Ramsey the Method of Successive Oscillatory Fields

7/30/2019 Ramsey the Method of Successive Oscillatory Fields

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The method of successive oscillatory fieldsNorman F. RamseyCitation: Phys. Today 66(1), 36 (2013); doi: 10.1063/PT.3.1857View online: http://dx.doi.org/10.1063/PT.3.1857View Table of Contents: http://www.physicstoday.org/resource/1/PHTOAD/v66/i1Published by theAmerican Institute of Physics.Additional resources for Physics TodayHomepage: http://www.physicstoday.org/Information: http://www.physicstoday.org/about_usDaily Edition: http://www.physicstoday.org/daily_edition

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2/736 January 2013 Physics Today www.physicstoday.org

the archives(July 1980, pages 2530)

In 1949 I was looking for a way to meas-ure nuclear magnetic moments by themolecular-beam resonance method, butto do it more accurately than was possi-

ble with the arrangement developed by

I. I. Rabi and his colleagues at ColumbiaUniversity. The method I found1,2 wasthat of separated oscillatory fields, inwhich the single oscillating magneticfield in the center of a Rabi device isreplaced by two oscillating fields at theentrance and exit, respectively, of thespace in which the nuclear magnetic

moments are to be investigated. Duringthe 1950s this method became exten-sively used in the original form. In thesame period more general applicationsof the method arose, and the principal

extensions included: Use of relative phase shifts betweenthe two oscillatory fields3

Extension generally to other reso-nance and spectroscopic devices,4 suchas masers, which depend on either ab-sorption or stimulated emission Separation of oscillatory fields in timeinstead of space4

Use of more than two successiveoscillatory fields4,5

General variation of amplitudes and

phases of the successive applied oscilla-tory fields.5

Since the 1950s the method hasbeen further extended; it has also beenapplied to lasers by Y. V. Baklanov, B. V.

Dubetsky and V. B. Chebotsev,6

byJames C. Bergquist, S. A. Lee and JohnL. Hall,7 by Michael M. Salour andC. Cohen-Tannoudji,8 by C. J. Bord,9

by Theodore Hnsch10 and by others.11

The device shown in figure 1 is amolecular-beam apparatus embodyingsuccessive oscillatory fields that has

been used at Harvard for an extensiveseries of experiments in recent years.

Let me now review the successiveoscillating field method, particularly as

The method of

successive oscillatory fieldsAn extension of Rabis molecular-beam resonance method, originallydevised for measuring nuclear magnetic moments, is proving useful alsofor microwave spectroscopy, masers and lasers.

Norman F. Ramsey

Editors note: Norman Ramsey, a giant of 20th-century physics anda scientific statesman, died on 4 November 2011 (see PHYSICS TODAY,February 2012, page 64). In March 2012 a memorial symposium washeld at Harvard University to celebrate his life and legacy. The arti-cles on pages 25 and 27 grew out of that symposium and address oneof Ramseys signature accomplishments, which he discusses here inan article that originally appeared in PHYSICS TODAY 33 years ago.

Norman F. Ramsey is Higgins Professorof Physics at Harvard University.

Figure 1. Molecular-beam apparatus with successive oscillatory fields. The beam of molecules emerges from a small source aperture

in the left third of the apparatus, is focussed there and passes through the middle third in an approximately parallel beam. It is focussedagain in the right third to a small detection aperture. The separated oscillatory electric fields at the beginning and end of the middlethird of the apparatus lead to resonance transitions that reduce the focussing and therefore weaken the detected beam intensity.

PHYSICS TODAY / JULY 1980



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it is applied to molecular beams, micro-wave spectroscopy and masers.

The methodThe simplicity of the original applica-tionmeasurement of nuclear mag-netic momentsprovides one of the

best ways to explain the method of sep-arated oscillatory fields, so my discus-sion will be, at first, in terms of thissimple model. Extension to the moregeneral cases is then straightforward.

