always maintaining H1 << Ho.

To summarize the above results, if the oscillationfrequency of the self-oscillator is greater than the linewidth, then it represents the true Larmor frequencywith possible small and known corrections. In a givenfield (such as 0.5 gauss) these corrections are the smallerthe narrower the line width. For fields less than aboutone line width, however, the oscillation frequency de-pends in a complicated way on orientation angle andother variables but does not in general become lessthan the line width. An output frequency close to theline width is therefore suspect unless the exact operatingconditions of the instrument are known.

Effects of Line StructureThe hyperfine splitting in the alkali atoms gives rise

to an incipient Back-Goudsmit effect, which is mani-fested as a splitting of the resonance line into 2F + 1components, the separation between components de-pending upon the hyperfine constant and being pro-portional to H0

2. It turns out that for virtually allstable alkali isotopes, this splitting is negligible forHo < 0.1 gauss, but is relatively large at Ho = 0.5gauss. Table I gives the details of this structure for afield of 0.5 gauss.

Table I. Splitting of the Zeeman Resonance in a Field of0.5 Gaussa

Nlm-berof -ynHo/7r

lines Separation between for21 adjacent lines H = 0 5

Isotope + 2 (cps) (10 - gauss) (cps)

Na2 3 5 138 19.8 1126K3 9 5 531 76 199K 4 1 5 1005 144 109Rb85 7 36 7.7 411Rb87 5 36 5.2 1393Cs13 3 9 6.7 1.9 558

a Only the hyperfine level F = I + J is considered here; theF = I - J level usually gives much weaker signals, for reasonsthat are not entirely clear. The column y0Ho/7r gives the sepa-ration between the centers of the (I + J) and (I - J) patterns.


In the presence of this structure, the designer of themagnetometer can do one of two things. He can eitherattempt to operate on only one of the individual com-ponents, hoping that the presence of the others will notperturb the operation appreciably, or he may attemptto operate under conditions of a relatively broad line inwhich case the structure is almost completely submergedunder the over-all resonance. Magnetometers designedaccording to the first principle have been made tooperate in the laboratory, but operation by the secondmethod is much to be preferred in most cases, since theline width of a hundred cycles or so is compatible withgood signal-to-noise ratio.

The line shape obtained by smearing over an unre-solved structure is bound to be unsymmetrical in arather complicated way, depending on the matrix ele-ments for the various individual transitions and otherconsiderations. However, this asymmetry should in-vert itself when the magnetic field is reversed in direc-tion, since this is equivalent to interchanging the signsof all magnetic quantum numbers. It is apparent thata single-cell self-oscillating magnetometer in Ho = 0.5gauss may therefore exhibit a fairly large orientationdependence as is varied between 0 and 1800. For-tunately the double-cell self-oscillator magnetometeravoids this situation, as it does many other situations ofasymmetry, provided that the sense of circular polariza-tion of the light beams is chosen to be opposite asobserved by a single observer (Fig. 5). In this way,the two components of the dual oscillator tend to"pull" themselves together to a common median fre-quency, which is also the center of symmetry of the twoline shapes. The requirement of perfect mirror sym-metry, however, requires also that the behavior of thesystem, i.e., gas cell absorption, photocell efficiency,amplifier gain, etc., be identical in both systems.

V. Response to Rapid Changes in MagneticField

One of the interesting characteristics of the self-oscillator magnetometer is its ability to respond torapid and large excursions in magnetic field value. Ingeneral, a freely precessing spin follows faithfully allinstantaneous changes in field; questions then arise asto (a) whether these changes can be detected in theoutput, and (b) whether the effect of the feedback loophas any effect on the instantaneous motion. Withregard to the first question, the output will be a faith-ful representation of the input provided that theamplifiers are of sufficient bandwidth to accommodateall of the various frequency components generated dur-ing the frequency excursion. As for the second ques-tion, it can again be shown that the feedback loop willremain tightly locked as long as the signals are withinthe amplifier bandwidths; however, it is not necessarythat this be so. As long as the time interval of the ex-

cursion is less than the T2 of the precessing spin system,then the rf in the feedback effectively has no drivingforce on the spins during this time interval, and thespins are in free precession as if the rf were not there.(For longer excursion times the bandwidth required,which is inversely proportional to the excursion time, iscertainly adequate.)

We will now support the statement that the value ofthe rf field in the feedback loop is never so great as toaffect the spin precession in a time less than T2. Thetime required for the rf field to interact with the spinsystem is approximately (yH,)- . If one attempts tooperate the oscillator with yHlT2 > 1, one finds that avery undesirable amplitude variation or "squegging"occurs, in which the oscillation alternately builds upand quenches at a rate roughly proportional to H1.The effect was first observed experimentally and thenit was found, on a theoretical basis, that effects of thissort can be expected in all quantum resonance systemsinvolving feedback, as for example in masers. A de-tailed treatment of the problem has been given bySinger and Wang.' It is sufficient to remark here onlythat the response of the spin system with regard to thefeedback loop is similar to that of a spin system ina maser (in which case the feedback loop consists ofthe radiation reaction inside the cavity). Since the"squegging" is very undesirable, gain controls must beintroduced in the magnetometer amplifiers to keep therf field down to a safe value, and this also automaticallyeliminated rapid transient perturbations of the rf onthe spin system.

