A UNITED STATES DEPARTMENT OF COMMERCE

PUBLICATION NBS TECHNICAL NOTE 612

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Frequency Shifts Due

to Ramsey Type Interrogation

in Atomic Beam Tubes
NATIONAL BUREAU OF STANDARDS

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VWtt BUREAU OF STANDARDS MAR 2 1972 - **v oct dt too

UNITED STATES DEPARTMENT OF COMMERCE

Maurice H. Stans, Secretary

d. NATIONAL BUREAU OF STANDARDS • Lewis M. Branscomb, Director

NBS TECHNICAL NOTE 612

ISSUED FEBRUARY 1972

Nat. Bur. Stand. (U.S.), Tech. Note 61 2, 25 pages (February 1 972) CODEN: NBTNA

Frequency Shifts Due to Ramsey Type

Interrogation in Atomic Beam Tubes

Helmut Hellwig, J. A. Barnes, and D. J. Glaze

Time and Frequency Division

Institute for Basic Standards

National Bureau of Standards

Boulder, Colorado 80302

and

Peter Kartaschoff Laboratoire Suisse de Recherches Horlogeres

Neuchatel, Switzerland

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NBS Technical Notes are designed to supplement the Bureau's regular publications program. They provide

a means for making available scientific data that are

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be listed or referred to in the open literature.

For sale by the Superintendent of Documents, U.S. Government Printing Office, Washington, D.C. 20402

(Order by SD Catalog No. C13.46:612), Price 35 cents
FOREWORD

This Technical Note consists of two related papers on the topic of

Frequency Shifts Due to Ramsey Type Interrogation in Atomic Beam

Tubes. The first paper (Part I) was presented at the 25th Annual Symposium on Frequency Control, Fort Monmouth, N.J., April 1971; the

second one (Part II) at the IEEE Eurocon, Lausanne, Switzerland,

October 1971. This Technical Note may, therefore, be considered to be a documentation of these talks.

Helmut Hellwig, J. A. Barnes, and D. J. Glaze are with the

National Bureau of Standards. Peter Kartaschoff was a National Bureau

of Standards' Visiting Scientist from October 1970 to September 1971;

he is with the Laboratoire Suisse de Recherche Horlogeres, Neuchatel,

Switzerland.
TABLE OF CONTENTS

Page

Part I: Frequency Biases in a Beam Tube Caused by

Ramsey Excitation Phase Differences 1 by Helmut Hellwig, J. A. Barnes, and D. J. Glaze

1. Introduction 2

2. Calculation of Frequency Shifts 2

3. Frequency Modulation Amplitude Dependence .... 5

4. Power Dependence 6

5. Experimental Results 6

6. Conclusions 8

Part II: Power -Linewidth Relations in Atomic Beam Tubes .... 14

by Peter Kartaschoff

1. Introduction 14

2. Single Velocity Power -Linewidth Relation 15

3. Conclusions 18

PART I: FREQUENCY BIASES IN A BEAM TUBE

CAUSED BY RAMSEY EXCITATION PHASE DIFFERENCES

Helmut Hellwig, J. A. Barnes, and D. J. Glaze

A phase difference between the two interaction regions

of a Ramsey excitation resonance structure results in a frequency bias in the measured beam resonance. A simple

mathematical model is discussed which describes the

dependence of this bias on the phase difference, the microwave power level, the modulation amplitude, and the resonance

linewidth. This dependence results from the interaction of the

modulated microwave excitation frequency with the asymmetric

shape of the slightly shifted resonance line. In a first order

approximation, no dependency on the frequency modulation

amplitude is expected. Near-linear dependencies on the

linewidth and microwave power level which are quite pronounced even at relatively small cavity phase differences are

predicted.

The theoretical results are compared with one set of

experimental data on the microwave power dependence as measured in 1969 with the cesium beam standard NBS-III.

After a correction is applied to remove the power dependence

due to spectral impurity of the microwave excitation, the

remaining measured power dependence agrees quantitatively

with that calculated using a cavity phase difference of about

3 milliradians.

