1962 IRE TRANSACTIONS ON INSTRUMENTATION 177

The Atomic Hydrogen Maser*NORMAN F. RAMSEYt

Summary-The atomic hydrogen maser is described. In this de- tures. Historically, the experiments were an outgrowthvice hydrogen atoms in the upper hyperfine state are focused onto of the previously described successive oscillatory fieldthe entrance aperture of a Teflon coated quartz bulb in which the . r * * oatoms are stored for about a second. This bulb is surrounded by a te atomic beamexerimns ithcylindrical radiofrequency cavity' When the cavity is tuned to the stored atoms [2]-[4]. The hydrogen maser also incor-hyperfine frequency of atomic hydrogen, maser radiation is produced. porates many of the features of beam maser developedDue to the large line Q resulting from the long storage time, the by Townes and his associates [5], [6]. The experimentsradiation is highly stable in frequency. Results are given of theo- are also related to the buffer gas experiments of Dickeretical calculations on the threshold flux of atoms required for maser [7 ] [8 ] and others although no buffer gas is used in theoscillations, on the various relaxation processes that limit the effec- 'tive storage time and on the possible sources of frequency shifts of hydrogen maser. A preliminary report on the hydrogenthe maser. Results are given on the relative stability of two hydrogen maser has been published [4], [9]- [12] and a detailedmasers. analysis of the theory of the hydrogen maser has been

INTRODUCTION given [13]. The hydrogen maser research at Harvardhas been carried on chiefly by D. Kleppner, H. M.

JVi/OST ATTEMPTS to observe radio frequency Goldenberg, N. Fortson, H. Berg, and E. Recknagel.or microwave spectral lines with high precisionincorporate one or m6re of the following fea- THE HYDROGEN MASER

tures: 1) observation of the resonance over a relatively The hydrogen maser consists of the apparatus shownlong period of time in order to obtain a narrow resonance schematically in Fig. 1. Atomic hydrogen from a radio-line; 2) observation of a spectral line which is as pure as frequency discharge in the source passes through thepossible so that there is no broadening due to different inhomogeneous state-selecting magnetic field from a 6-components of the line or to the environment of the pole permanent magnet. This field focuses atoms in theatom or molecule concerned; 3) a technique for eliminat- [F= 1, m = 0] and [F= 1, m = 1 ] states onto an apertureing, or at least greatly reducing, the first-order Doppler in a Teflon coated quartz bulb. The energy levels forshift; and 4) a means for obtaining a favorable signal-to- atomic hydrogen are shown in Fig. 2. The quartz bulbnoise ratio such as is provided in the low-noise amplifica- is located in the center of a cylindrical radiofrequencytion which characterizes a maser oscillator. cavity, operating in the TEo1l mode, which is tuned toAlthough most high-precision radio frequency and the [F=1, m=0]-,[F=0, m=0] hyperfine transition

microwave experiments depend upon one or more of the frequency at approximately 1420.405 Mc/sec. Theabove characteristics, none of them in the past has atoms make random collisions with the Teflon-coatedattained high quality in all of these features in a single bulb wall and eventually leave the bulb through themethod. Atomic beam hyperfine structure resonance entrance aperture. Due to their small interaction withexperiments are excellent with regard to purity of the the Teflon surface the atoms are not seriously perturbedspectral line, but the atoms have only moderately long even though they are retained in the bulb for more thanlifetimes. The original ammonia maser was excellent a second and undergo up to 105 collisions with the wallwith regard to signal-to-noise ratio but had only a short during the storage time. Under these conditions thelifetime and used a complicated spectral line. Solid-state resonance line is so sharp that self-excited maser oscilla-masers are good with respect to all of the criteria except tions at the hyperfine frequency can take place.for broadening of the lines by the influence of neighbor- The hydrogen maser has advantages in all of the de-ing atoms in the material. Optical pumping experi- sirable features listed in the Introduction: 1) since thements with buffer gases are excellent in every point ex- transition time is longer than one second the resonancecept for the effects of perturbations due to the frequent line is narrow; 2) the hydrogen atom spends most of itscollisions of the radiating atoms with the atoms of the time in free space where it has a simple unperturbed hy-buffer gas. perfine spectrum and the effects of wall collisions areThe hydrogen maser experiments described in the small due to the low electric polarizability; 3) the effect

present paper originated in an effort to obtain a single of the first-order Doppler shift is greatly reduced by thedevice which was highly favorable in all of these fea- fact that the velocity of the atom in the bulb, when suit-

ably averaged, is close to zero; and 4) the ability of the* Received August 21, 1962. Presented at the 1962 International device to operate as a self-excited maser oscillator pro-

Conference on Precision Electromagnetic Measurements as Paper vides the advantages of low noise amplification which

t Harvard University, Cambridge, Mass. characterizes masers.