First let us remember, in outline,Rabis molecular-beam resonancemethod (figure 2). Consider classicallya nucleus with spin angular momen-tum J and magnetic moment = (/J)J.Then in a static magnetic field H

0= H

0k

the nucleus, due to the torque on thenuclear angular momentum, will pre-cess like a top about H0 with the Larmorangular frequency

(1)

as shown in figure 3. Consider an addi-tional magnetic field H1 perpendicularto H0 and rotating about it with angular

frequency . Then, if at any time H isperpendicular to the plane of H0 and J,it will remain perpendicular to it pro-vided = 0. In that case J will alsoprecess about H1 and the angle willcontinuously change in a fashion anal-ogous to the motion of a sleeping top;the change of orientation can be de-tected by allowing the molecular beamcontaining the magnetic moments topass through inhomogeneous fields asin figure 2. If is not equal to 0, H willnot remain perpendicular to J; so willincrease for a short while and thendecrease, leading to no net change. Inthis fashion the Larmor precession fre-quency 0 can be detected by measur-ing the oscillator frequency at whichthere is maximum reorientation of theangular momentum. This procedure isthe basis of the Rabi molecular-beamresonance method.

The separated oscillatory fieldmethod is much the same except thatthe rotating field H1 seen by the nucleusis applied initially for a short time , theamplitude of H1 is then reduced to zerofor a relatively long time Tand then in-

creased to H1 for a time , with phasecoherency being preserved for theoscillating fields as shown in figure 4.This can be done, for example, in amolecular-beam apparatus in whichthe molecules first pass through a rotat-ing field region, then a region with norotating field and finally a region witha second rotating field driven phasecoherently by the same oscillator.

If the angular momentum is ini-tially parallel to the fixed field (so that is equal to zero initially) it is possibleto select the magnitude of the rotatingfield so that is /2 radians at the endof the first oscillating region. While inthe region with no oscillating field, the

magnetic moment simply precesseswith the Larmor frequency appropriateto the magnetic field in that region.When the magnetic moment enters thesecond oscillating field region there isagain a torque acting to change . If thefrequency of the rotating field is exactlythe same as the mean Larmor frequencyin the intermediate region there is norelative phase shift between the angularmomentum and the rotating field.

Consequently, if the magnitude ofthe second rotating field and the lengthof time of its application are equal tothose of the first region, the second

rotating field has just the same effectas the first onethat is, it increases by another /2, making = , corre-sponding to a complete reversal of thedirection of the angular momentum.On the other hand, if the field and theLarmor frequencies are slightly differ-ent, so that the relative phase angle be-tween the rotating field vector and the

H0

H1

J

0

H0

T

TIME

Figure 2. Molecular-beam magnetic resonance. A typical detected molecule emergesfrom the source, is deflected by the inhomogeneous magnetic field A, passes through

the collimator and is deflected to the detector by the inhomogeneous magnetic field B.If, however, the oscillatory field in the C region induces a change in the molecular state,the B magnet will provide a different deflection and the beam will follow the dashed

lines with a corresponding reduction in detected intensity. In the Rabi method the oscil-latory field is applied uniformly throughout the C region as indicated by the long rf linesF, whereas in the separated oscillatory field method the rf is applied only in the regions

E and G.

Figure 3. Precession of the nuclear angular

momentumJ (left) and the rotating mag-netic field H1 (right) in the Rabi method.

Figure 4. Two separated oscillatory fields, each acting for a time , with zero field act-

ing for a time T. Phase coherency is preserved between the two oscillatory fields.

0=

H0

I

www.physicstoday.org January 2013 Physics Today 37





From the archives

precessing angular momentum ischanged by while the system is pass-ing through the intermediate region,the second oscillating field has just theopposite effect to the first one; the resultis that is returned to zero. If the Lar-mor frequency and the rotating fieldfrequency differ by just such an amountthat the relative phase shift in the inter-mediate region is exactly an integralmultiple of 2, will again be left at

just as at exact resonance.In other words if all molecules

have the same velocity the transitionprobability would be periodic as infigure 5. However, in a molecular beamresonance experiment one can easilydistinguish between exact resonanceand the other cases. In the case of exactresonance the condition for no changein the relative phase of the rotating field

and of the precessing angular momen-tum is independent of the molecularvelocity. In the other cases, however, thecondition for integral multiple of 2 rel-ative phase shift is velocity dependent,

because a slower molecule is in the in-termediate region longer and so experi-ences a greater shift than a faster mole-cule. Consequently, for the molecular

beam as a whole, the reorientations areincomplete in all except the resonancecases. Therefore, one would expect aresonance curve similar to that shownin figure 6, in which the transition prob-ability for a particle of spin 12 is plotted

as a function of frequency.From a quantum-mechanical pointof view, the oscillating character of thetransition probability in figures 5 and 6is the result of the cross term CiifCiff* inthe calculation of the transition proba-