Key words: Cavity phase shift; cesium beam tube; frequency

accuracy; frequency standard; power shift; resonance line shape,
1. INTRODUCTION

In accordance with the international definition [l], the unit of time

interval, the second, is realized with a cesium beam apparatus. Several

bias corrections have to be applied to the measured resonance frequency

in order to obtain the resonance frequency of the unperturbed, free

cesium atom [2]. In this paper we consider only those bias corrections

which are associated with a phase difference between the two interaction

regions of a Ramsey excitation resonance structure [3].

In this paper we present a simple mathematical model which allows

analytical solutions to the question of frequency shifts in the presence of

a cavity phase difference. The results are intended to aid in the understanding of the physical mechanisms involved. Although our mathematical

model is only an approximation to the physical situation, and is tailored

to a particular set of conditions, we feel that it is close enough to the

real conditions which were encountered in the National Bureau of Standards Frequency Standard [Z], NBS-III, to warrant a quantitative comparison

with experimental data from this apparatus. This is done in Section 5 of

this paper.

2. CALCULATION OF FREQUENCY SHIFTS

We proceed on the basis of the following set of assumptions and

approximations: (a) No frequency deviations from resonance exceed the

linewidth; (b) the microwave interrogation power does not deviate greatly

from optimum power; (c) the modulation of the microwave signal is sinusoidal; (d) the modulation frequency is less than the resonance linewidth;

(e) the velocity distribution in the atomic beam is Maxwellian; and (f)

I << L where SL and L are the lengths of the interaction and drift regions,

respectively, as defined by Ramsey [3].

In the presence of a cavity phase difference the central peak of the

Ramsey resonance pattern is displaced from the resonance frequency

Optimum power is that microwave power which leads to a maximum in

the detected beam intensity.
of the unperturbed atom. Furthermore, the lineshape displays a certain asymmetry. We restrict ourselves to the conditions (a) and (b) above and can in first order approximate the central peak of the Ramsey

pattern, I [v] , by

TT(V - V l[v) = A + Bpsin1T(V - V ) U

+ C cos o W (1-1

In eq(I-l) A, B, and C are constants under given experimental conditions;

W is the linewidth at half intensity; U has the characteristic of a line

width, U - W for monovelocity atoms, U is the same order of magnitude

as W for our assumption (e) above; and V is a parameter related to the

cavity phase difference (p. Using condition (e) above, it can be shown

that

3<p V - V = — "W.

<P O 477 (1-2)

In e<\{l-2)V is the resonance frequency in the absence of a cavity phase

difference. Because of the asymmetry, the frequency of the central

peak V differs from V . By setting dl [l>] / dV = 0, we obtain

V + B W*Q

<p T7CU (1-3)

We now proceed to calculate the frequency to which the slave

oscillator frequency servo will "tune-in." If we modulate V in a sinusoidal fashion [condition (c) above] about some value V with the amplitude V and the angular frequency CO we can write m

V {tl = V^ + V sin COt

i m

(1-4)

We now make use of assumption (d) above and substitute eq (1-4) into eq

(1-1), using eq (1-3) to express B. We obtain

I [tl = A + C

,77U .

+ COS

— (V - V + V sin COt) U i <p m — (V - V + V sin COt) W i cp m

(1-5)
We are interested In the coefficient of that term in I { t } which varies as

sin COt, because the servo forces this term to be zero. Now

sin -TT {V - V + V sin COt) U i cp m

= 2 cos t "i - V

rrv

and

cos — (V - V + V sin COt) W i tp m

= - 2 sin j

i

u

VV

sin CO t + harmonics

W

sin CO t + harmonics,

Then the coefficient of sin COt in l{t} [eq (1-5)] vanishes when

sin - 1\ - V JIV J m

p <p W U i <p

(1-6)

irv J m

W

V is the frequency to which the servo will "tune -in", and thus the

l resonance frequency of the beam tube. Note that V is not equal to eith

V or V . p <P "We have assumed that the offset is always small compared to the

linewidth, i.e., (V - V ) << W, [V - V)<< U, and we can rewrite eq(I-6)

l <P 10

V - V « (V - V ) l <P P

%{^ u

l (W mj

Substituting eq (1-2) and eq (1-3) into eq (1-7) we obtain

i(W Vm/_

(1-7)