178 IRE TRANSACTIONS ON INSTRUMENTATION December

PICKUPLOOP

STOP

DROGI STATE SELECTOR QUARTZHYDROGEN COATEDWTSOURCE ~~~~TEFLON TUNED RF C-AV-ITY

Fig. 1-Schematic diagram of atomic hydrogen maser.

H 12Sk / 0

T F=l-_

hA\)

- Fig. 3-Photograph of original atomic hydrogen maser. The ap-paratus is about 4 ft tall and the source is at the right and themaser cavity is at the left inside the Helmholtz coils used forcompensating external magnetic fields.

0

Fig. 2-Energy levels for hyperfine structure of atomic hydrogen inits electronic ground state 12S112. The electron and proton spinsare parallel for the F= 1 state and antiparallel for F=O. TIheindicated Zeeman splitting corresponds to the external magneticfield being increased toward the right side of the figure.

A photograph of the original hydrogen maser isshown in Fig. 3. This apparatus was quite large becauseof the fact that it was adapted from an apparatus orig-inally used for another purpose. In particular a largeelectro-magnet was used to produce the focusing fieldanid large coils were used to cancel the earth's miagnieticfield. The seconid model of the atomic hydrogen maserwas much simplified over the original one, as shown inFig. 4. In these figures the cylinders with vertical axesare the diffusion pumps used to evacuate the hydrogen.They are much larger than necessary because one of theexperiments to be done with this apparatus is to investi-gate the effects of excessive amounts of hydrogen flow.The cylinder with the horizontal axis is the tuned silver-plated radio frequency cavity. Inside the cavity is thequartz bulb of about 10-cm diameter which is coatedwith Teflon. In this apparatus the focusing magnet isgreatly reduced in size and is a permanent magnet. Thisis well illustrated by Fig. 5 in which the permanent mag-net use(din the later apparatus is contrasted with theelectro-magnet used for the same purpose in the original Fig. 4-- -Second hydrogen maser. The apparattus is about 4 ft

apparatus. In the new hydrogen maser the earth's mag- tall. The magnetic shields shown in Fig. 6 are removed.netic field is cancelled with concentric mu-metal shield-ing cylinders. A photograph of the apparatus with the such circumstances if a 1400-megacycle pLilse is given tomagnetic shields in place is shown in Fig. 6. the cavity, the device will emit a decaying signal for a

Ordinarily the hydrogen maser is operated with the length of time determined by the storage time of thecoupling loop in such a position that when the hydrogen atoms in the quartz bottle. Such a decaying signal isbeam is turned on, the maser immediately breaks into illustrated in Fig. 7 which shows the decaying amplitudeoscillation at the 1400-megacycle hyperfine frequency. of the beat note between the cavity output and a 1400-Ilowever, if desired, the output can be overcoupled in megacycle oscillator. The (lecay time showni in Fig. 7which case continuous oscillation does not occur. In provides a measure of the storage time of the atomis in

1962 Ramsey: The Atomic Hydrogen Maser 179

field independenit to the first approximation. flowever,it has also been found possible to operate the maser be-tween the [F=1, m=1] and [F=O, m=O] levels. Suchoperation provides a means of measuring the averagestrength of the magnetic field inside the cavity. Thisinformation can also be obtained even more easily byoperating the maser on the field independent transitionwith a separate oscillatory field inducing transitions be-tween the [hF=1, m=] state to the [xFi=1,mm=en1state. These Zeeman transitioniis also provide a measureof the average magnietic field. Furthermiore, the line ob-served in this case should be a doublet and the separa-tion of the doublet provides a measuremenit of the eanisquare magnetic field. A determination of these valuesis useful in the highest precision experimentts as a meansof making higher order corrections for field variations inthe transition which is field independent to the first