bility; Ciif is the probability amplitudefor the nucleus to pass through the firstoscillatory field region with the initialstate i unchanged but for there to be atransition to state f in the final field,whereas Ciff is the amplitude for thealternative path with the transition tothe final state f being in the first fieldwith no change in the second. The

interference pattern of these cross termsfor alternative paths gives the narrowoscillatory pattern of the transitionprobability curves in figures 5 and 6.Alternatively the pattern can in part beinterpreted in terms of the Fourieranalysis of an oscillating field, such asthat of figure 4, which is on for a time, off for Tand on again for . However,

the Fourier-analysis interpretation isnot fully valid since with finite rotationsof J, the problem is a non-linear one.

For the general two-level system,the transition probability P for the sys-

tem to undergo a transition from state ito f can be calculated quantum mechan-ically in the vicinity of resonance and isgiven2by

P = 4 s in2 sin2a/2 [cosT/2 cosa/2 cos sinT/2 sina/2]2 (2)

where

cos = (0 )/, sin = 2b/ = [(0 )

2 + (2b)2]1/2 (3)

0 = (Wi Wf)/ (4)

= [(W

i W

f)/] (5)

and where Wi is the energy of the initialstate i, Wf of the final state f, and b is theamplitude of the perturbation Vif induc-ing the transition as defined2by

Vif = beit (6)

and the averages in (W

i W

f) are overthe intermediate region. For the specialcase of spin 12 and a nuclear magneticmoment, 0 is given in equation 1 and

= 0 , 2b = 0 H1/H0 (7)

The results for spin 12 can be extended tohigher spins by the Majorana formula.12

If equation 2 is averaged over aMaxwellian velocity distribution the

NORMALIZED FREQUENCY ( - ) /v 0 v

-30

0.25

0.50

o.75

1.0

-1 0 1 2 3-2

TRANSITION

PROBABILITY

Figure 6. When the molecules have a Maxwellian velocity distribution, the transi-tion probability is as shown by the black line for optimum rotating field amplitude.

(L is the distance between oscillating field regions, is the most probable molecularvelocity and is the oscillator frequency.) The colored line shows the transition proba-

bility for an oscillating field of one-third strength, and the dashed line represents thesingle oscillating field method when the total duration is the same as the timebetween separated oscillatory field pulses.

Figure 5. Transition probability that would be observed in a separated oscillatoryfield experiment if all the molecules in the beam had a single velocity.




5/7www.physicstoday.org January 2013 Physics Today 39

result in the vicinity of the sharp reso-nance is given in figure 6.

The separated oscillatory fieldmethod possesses a number of advan-tages, which we will discuss next.

AdvantagesAmong the benefits are: The resonance peaks are only 0.6

times as broad as the correspondingones with the Rabi method and thesame length of apparatus. This narrow-ing corresponds to the peaks in a two-slit optical interference pattern beingnarrower than the central diffractionpeak of a single wide slit aperturewhose width is equal to the separationof the slits. The sharpness of the resonance isnot reduced by non-uniformities of theconstant field since from both the qual-itative description and from equations2 and 5 it is only the space-averagevalue of the energies along the beam

path that is important. This advantageoften permits increases in precision bya factor of 20 or more. The method is often more conven-ient and effective at very high frequen-cies where the wavelength may be com-parable to the length of the region inwhich the energy levels are studied. Provided there is no unintended

phase shift between the two oscillatoryfields, first-order Doppler shifts areeliminated. The method may be applied to studyenergy levels in a region into which anoscillating field cannot be introduced;

for example, the Larmor precession ofneutrons can be measured while theyare inside a magnetized iron block. The lines can be narrowed by reduc-ing the amplitude of the rotating field

below the optimum, as shown by thecolored curve in figure 6. The narrow-ing is the result of the low amplitude fa-voring slower-than-average molecules. If the atomic state being studied de-cays spontaneously, the separated oscil-latory field method permits the obser-vation of narrower resonances thanthose anticipated from the lifetime andthe Heisenberg uncertainty principle

provided the two separated oscillatoryfields are sufficiently far apart; onlystates that survive sufficiently long toreach the second oscillatory field cancontribute to the resonance. Thismethod, for example, has been usedeffectively by Francis Pipkin, Paul Jes-sop and Stephen Lundeen13 in studiesof the Lamb shift.