3tpW

i o 4TT

1 + 4B

3C j/jl

(1-8)
Equation (I' 8) gives us the frequency bias Af which we define

v = A v

o

(1-9)

In order to evaluate eq(I-8) we have to express B/C in terms of the operating conditions. Following eq(I-l)we. choose a linear approximation based

on the numerical results of [3], and we obtain B<p77/CU « 2(£/3TT W . W is the linewidth at optimum power P . Equation (1-8) can now be

o written

Lv 3(3 W

4TT

1 + 8U \ (5 vJ

9 it" Wo ilW ml

(1-10)

3. FREQUENCY MODULATION AMPLITUDE DEPENDENCE

In eq([-10)any dependence on the frequency modulation amplitude is

solely due to the arguments of the Bessel functions which contain V . m

The approximate nature of our discussion requires that we restrict our discussion to modulation amplitudes not exceeding the optimum modulation, that is to

V ^ V where V (I-H) m mo mo 2 o

This and the fact that U and W can be expected not to differ greatly

leads us in a first order approximation to

Lv 3cpW

47T

1 + 8W

977

b Wo J

(1-12)

According to eq (1-12), btV has no functional dependence on V

We conclude that (in the limits of our approximation)no frequency modulation amplitude dependent frequency bias is to be expected for V ^ V r c m mo

This result is in accordance with our experimental observations on the

cesium beam frequency standards at the National Bureau of Standards.
4. POWER DEPENDENCE

We can use eq (1-12) to obtain the dependence of the frequency bias

Av on the microwave power P. Equation (1-12) shows that the frequencybias is a function of the phase difference and the resonance linewidth.

The linewidth, moreover, is a function of the microwave power level.

This can be understood intuitively if one realizes that with decreasing

microwave power the slower molecules become relatively more effective

which results in a corresponding line -narrowing [3]. The frequency bias

Av thus becomes power dependent. A numerical calculation of the relationship between linewidth and microwave power is depicted in figure 1. In figure 2 we depict the frequency bias Av as a function of both linewidth

[eq (1-12)] and microwave power [eq (1-12) and fig. l]. The ordinate is normalized to AlVA V= 1 at optimum power, P = P and W = W , where ° o o Av denotes the frequency bias at optimum power.

Equation (1-12) and figure 2 show that the power dependence of the

frequency bias is almost linear; however, we note that the extrapolation

of this near-linear portion to P -» does not yield a vanishing frequency

bias. A reduction of power from P to P /2 will result in a frequency

o o bias change of about 1/3 of the total bias at optimum power or more

accurately

AV [P IZ\ w 0.70 Av . (1-13) o o

5. EXPERIMENTAL RESULTS

The reported measurements were performed during the accuracy

evaluation of the cesium beam frequency standard, NBS-III, in 196 9 [2].

Figure 3 depicts the experimental results. The solid lines are a plot of

the fraction frequency change as a function of the microwave power level

for the two opposite beam directions. The precision of these measurements is discussed in [2]. The microwave power changes ranged from

P (optimum power) to not less than one -fourth P . The actual value for P was
P =1.4 mW; the frequency modulation amplitude was adjusted to

V « V . The two slopes are +22 X lO^per mW and -11 X 10~13 per mW. m mo

The total fractional frequency change with beam reversal at P = P is o 78 X 10"13 which gives us Ay /V = 39 X 10"13

. o o We believe that the asymmetry in the two slopes of figure 3 is caused by asymmetries in the spectrum of the microwave signal. Such

effects may be expected to be unchanged under beam reversal and to depend

linearly on the microwave power (for a small single sideband perturbation)

[3]. We obtain symmetric slopes if we subtract a slope of +5. 5X10

per mW. Thus we can conclude that the spectrum causes a power shift

of +5. 5X10 per mW (dashed line in fig. 3), and the cavity phase shift

a power dependence of ±16. 5X10 per mW (dashed-dotted lines in fig. 3).