Fig. 5--Contrast lbetween 6-pole focusing mtpgfietic fields used in order.o_riginal and second hvdrogen maser. 'Ihe lier focusinig magnet Since the field dependence of the tranfsition most

is matelsmallpeitoeiMane incthendonothedisributondo

studied is quadratic in the magnetic field, the effect ofthe magnetic field is hiarkedly reduced at lower values ofthe field. Coinsequetly magnetic shielsiig is ordinarilyused todiineaish the iagnetic field to a few nilligauss.

THRESHOLD FOR OSCILLATION

For oscillation to occur the power delivered to thecavity by the beam must equal the power dissipated inthe cavity. If theith is the thresholdiintensity of theatomic beam, v the hyperfine frequency, Q the qualityfactor of the cavity,7o the geometrical factor approxi-mately equal to 3 which depends on the distribution ofthe radio frequency magnetic field in the cavity, V thevolume of the cavity, H the oscillatory field amplitude,JOnthe Bohr magneton andHy the relaxation constant ofthe atomr in the bulb, so that e/iy is approximately theeffective storage time in the bulb, theni the above condi-tion directly gives

Fig. 6--nlu ietal magetic shields for hydrogen maser. ae 2

Q 8wr

0_ 4 rrse provided the oscillatory field is sufficiently strong for thetransition between the hyperfine states to be induced.The condition [121 for this is

j.oH'=

(l,by) = 1. (2)

Fig. 7----Output signial fromi puilsed stimiulated emission h2r

whenbeataganst klstro osillaor.On the elimination of H between these equations, the

the qluartz bulb. In typical experimenits this storage timebemitntyathsolbcmsis approximately 2 seconids. When the hydrogen maser Ith =hV-y2/8r1jAo2Qtn. (3)is used as a frequenicy stanidard, the coupling loop isadjusted in such a fashioni thatt the oscillation is pro- If typical values suitable for the hydrogen maser areduced continuously, substituted in this relationship, the threshold flux be-The hydrogen miaser is niormially used for transitions comes about 1012 atoms per sec. An intensity of this

betweeni the [F= 1, m=0] antd [F=O, m=O] energy magnitude can be achieved with an atomic beam ap-levels of Fig. 2 because this eniergy difference is magnetic paratus employing a 6-pole focusing magnet.

180 IRE TRANSACTIONS ON INSTRUMENTATION December

RELAXATION PROCESSES [13] byIn (3) it is apparent that the threshold flux is strongly lys = 1))2. (6)

dependent upon the relaxation constant -y. Likewise the In addition to the above adiabatic wall relaxationaccuracy of the hydrogen maser is also dependent upon process, a nonadiabatic chemical reaction of the atom-y. For this reason it is important to consider the various with the wall is equivalent to escape from the bulb. Therelaxation processes which contribute to y. . . . .iA variety of processes can limit the radiative lifetime

of a beam in the storage bulb. Most of the processes are 'yr = (2vP/ 1/21) exp (-E,EakT) (7)random and lead to time independent relaxation rates,so that the total relaxation rate is the sum of the rates ea is theatiatio for teracin For atmfor each process. Because of this it is possible to analyze hydrogen with hydrocarb on . sec-1 boththe relaxation processes separately. The total relaxationhyrgnwthdocbnwal,y,07sc1ohathe rstelaxationprocesses separtely The otalrelaxtion theoretically and experimentally. However, with fluor-

carbon walls such as Teflon, the decay rate is found to

rY= 'YO + Ys + 'Yr + 'YH1 + 'YH2+±'Yse (4) be much smaller.Magnetic field inhomogeneities cause relaxation in

where the subscripted y's on the right-hand side of the two different ways. One of these, yH1, is due to the mo-above equation correspond to the different relaxation tion of the atom through the inhomogeneous field induc-processes as defined subsequently. ing transitions which change the component of magnet-