These advantages have led to theextensive use of the method in molecu-lar and atomic-beam spectroscopy. Oneof the best-known of these uses is inatomic cesium standards of frequencyand time.

As in any high-precision experi-ment, care must be exercised with theseparated oscillatory field method toavoid obtaining misleading results. Or-dinarily these potential distortions aremore easily understood and eliminatedwith the separated oscillatory fieldmethod than are their counterpartsin most other high-precision spec-troscopy. Nevertheless the effects areimportant and require care in high-precision measurements. I have dis-cussed the various effects in detail else-where13,14,15 but I will summarize themhere.

PrecautionsVariations in the amplitudes of theoscillating fields from their optimumvalues may markedly change the shapeof the resonance, including the replace-ment of a maximum transition proba-

bility by a minimum. However, sym-metry about the exact resonance

frequency is preserved, so no measure-ment error need be introduced by suchamplitude variations.14,15

Variations of the magnitude of thefixed field between (but not in) the os-cillatory field regions do not ordinarily

distort a molecular beam resonanceprovided the average transition fre-quency (Bohr frequency) between thetwo fields equals the values of the tran-sition frequencies in each of the twooscillatory field regions alone. If thiscondition is not met, there can be someshift in the resonance frequency.14,15

If, in addition to the two energylevels between which transitions arestudied, there are other energy levelspartially excited by the oscillatoryfield, there will be a pulling of the res-onance frequency as in any spectro-scopic study and as analyzed in detail

in the literature.13,14,15

Even in the case when only twoenergy levels are involved, the applica-tion of additional rotating magneticfields at frequencies other than theresonance frequency will produce anet shift in the observed resonance

CHANGEIN

TRANSITIONPROBABILITY

-3

-0.6

-0.4

-0.2

0

0.2

0.4

0.6

3210-1-2

NORMALIZED FREQUENCY ( - ) /v 0 v

Figure 7. Theoretical change in transi-tion probability on reversing a /2 phaseshift. This resonance shape gives the maxi-

mum sensitivity by which to detect smallshifts in the resonance frequency.

Advice from Rabi

The first advice I received from Rabi

in 1937 when I applied to him to

begin my research was that I should

not go into the field of molecular

beams since the interesting prob-lems amenable to that technique

had already been solved and there

was little future to the field. I have

often wondered how I . . . had the

temerity to disregard this bit of

advice from the master. However, I

am grateful that I did since the ad-

vice was given only a few months

before Rabis great invention of the

molecular beam resonance method

. . . which led to such fundamental

discoveries as the quadrupole mo-

ment of the deuteron, the Lamb

shift, the anomalous magneticmoment of the electron and [to]

numerous other discoveries and

measurements.

(Quoted from Norman Ramseys

contribution to A Tribute to Professor

I. I. Rabi, Columbia University, New

York, 1970.)





From the archives


frequency, as discussed elsewhere.13,14,15

A particularly important special case isthe effect identified by Felix Bloch andArnold Siegert,16 which occurs whenoscillatory rather than rotating mag-netic fields are used. Since an oscilla-

tory field can be decomposed into twooppositely rotating fields, the counter-rotating field component automaticallyacts as such an extraneous rotatingfield. The theory of the BlochSiegert ef-fect in the case of the separated oscilla-tory field method has been developed

by Ramsey,17,19 J. H. Shirley,18 R. FraserCode19 and Geoffrey Greene.20 Anotherexample of an extraneously introducedoscillating field is that which resultsfrom the motion of an atom through afield H0 whose direction varies in theregion traversed.

Unintended relative phase shifts

between the two oscillatory field re-gions will produce a shift in the ob-served resonance frequency.13,14,15 This isthe most common source of possibleerror, and care must be taken to avoidit either by eliminating such a phaseshift or by determining the shiftsay

by measurements with the molecularbeam passing through the apparatusfirst in one direction and then in theopposite direction.

In some instances of closely over-lapping spectral lines the subsidiarymaxima associated with the separatedoscillatory field method can cause con-

fusion. Sometimes this problem can beeased by using three or four separatedoscillatory fields as we shall see, but or-dinarily when there is extensive over-lap of resonances and the resultant en-velope is to be studied, it is best to usea single oscillatory field.