As we expected theoretically, we have a seemingly linear functional

dependence. The measured biases at optimum power and half -optimum

power are respectively, tSV /V = 39 X 10

_13 and £^{P /Z)/V = 27.5 X 10"13 o o o o or 6v{P IZ\ « 0.71 Av (1-14)

o o which is in agreement with the theoretical results of figure 2 and eq (I - 1 3 )

We can now calculate the cavity phase shift <p from eq (1-12). The

numerical calculation yields

A V = 0.26 W (p. (1-15)

o o

The linewidth was measured to be W = 45 Hz and we obtain from eq (1-15)

o

— o with the power dependent frequency change discussed before (p ^ 3 X 10

radians.

2 The second-order Doppler effect is totally ignored in this paper; however, it must be taken into consideration when extreme accuracies are

the objective. A. G Mungall recently treated this problem [4].
6. CONCLUSIONS

We presented an analytical discussion of frequency shifts in a beam tube which relate to the presence of a cavity phase difference

between the two Ramsey excitation regions. The results are approximate

and may be expected to be different for different experimental conditions

(see Section 2).

The results, as summarized in eqs (1-10) and (1-12) and in figure 2,

show that frequency shifts caused by cavity phase differences, the microwave power level, the resonance linewidth (velocity of atoms), and the

frequency modulation amplitude are closely interrelated.

Frequency changes due to changes in the microwave power level are quite pronounced, which is contrary to the result of a previous treatment of this subject [5]. In fact, the power dependence could be utilized

to determine the frequency bias when other causes for frequency bias are known to be absent, e.g., microwave spectrum effects (see Section 5).

In this case the measurement of the frequency change with reduction of

the microwave power to, for example, P /2 yields directly the frequency

bias according to eq (1-13). We have used this method in recent experiments on new cesium beam tubes.

The treatment of the power dependence due to cavity phase differences, as presented in this paper, leads to a rather simple physical picture:

The chosen microwave power level acts like a velocity selector because

only atoms within a rather narrow velocity range will have a significant

transition probability. Atoms with velocities other than that selected by

the given power level do contribute, but only in some minor fashion as may be seen from eq (1-12) and figures 1 and 2.
A cavity phase difference will, in general, also cause frequency

shifts to occur if the frequency modulation amplitude is changed. The

frequency changes are virtually absent if a frequency modulation amplitude of less than half the linewidth is chosen (Section 3). However, if larger frequency modulation amplitudes are used or if the cavity phase

difference is unusually large (large bias) this effect could become significant. An analytical treatment which is valid for these conditions would

require a higher order approximation than was attempted in this paper.

In the presence of a spectrum-related frequency bias of unknown

magnitude, methods like the one discussed above will not be adequate.

Beam reversal presently appears to be the only method which then allows

the separation and individual measurement of the different frequency

biases. Beam reversal changes the sign in eq (1-12); consequently, one

should then obtain microwave power (and frequency modulation amplitude)

dependencies which are identical for the two beam directions, except for

the sign reversal. Any deviations from this symmetry would indicate

the presence of additional effects, e.g., signal spectrum asymmetry.

The frequency biases can then be obtained as was demonstrated in Section

5 (fig. 3).

We summarize: In the absence of other biases, e.g., spectrumrelated biases, variation of the microwave power offers a way to easily

detect and correct for a cavity phase difference and the related frequency

bias. This method requires a rather broad velocity distribution, e.g., a Maxwellian, and would not lead to any useful results in the limit of a monovelocity beam.

Beam velocity changes [6], as applied to the detection and correction of

cavity phase differences, act in a way quite similar to the variation of the

microwave power. Both act on W in eq(I-12). However, this method also

should only be used with great caution if spectrum-related frequency

biases are present.
ACKNOWLEDGMENT

We thank Dr. Stephen Jarvis, Jr. for his assistance in computing

the data of figure 1 and for his very valuable, constructive criticism.