In the case of nuclear magnetic resonance the dy- ization parallel to the field. If (H,2) is the average squarenamical equations of the magnetization are often of the varying transverse component of the field and ifdescribed by the Bloch equations in terms of the relaxa- to is the mean time between wall collisionstion times T1 and T2, the time constants which describe 'YH1 = 2YF2(Ht2)to (8)the return of magnetization in a given direction to itsequilibrium value, and the decay of the oscillating where 'YF iS the gyromagnetic ratio of the atom in statedipole moment, respectively. These relaxation times are F. The second process, which produces the relaxationnot used in the present analysis because the Bloch equa- 'YH2, arises from the loss of coherence between the atomtions do not apply due to the presence of hyperfine and the oscillatory field when the static magnetic field isstructure. It is important to remember, however, that a not uniform. It can be shown [13] thatgiven perturbation frequently causes relaxation by both 'YH2 = t0(16a2H02zAH2) (9)changing the magnetization along the axis of quantiza-tion and by causing loss of coherence between the oscil- where Ho is the magnitude of the static field, /H is itslating moment and the radio frequency field, and that typical variation and ax is the coefficient of the depend-these two rates may be considerably different. To ence of the hyperfine frequency on H02.emphasize this, the subscripts 1 and 2 are used to iden- If the hydrogen pressure in the bulb is raised suffi-tify decay rates due to each of these processes, respec- ciently there will be a relaxation yse by the process oftively. A detailed description of the different relaxation spin exchange in the hydrogen-hydrogen collisionsprocesses has already been given in the literature [13] where [13]along with suitable derivations. Consequently, in the Yse 5 X 10-"°N sec-1 (10)present article merely the results of the derivations willbe given. with N being the number of hydrogen atoms per cubicThe escape rate of atoms from the bulb through its centimeter.

hole is a basic source of relaxation designated Tyo. It may In addition to the above, relaxation can also be pro--easily be seen [13] that duced by Doppler and pressure broadening but these are

normally too small to justify reproducing the theoretical'Yo = iAe (4KVb), (5) expressions here [13].

XVhen all the above relaxation processes are combinedwhere v is the mean velocity of the atoms, Ae the total by (4), to yield the resultant relaxation y, it is found thatescape area, K a numerical factor depending on the y-.0.5 sec-1 should be achieved, i.e., storage times ofgeometry of the hole (unity for a thin hole) and Vb the several seconds should be obtainable. Experimentallyvolume of the storage bulb. this is found to be the case when atomic hydrogen isAlthough the atom spends most of its time in the free stored in Teflon-coated bulbs.

space of the bulb, a small fraction is spent on the wallsurface and during this time the hyperfine frequency is FREQUENCY STABILITY AND ACCURACYslightly altered. If 4) is the average phase shift per col- The frequency stability and accuracy of the hydrogenlision caused in this way and if il is the collision rate, the maser is determined in part by the relaxation times dis-relaxation rate 'y8 by this adiabatic wall process is given cussed in the previous section but also by other factors

1962 Ramsey: The Atomic Hydrogen Maser 181

as well. One of these is thermal noise since with thermal Due to the high value of the line Q, the cavity pulling isnoise the apparent position of the resonance peak will much less for the hydrogen maser than for other oscil-deviate slightly from the true resonance. It can be lators. On the other hand this feature is used to provideshown that the root mean square deviation of the fre- greater stability so great care must be still used withquency is given [6], [13] by regard to cavity pulling if the ultimate stability of the

maser is to be achieved. As a result the cavity must be1 1 /kT thermally stabilized to better than 0.01°C to diminish

(,AC,)2)I /(= _/_o_ l _ (11) drifts due to thermal expansion of the cavity. It is alsohelpful to design the cavity for approximate tempera-

where Q= coo/(2,y) is the line quality factor, P is the ture compensation. Cavity detuning can also resultpower delivered by the beam to the cavity and t is the from atmospheric pressure changes so it is best to sur-

observation time. For observation times of 1 second and round the cavity with an evacuated cylinder to elimi-for values characteristic of the hydrogen maser the nate such detuning. Even when cavity tuning drifts

abovefratinaldeiaion*d 1-15 are eliminated special care must be taken to assureabove fractional deviations should be about 10 . I

In addition to thermal noise in the frequency output, that the cavity is tuned to the correct frequency. It ap-there are several potential sources of frequency shift. pears that this can best be done by changing the lineSince the hyperfine frequency will ordinarily be shifted Qi either by changing the hole size in the bulb or bywhen the atom is in the immediate vicinity of the bulb introducing a relaxing gas such as oxygen. It can bewalls, the average frequency will be slightly shifted as seen from the above equation that when w, - wo =0well by the relative amount there will be no change in the output frequency with Q,

but if the cavity is detuned there will be a change in fre-Aw" quency. With sufficient care in the cavity design, the

= 4 (coto). (12) maser signal should be stabilized to an accuracy of1 0-14.