Extensions of the methodAlthough, as we discussed above, unin-tended phase shifts can cause distor-tions of the observed resonance, it isoften convenient to introduce phaseshifts deliberately to modify the reso-nance shape.21 Thus, if the change in

transition probability is observed whenthe relative phase is shifted from + /2to /2 one sees a dispersion curveshape21 as in figure 7. A resonance withthe shape of figure 7 provides maxi-mum sensitivity for detecting smallshifts in the resonance frequency, say byapplying an external electric field.

For most purposes the highest pre-

cision can be obtained with just two os-cillatory fields separated by the maxi-mum time, but in some cases it is betterto use more than two separated oscilla-tory fields.4 The theoretical resonanceshapes with two, three, four and infi-nitely many oscillatory fields are givenin figure 8. The infinitely many oscilla-

tory field case, of course, by definitionbecomes the same as the single long os-cillatory field if the total length of the

transition region is kept the same andthe infinitely many oscillatory fields fillin the transition region continuously aswe assumed in figure 8. For many pur-poses this is the best way to think of thesingle oscillatory field method, and thispoint of view makes it apparent that thesingle oscillatory field method is sub-

jected to complicated versions of all thedistortions discussed in the previoussection. It is noteworthy that, as the

Figure 8. Multiple oscillatory fields.The curves show molecular-beam resonances

with two, three, four and infinitely many successive oscillating fields. The case with aninfinite number of fields is equivalent to a single oscillating field extending throughout

the entire region.

High-leveldriving cavity

rf amplifier

Low-level cavity

Defining aperture

State-selecting magnet

Atomichydrogen

source

Teflon-coated storage box

Figure 9. A large box hydrogen maser shown schematically. The two cavities on the

right constitute two separated oscillatory fields; atoms move randomly in and out ofthese cavities but spend the greater part of their time in the large field-free container.



7/7www.physicstoday.org January 2013 Physics Today 41

number of oscillatory field regions is in-creased for the same total length of ap-paratus, the resonance width is broad-ened; the narrowest resonance isobtained with just two oscillatory fieldsseparated the maximum distance apart.

Despite this advantage, there are validcircumstances for using more than twooscillatory fields. With three oscillatoryfields the first and largest side lobe issuppressed, which may help in resolv-ing two nearby resonances; for a largernumber of oscillatory fields additionalside lobes are suppressed, and in thelimiting case of a single oscillatory fieldthere are no sidelobes. Another reasonfor using a large number of successivepulses can be the impossibility of ob-taining sufficient power in a singlepulse to induce adequate transitionprobability with a small number of

pulses.The earliest use of the successive

oscillatory field method involved twooscillatory fields separated in space, butit was early realized that the methodwith modest modifications could be ap-plied to the separations being in time,say by the use of coherent pulses.4

If more than two successive oscil-latory fields are utilized it is not neces-sary to the success of the method thatthey be equally spaced in time;4 the onlyrequirement is that the oscillating fields

be coherentas is the case if the oscil-latory fields are all derived from a sin-gle continuously running oscillator. Inparticular, the separation of the pulsescan even be random,4 as in the case ofthe large box hydrogen maser22 shownin figure 9. The atoms being stimulatedto emit move randomly into and out ofthe cavities with oscillatory fields andspend the intermediate time in the largecontainer with no such fields.

The full generalization of the suc-cessive oscillatory field method is exci-tation by one or more oscillatory fieldsthat vary arbitrarily with time in bothamplitude and phase.5

More recent modifications of thesuccessive oscillatory field method in-clude the following three applications.

V. F. Ezhov and his colleagues,23 ina neutron-beam experiment, used aninhomogeneous static field in the re-gion of each oscillatory field regionsuch that initially when the oscillatoryfield is applied conditions are far from

resonance. Then, when the resonancecondition is slowly approached, themagnetic moment that was originallyaligned parallel to H0 will adiabaticallyfollow the effective magnetic field on acoordinate system rotating with H1

until at the end of the first oscillatoryfield region the moment is parallel to H1and thereby at angle = /2. As in theordinary separated oscillatory field ex-periment, the moment precesses in theintermediate region, and the phase ofthe precession relative to that of theoscillator is detected in the final region

by an arrangement where the fieldsare such that the effective field in therotating coordinate system shifts fromparallel to H1 to parallel to H0. Thisarrangement has the theoretical advan-tage that the maximum transition prob-ability can be unity even with a velocity

distribution, and the resonance is lessdependent on the value of the field inthe oscillatory field region. On the otherhand, the method may be less welladapted to the study of complicatedspectra, and it requires a special non-uniform magnetic field.