10
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13
PART II: POWER -LINE WIDTH RELATIONS IN ATOMIC BEAM TUBES

Peter Kartaschoff

One of the most serious effects limiting the accuracy

of atomic beam resonators is the uncertainty of phase shifts

between the oscillating fields in a Ramsey excitation cavity.

A technique using the linewidth dependence on the excitation

power to measure the phase -shift induced bias has recently

been proposed. The conditions under which this method is

valid and their implications on the design of beam optics will

be discussed with consideration of available experimental

results.

Key words: Cavity phase shift; cesium beam tube; frequency

accuracy; frequency standard; power shift; resonance line shape,

1. INTRODUCTION

One of the most serious effects limiting the accuracy of atomic

beam resonators is the uncertainty of the phase difference between the

two separated oscillating fields in a Ramsey cavity. A technique for

measuring the frequency bias caused by this phase difference has been

described by H. Hellwig, J. A. Barnes, and D. J. Glaze (Part I). This

technique is based on the dependence of the resonance linewidth on the

applied microwave power, which results in a power -dependent frequency

shift if any phase difference is present. In this part, a different theoretical

approach based on an approximation to the transition probability for single -

velocity atoms leads to a simple relation between excitation power and

linewidth which is valid for any sufficiently broad, but not necessarily

Maxwellian, velocity distribution.

14
2. SINGLE VELOCITY POWER-LINE WIDTH RELATION

The theoretical considerations presented in Part I are valid only

for a resonator where the full modified Maxwellian velocity as defined in

([3], eq 11-26) is present at the detector. In many cases, however,

especially in commercial -type beam tubes and in designs using multipole

state -selectors, the velocity distribution of the detected atoms is severely

restricted by the beam optics. This appears to be the result of ray-tracing

optimizations attempting to maximize the "figure of merit" which is proportional to the ratio between the square root of the resonance amplitude

and the linewidth.

In particular, a sharp cutoff in the velocity distribution is observed

below the optimum velocity selected by the state selectors. In these

cases, no significant narrowing of the linewidth is observed if the micro- wave excitation is reduced below the optimum value P . o On the other hand, there remains the possibility to broaden the

linewidth by increasing the power beyond the optimum value provided that

faster atoms can still be detected. Pending experimental verification,

this technique appears feasible if the microwave signal is free from

undesired sidebands.

The bias due to second order Doppler shift also depends on the

velocity distribution and thus on the applied microwave power. This

problem has recently been treated by A. G. Mungall [4].

For single velocity atoms, the transition probability given by

Ramsey ([3], eq V-44) can be approximated near resonance in the following

way, leading to his eq (V-44a):

P = —^— = - sin2 2br [l + cos (XT + <p)], (II-l)

pq I 2 max

using Ramsey's notation, i.e.,

15
b is the perturbation amplitude in s , as defined in [3];

I T= —the time of flight through each cavity; v T= —the time of flight through the drift region between the 2 cavities; v

(0 = the phase difference in radians between the oscillating fields;

X= CO - CO the angular frequency detuning, CO = 277V . ° o o Note that I have changed the sign of cp with respect to that used by Ramsey,

i.e., the first field is assumed leading the second. This has been done

in order to remain consistent with Part I, where the same situation has

been implicitly assumed.

Equation (II - 1) is valid under the following assumptions:

2b > > |X|

is the "near resonance condition" as stated by Ramsey.

It can be easily shown that this condition remains valid for a detuning

larger than W/2 and also for a wide power range with a lower limit of

about 0. 3 P with & « 1 cm. The upper limit of applied power is only

given by the validity of the perturbation method used in calculating the

probability distribution and is thus beyond our considerations, since it requires b << CO . We now compare eq (II- 1 ) with eq (1-1). The line

width being equal to W = —, the argument of the cosine term is

W o and with <p<< 1, we can write

P = - sin2 2bT (1 + <p sin -7- (V - V ) + cos -^r (V - V ). (II-2)

pq 2 Wo W v o

Equation (1-1) reduces to the same form by setting there:

I a - -r r- max • 2 ou _ A = B = C = —-— sin 2bT

U = W and V = V

<p o

16
The peak frequency (d I/AV = 0) is then given by

Wffl V - V = —- . p O 77 The "near resonance" condition assumed above replaces conditions (a), (b), and (f) and is less restrictive. Conditions (c ) and (d) remain unchanged

insofar as sinusoidal modulation is considered. (See Part I, Section 2.)