It is difficult to estimate reliably the value of the mean A final source of frequency shift is the Zeeman effectphase shift 0 per wall collision. For a phase shift of on the hyperfine frequency. Fortunately, the [F=1,-3.5X10-2 radians per collision, which seems reason- m=0]-[F==0, m =0] transition in atomic hydrogen isable for atomic hydrogen with hydrocarbon lined walls, independent of the magnetic field to first order as seenthe above expression would indicate a relative frequency in Fig. 2. However, there is a second order dependenceshift of - 10-12. (However, the shift per collision might of frequency upon field. If the magnetic field differs bybe larger than that assumed since there is no direct data an amount AHo from the assumed value H0, the fre-on this yet.) With fluorocarbon walls like Teflon the quency error will be [13]shift should be smaller. Since the magnitude of the phaseshift should be measurable by comparing frequencies of ,0masers with different sized bulbs, the hydrogen hyper- -= 3.9 X 10-9H0AH0. (15)fine frequency should be measurable more accuratelythan indicated by the magnitude of the wall shift. Hence, if Ho is 1 milligauss it must be known to about 1The first order Doppler shift should be negligibly per cent if this error is to be 10-'4.

small in the hydrogen maser since the average velocity From a consideration of the above sources of fre-of the atoms during their time of radiation is essentially quency shifts, it appears that an accuracy of betterzero, as a result of their leaving by the same hole as they than 10-11 might be achievable with the hydrogenentered a second or so earlier. However, the second order maser. An accuracy of 1t-n is the objective of the pres-Doppler shift is important. It is [13] ent hydrogen masers. The masers that have been so far

ZAcwo 3kT used have not had hermetically sealed radio frequency= ~~ = 1.4 X 10-13T. (13) cavities as a result of which the change of cavity tuningcWo 2mc2 with atmospheric pressure produces drifts. Conse-

quently the relative stability of the two masers haswher m s temss f te hdroen tom Ths mansbeen good to only about a part in 1012, whereas it isthat the temperature must be stabilized to 0.01°C for a h odwth h tly sealed cavtie to aheve bthstblt*or 101 to h*ri--, hoped with hermetically sealed cavities to achieve bothstability Of 10-15 to be achieved.One of the most important sources of frequency shiftstblyanacucyoaprti10.

is cavity pulling. If the cavity is tuned to a frequencyEXRINTWTHYDONMARcoo the maser oscillation will be pulled an amount Acoc EPRMNSWT YRGN1AEwhere [13] Although one of the principal objectives of the re-

Aco~~~~~ Q ~~search with an atomic hydrogen maser is to provide ac0-=-(co)b-(°). (14) reliable frequency standard with both stability andcooQl ~~~~~~~absolute accuracy of one part in 1013 or better, it should

182 IRE TRANSACTIONS ON INSTRUMENTATION December

be noted that there are also a number of basic physics In strong external magnetic fields it should be pos-experiments that should be possible utilizing the hydro- sible to measure the proton magnetic moment by itsgen maser as a research tool. Some of these experiments interaction with the external magnetic field. Suchare discussed in the following paragraphs. measurements with atomic hydrogen when compared toThe atomic hydrogen hyperfine separation in terms measurements with molecular hydrogen should provide

of the corresponding quantity for cesium has already a check of the theory of magnetic shielding in moleculesbeen measured by the atomic hydrogen maser to a and a value of the proton magnetic moment that is in-greater accuracy [9] than was known previously. How- dependent of the molecular theory of shielding. This re-ever, the precision of this measurement should be sig- sult might also provide some insight on the discrepancynificantly improved in subsequent studies. between the fine structure constant a when it is de-The ratios of the atomic hydrogen hyperfine structure termined from hydrogen hyperfine and fine structure ex-

separations for the three isotopes of atomic hydrogen periments.can also be measured with the hydrogen maser. Evenwith the present accuracy of the maser a marked im-provement over the published values can be obtained. REFERENCES