I emphasized in an earlier sectionthat one of the principal sources of errorin the separated oscillatory field methodis that which arises from uncertaintyin the exact value of the relativephase shift in the two oscillatory fields.David Wineland, Helmut Hellwig andStephen Jarvis24 have pointed out thatthis problem can be overcome with aslight loss in resolution by driving thetwo cavities at slightly different fre-quencies so that there is a continualchange in the relative phase. In this casethe observed resonance pattern willchange continuously from absorptionto dispersion shape. The envelope ofthese patterns, however, can be ob-served and the position of the maxi-mum of the envelope is unaffected byrelative phase shifts. Since the envelopeis about twice the width of a specificresonance there is some loss of resolu-

tion in this method, but in certain casesthis loss may be outweighed by the free-dom from phase-shift errors.

Finally, the extension of themethod to laser spectroscopy hasaroused a great deal of interest. Theseapplications of course require somemodifications from the form of the tech-nique most widely applied to molecular

beams,610 due to differences in wave-lengths, state lifetimes and so on. How-ever, the necessary modifications have

been made and the method continues tobe of real value in laser spectroscopyparticularly in cases where the extra

effort required is justified by the needfor multiple pulses or high precision.

This article is an adaptation of a paper pre-sented at the Tenth International QuantumElectronics Conference, held in Atlanta,Georgia, in May 1978.

References1. N. F. Ramsey, Phys. Rev. 76, 996 (1949).2. N. F. Ramsey, Phys. Rev. 78, 695 (1950).3. N. F. Ramsey, H. B. Silsbee, Phys. Rev. 84,

506 (1951).4. N. F. Ramsey, Rev. Sci. Instr. 28, 57 (1957).5. N. F. Ramsey, Phys. Rev. 109, 822 (1958).6. Y. V. Baklanov, B. V. Dubetsky, V. B.

Chebotsev, Appl. Phys. 9, 171 (1976) and11, 201 (1976).

7. J. C. Bergquist, S. A. Lee, J. L. Hall, Phys.Rev. Lett. 38, 159 (1977) and Laser Spec-troscopy III, 142 (1978).

8. M. M. Salour, C. Cohen-Tannoudji, Phys.Rev. Lett. 38, 757 (1977), Laser SpectroscopyIII, 135 (1978),Appl. Phys. 15, 119 (1978)and Phys. Rev. A17, 614 (1978).

9. C. J. Bord, C. R. Acad. Sci. Paris 284B, 101(1977).

10. T. W. Hnsch, Laser Spectroscopy III, 149(1978).

11. V. P. Chebotayev, A. V. Shishayev, B. Y.Yurshin, L. S. Vasilenko, N. M. Dyuba,M. I. Skortsov,Appl. Phys. 15, 43, 219 and

319 (1987).12. S. R. Lundeen, P. E. Jessop, F. M. Pipkin,Phys. Rev. Lett. 34, 377 and 1368 (1975).

13. N. F. Ramsey, Molecular Beams, OxfordUniversity Press (1956).

14. N. F. Ramsey, Le Journal de Physique et Ra-dium 19, 809 (1958).

15. N. F. Ramsey, in Recent Research in Molec-ular Beams (I. Estermann, ed.) AcademicPress, New York (1958); page 107.

16. F. Bloch, A. Siegert, Phys. Rev. 57, 522(1940).

17. N. F. Ramsey, Phys. Rev. 100, 1191 (1955).18. J. H. Shirley,J. Appl. Phys. 34, 783 (1963).19. R. F. Code, N. F. Ramsey, Phys. Rev. A4,

1945 (1971).20. G. Greene, Phys. Rev. A18, 1057 (1978).

21. N. F. Ramsey, H. B. Silsbee, Phys. Rev. 84,506 (1951).22. E. E. Uzgiris, N. F. Ramsey, Phys. Rev. A1,

429 (1970).23. V. F. Ezhov, S. N. Ivanov, I. M. Lobashov,

V. A. Nazarenko, G. D. Porsev, A. P. Sere-brov, R. R. Toldaev, Sov. Phys.-JETP 24, 39(1976).

24. S. Jarvis Jr., D. J. Wineland, H. Hellwig,J. Appl. Phys. 48, 5336 (1977).


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Ramsey the Method of Successive Oscillatory Fields