Condition (e) has no meaning here since we start from a single

velocity approximation. From any known velocity distribution including

the full modified Maxwellian, averaging and weighting can easily be done

on a computer.

On the other hand, it is not possible to draw conclusions for a non -Maxwellian distribution from results assuming a full Maxwellian

distribution. The usefulness of the latter assumption is therefore rather

restricted. We therefore replace condition (e) by the following assumption:

The velocity distribution function is assumed to be broad and to have

bounded first and higher derivatives.

In other words, this means that we should be able to detect a significant number of atoms over a wide range, e.g., 2:1 velocity range,

with intensity variations of not more than 2:1 over that range. Then we

may consider the velocity selection being performed by the microwave

power according to the factor sin 2bT in eq (II-l).

This factor has a maximum of unity for br = 77/4. Since the perturbation amplitude b is proportional to the square root of the applied power,

the higher the applied microwave power, the higher is the velocity of the

atoms for which the transition probability is maximum.

For the assumed fairly uniform velocity distribution the average

velocity of the detected atoms is very close to the velocity where sin bT

is maximum and the linewidth can be calculated to a very good approximation by the relation

i v W=^— = -££

2T 2L

av

17
where T and v are the average time of flight and velocity, respectively, av av

This is an approximation with an error of less than 3 percent even for the

full modified Maxwellian, where

W=0.65^ = "aV

L 2.05 L

If we now call W the linewidth at the highest useful power P , the

o o condition bT = 77/4 = const, leads to the relation

_W_ Pp

wo Comparing this relation to figure 1 we see an exact fit at P = P and

P = 0. 5 P and a very small error between these values. At very low

o power, our simple approximation is no longer valid.

Using eq (II - 1) to calculate - -as in Part I--the frequency V to

l which an electronic servo using sinusoidal modulation locks leads to the

simple result:

W(p

V - V -= V - V - " 1 o p o 77

That there is no dependence on modulation amplitude is trivial in our simple case because of the symmetry of the line approximated by eq (II - 1 )

.

Hellwig, et al. , have shown that there is no significant dependence even

for the full modified Maxwellian distribution. The total shift due to the

phase difference (p is 25% larger than that calculated for the full modified

Maxwellian velocity distribution. This value appears to be more conservative for resonators having a restricted velocity distribution.

3. CONCLUSIONS

With the simple approximation of eq (II-l) derived directly from

Ramsey's solution, we have thus been able to derive a relationship

between power and linewidth which fits closely to the numerical data

given in figure 1. We must point out again, however, that

the expected variation of linewidth with excitation power is not observed
in resonators having a narrow velocity distribution, or a sharp cutoff at

the low velocity side of the distribution. There might be cases where

there is a less sharp cutoff on the high velocity side and a correspondent

line broadening could then be expected by applying higher than "optimum"

power. Experimental investigation of this possibility is recommended.

Results obtained with a commercial cesium beam tube are shown

in Table 1

TABLE 1 p/p

o

i (P/P ) s o W/W

o

0. 971

I/I

max

0. 80

sin 2bT

0. 5 0.707 0. 80

1 1 1 1 1

2 1.414 1. 17 0.638 0.632

These results are consistent with the assumption of a very narrow velocity

distribution. The variation of the linewidth as a function of excitation

power is much smaller than that expected for a wide or full modified

Maxwellian velocity distribution. The resonance amplitude behaves

almost exactly as if only one single velocity were present. This behavior

is indeed very different from that reported on the NBS-III cesium beam

resonator in Part I. ACKNOWLEDGMENT

The author would like to thank Dr. L. S. Cutler* and Mr. R. H.