It has recently been found in the hydrogen maser [1] N. F. Ramsey, "Successive oscillatory field resonance method,"laboratory at Harvard University that with the pre- Rev. Sci. Instr., vol. 28, pp. 57-59; August, 1957; "Molecularcision*of the maser the effect of an externally applied Beams," Oxford University Press, New York, N. Y., p. 124;cision of the maser the effect of an externally applied 1956.

strong electric field in shifting hydrogen hyperfine fre- [2] D. Kleppner, N. F. Ramsey, and P. Fjelstad, "Broken atomicbe observed. Although this shift has been beam experience," Phys. Rev. Lett., vol. 1, pp. 232-233; August,quency can De oDservea. altnougn tnls snlIt nas oeen 1958.

too small to be observable in previous studies of atomic [3] H. M. Goldenberg, D. Kleppner, and N. F. Ramsey, "Atomichydrogen, an accurate measurement of the shift should beam resonance experiments with stored atoms," Phys. Rev.,

vol. 123, pp. 530-537; November, 1961.be a possibility with the hydrogen maser. [4] H. M. Goldenberg, D. Kleppner, and N. F. Ramsey, "HydrogenWhen the hydrogen beam in the maser is increased it maser," Phys. Rev. Lett., vol. 5, pp. 361-362; August, 1960.

[5] J. P. Gordon, H. J. Zeiger, and C. J. Townes, "Ammoniais found that eventually the effective storage time of the maser," Phys. Rev., vol. 95, pp. 282-283; September, 1954.atoms is diminished due to spin exchange collisions of N. G. Basov and A. M. Prokhorov, "Microwave spectroscopy

methods," J. Exptl. Theoret. Phys. (U.S.S.R.), vol. 27, pp. 431-the atoms. This observation can be used to measure the 433; September, 1954.'spin exchange cross section. [6] K. Shimoda, T. C. Wang, and C. H. Townes, "Maser Theory,"When extraneous gases, such as oxygen, are intro- [7] Phys. Rev., vol. 102, pp. 1308-1320; June, 1956.

[7] R. J. Dicke, "Doppler narrowing," Phys. Rev., vol. 89, pp. 472-duced into the storage bottle, the effective storage time 480; February, 1953.is found to be diminished. This observation can be used [8] J. P. WVittke and R. H. Dicke, "Atomic hydrogen hyperfinestructure," Phys. Rev., vol. 103, pp. 620-628; September, 1956.to study the interaction of the two gases. Likewise, most [9] D. Kleppner, J. M. Goldenberg, and N. F. Ramsey, "The hydro-surface materials produce a quenching effect which can gen maser," Appl. Optics, vol. 1, pp. 55-60; January, 1962.

[10] H. M. Goldenberg, Ph.D. dissertation, Harvard University,be used to study the interaction of the atom with the Cambridge, Mass.; 1960 (unpublished).various surfaces. [11] J. P. Gordon, H. J. Zeiger, and C. H. Townes, "Ammonia

Although atomic hydrogen appears to be the most maser," Phys. Rev., vol. 99, pp. 1264-1270; October, 1955.R. P. Feynman, F. L. Vernon, and R. NA. Hellwarth, "Applica-suitable substance for atomic maser experiments, other tions of electrodynamics," J. Appl. Phys., vol. 28, pp. 49-56;gaseous atoms, such as nitrogen, might also be studied January, 1957.W. E. Lamb and J. C. Helmer, Microwave Lab., Stanford Uni-in this fashion. Likewise it may be desirable to investi- versity, Calif., Tech. Rept. No. ML-311; 1957 (unpublished).gate alternative means of polarizing the hydrogen [121 Ramsey, op. cit., see p. 119.

[13] D. Kleppner, H. M. Goldenberg, and N. F. Ramsey, "Theory ofatoms, such as by means of optical pumping. hydrogen maser," Phys. Rev., vol. 126, pp. 603-613; June, 1962.