A more detailed study of the rapid response character-istics of the magnetometer was made by simulatingboth single- and double-cell magnetometers on ananalog computer. In this study the time developmentwas started with the spins in equilibrium with thedriving rf field corresponding to continuous oscilla-tion. A transient was then introduced equivalent tomaking Ho first slightly negative and then highlypositive in a short time interval. An example of sucha run is shown in Fig. 7. It can be seen there that thequantity given by do/dt, where

1p = tan-1(M,/Mz)

does indeed represent a faithful description of theinstantaneous Larmor frequency. However, if thereceived information consisted of either M or yalone, then it might be difficult to resynthesize theexact frequency and phase variations, particularlywhen the field reverses direction. There is therefore agreat advantage in two-phase relative to single-phaseoutput information for this type of situation. Inthis case, the double gas cell magnetometer has adefinite advantage over the single cell magnetometerin that two-phase information is actually available fromthe outputs of the two photocells.


Fig. 7. Analog computer curves showing response of self-oscillator system to relatively large and rapid magnetic fieldtransients.

The above comments pertain to the situation inwhich the magnetic field transient consists of a vectorparallel to the average magnetic field Ho. If this is notthe case, then the behavior of the self-oscillator issomewhat more complicated, but to a certain extent, byemploying two-phase output, one can obtain someinformation as to both the magnitude and the directionof the transient. Under severe situations, a transientat right angles to Ho can quench the oscillations com-pletely, in which case they will require the normal periodof (yH) 1 in which to build up.

VI. Conclusions

Starting from a discussion of optically pumpedmagnetometers in general, we have concentrated onthe two types of self-oscillating rubidium magnetome-

R E F E R E E S

ters represented by the single cell and double cellsystem. It has been shown that these systems have anintrinsically extremely high signal-to-noise ratio, thepossibility of a wide dynamic range, an orientationdependence (with regard to signal-to-noise ratio) whichis no worse than other types, and an ability to respondto, and to give data on, extremely rapid field fluctu-ations. In addition, the double gas cell system has theadvantage of a north-south orientation independence,a symmetrized line eliminating possible second-orderheading error effects, and the ability to present two-phase information. Magnetometers of both the singleand double gas cell types have been flown in spaceexploration missions and have demonstrated theirusefulness. It is expected that these instruments willfind increasing use both for outer space and for geo-physical explorations.

References

1. H. G. Dehmelt, Phys. Rev. 105, 1487, 1924 (1957).2. W. E. Bell and A. L. Bloom, Phys. Rev. 107, 1559 (1957),

hereinafter referred to as I.3. W. E. Bell, A. L. Bloom, and J. Lynch, Rev. Sci. Instr. 32,

688 (1961).4. F. Bloch, Phys. Rev. 70, 460 (1946).5. W. E. Bell and A. L. Bloom, Phys. Rev. Letters 6, 280

(1961).6. R. G. Aldrich, Thesis, U.S. Naval Postgraduate School,

Monterey, 1961 (unpublished).7. T. L. Skillman and P. L. Bender, J. Geophys. Res. 63, 513

(1958); L. Malnar and J. P. Mosnier, Ann. Radioelec. 16,No. 63, 3 (1961).

8. F. Bloch and A. J. F. Siegert, Phys. Rev. 57, 522 (1940).9. J. R. Singer and S. Wang, Phys. Rev. Letters 6, 351 (1961).

The following people referee papers submitted to APPLIED OPTICS from time to time,and the Editors wish to acknowledge with gratitude this service:

H. H. Allen, Jr., G. F. Aroyan, A. V. Baez, J. G. Baker, S. S.Ballard, R. B. Barnes, E. Barr, E. S. Barr, A. M. Bass, J. R. Ben-ford, L. E. Bergstein, L. S. Birks, F. F. Byrne, H. Cary, R. M.Chapman, L. H. Chasson, K. C. Clark, G. W. Cleek, V. J. Coates,W. A. Craven, Jr., A. Danti, J. A. Dobrowolski, K. Dressler, W.G. Driscoll, S. Q. Duntley, D. F. Eggers, Jr., R. S. Estey, J. W.Evans, J. A. Eyer, W. Fastie, D. P. Feder, J. S. Garing, N.Ginsburg, G. E. Gross, F. F. Hall, Jr., A. Hardy, L. W. Herscher,M. Herzberger, I. C. Hisatsune, R. E. Hopkins, G. A. Hornbeck,E. 0. Hulburt, R. S. Hunter, W. L. Hyde, J. A. Hynek, S. S.Impiombato, K. Innes, J. A. Jamieson, L. D. Kaplan, J. W. Kemp,K. G. Kessler, J. I. F. King, R. Kingslake, W. F. Koehler, N.Kriedl, E. W. Kutzscher, J. Lambe, H. Levinstein, E. V.

Lowenstein, D. J. Lovell, T. K. McCubbin, R. K. McDonaldR. H. McFee, J. R. McNally, Jr., R. P. Madden, A. B. Meinel,P. E. Mengers, L. H. Meuser, P. Nolan, R. A. Oetjen, J. Parsons,F. H. Perrin, G. N. Plass, E. K. Plyler, H. D. Polster, R. Potter,R. W. Powell, D. Richardson, D. W. Robinson, D. Z. Robinson,N. Rosenberg, J. A. Sanderson, A. L. Schawlow, B. F. Scribner,J. H. Shaw, W. Sinton, F. S. Smith, V. J. Stakutis, S. Sternberg,H. S. Stewart, B. Stoicheff, G. W. Stroke, R. E. Stroup, R.Tabeling, R. M. Talley, Y. Tanaka, J. H. Taylor, R. Tousey,A. F. Turner, G. A. Vanasse, M. E. Warga, J. U. White, B. W.Wild, P. A. Wilks, Jr., V. Z. Williams, M. K. Wilson, W. Wolfe,R. A. Woodson, E. M. Wormser, N. Wright, H. W. Yates, M.Zelikoff, and G. J. Zissis.


MY

H, 0,~T

TIME -*

l

principles of operation of the rubidium vapor magnetometer

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