Kern'" for the communication and permission to use the results presented

in Table 1

'"Hewlett-Packard Co., Palo Alto, California

'Frequency and Time Systems, Inc., Danvers, Massachusetts.

19
REFERENCES

[l] Thirteenth General Conference of Weights and Measures (CGPM),

Resolution 1 (1967).

[2] Glaze, D. J. , "Improvements in atomic cesium beam frequency

standards at the National Bureau of Standards, " IEEE Trans.

Instrumentation and Measurements, IM-1

9

, No. 3, pp. 156-160

(August 1970).

[3] Ramsey, N. F. , Molecular Beams , Clarendon Press, Oxford,

England (1956).

[4] Mungall, A. G. , "The second order Doppler shift in cesium

atomic frequency standards, " Metrologia, 7_, No. 2, pp. 49-56

(April 1971).

[5] Harrach, R. J., "Radiation -field-dependent frequency shifts of

atomic beam resonances, " J. Appl. Phys., 3_8_, No. 4, pp. 1808-

1819 (March 15, 1967).

[6] Becker, G. , Fischer, B., Kramer, G. , and Miiller, E. K. , "Neuentwicklung einer Casium-Strahl-Apparatur als primares

Zeit und Frequenz -Normal an der Physikalisch-Technische

Bundesanstalt, " PTB -Mitteilungen, 79, pp. 77-80 (February 1969).

20
FORM NBS-114A (1-711 U.S. DEPT. OF COMM. BIBLIOGRAPHIC DATA

SHEET

1. PUBLICATION OR REPORT NO. 2. Gov't Accession No.

3. Recipient's Accession No.

4. TITLE AND SUBTITLE Frequency Shifts Due to Ramsey Type Interrogation

in Atomic Beam Tubes

5. Publication Date January 1972

6. Performing Ofganization Code

7. AUTHOR(s) Helmut Hellwig, J. A. Barnes, D. J. Glaze, and

Peter Kartaschoff

8. Performing Organization

10. Project/Task/Work Unit No. 2730101

9. PERFORMING ORGANIZATION NAME AND ADDRESS NATIONAL BUREAU OF STANDARDS, Boulder labs DEPARTMENT OF COMMERCE Boulder, Colorado 80302

11. Contract/Grant Nc

12. Sponsoring Organization Name and Address Same as 9

13. Type of Report & Period Covered

14. Sponsoring Agency Code

15. SUPPLEMENTARY NOTES

16. ABSTRACT (A 200-word or less factual summary of most significant information. If document includes a significant bibliography or literature survey, mention it here.) part I ; A phase difference between the two interaction regions of a Ramsey excitation resonance structure results in a frequency bias

in the measured beam resonance. A simple mathematical model is discussed 'which

describes the dependence of this bias on the phase difference, the microwave power

level, the modulation amplitude, and the resonance linewidth. This dependence results

from the interaction of the modulated microwave excitation frequency with the asymmetric shape of the slightly shifted resonance line. In a first order approximation, no dependency on the frequency modulation amplitude is expected. Near-linear dependenci on the linewidth and microwave power level which are quite pronounced even at relatively small cavity phase differences are predicted. The theoretical results are compared with one set of experimental data on the microwave power dependence as measured in 1969 with the primary cesium beam standard NBS-III. After a correction

is applied to remove the power dependence due to spectral impurity of the microwave

excitation, the remaining measured power dependence agrees quantitatively with that calculated using a cavity phase difference of about 3 milliradians.

Part II : One of the most serious effects limiting the accuracy of atomic beam resonato

is the uncertainty of phase shifts between the oscillating fields in a Ramsey excitation

cavity. A technique using the linewidth dependence on the excitation power to measure

the phase-shift induced bias has recently been proposed. The conditions under which

this method is valid and their implications on the design of beam optics will be discusse

with consideration of available experimental results.

17. KEY WORDS (Alphabetical order, separated by semicolons) Cavity phase shift; cesium beam tube; frequency accuracy; frequency standard;

power shift; resonance line shape.

18. AVAILABILITY STATEMENT

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21. NO. OF PAGES

25

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