39

1 Introduction

The center frequency of an eigenspectrumof an atom, a molecule, or an ion is as fixedand unchangeable as the basic physical con-stants. Based on this principle, an atomic fre-quency standard consists of an oscillator thatuses a high-resolution spectroscopic techniqueto obtain a highly accurate spectrum.

The second is currently defined in terms offrequency as "equal to 9,192,631,770 periodsof the radiation corresponding to the transitionbetween the two hyperfine levels of theground state of an atom of Cs133," as stipulatedat the CGPM (General Conference on Weightsand Measures) in 1967. Under this definition,it is assumed that the atom is in an ideal state;i.e., free from any perturbations. However, inorder to measure a physical quantity, it is nec-essary to add a certain perturbation to anobject and to observe the response. Conse-

quently, a measured frequency will deviatefrom the defined value due to various physicaleffects. Therefore, if the factors and extent ofthe measurement-induced shift in frequencyare not known, measurement results will notbe accurate in terms of the defined units. Aprimary frequency standard consists of equip-ment that can evaluate and adjust for this shift,thus ensuring accurate time measurementbased on the standard frequency [1][2]. Accu-racy is therefore determined by the degree towhich uncertainty induced by factors affectingthe shift may be measured and corrected.Accordingly, continuous operation of the stan-dard is challenging, due to the complexity ofthe evaluation of these factors.

Almost all of the various global standardtimes, including Japan Standard Time―gener-ated and maintained by the CommunicationsResearch Laboratory (CRL)―are based oncommercial cesium atomic clocks capable of

FUKUDA Kyoya et al.

3-2 Cesium Primary Frequency Standard

3-2-1 Optically Pumped Cesium Primary Fre-quency Standard

FUKUDA Kyoya, HASEGAWA Atsushi, ITO Hiroyuki, KUMAGAI Motohiro, KOTAKE Noboru, KAJITA Masatoshi, HOSOKAWA Mizuhiko, and MORIKAWA Takao

Communications Research Laboratory (CRL) has developed an optically pumped pri-mary frequency standard named CRL-O1 in cooperation with the National Institute of Stan-dards and Technology (NIST). The accuracy of CRL-O1 has been evaluated and reportshave been sent to the BIPM. In these reports, the two type uncertainties, that is type A andB involved in the frequency shift, are estimated. The total combined uncertainty is less than6×10-15 which normalized by the frequency of Cs clock transition. The results of the evalua-tion were published in the Circular-T. The evaluated frequency of CRL-O1 is in good agree-ment with that of other primary frequency standards.

Keywords Optically pumped primary frequency standard, CRL-O1, Accuracy evaluation, Frequency shift, Uncertainty

40

continuous operation (secondary frequencystandards). Although these atomic clocks pro-vide excellent long-term stability, the devicesthemselves cannot measure frequency shiftfactors on their own. Therefore, these clocksmust be evaluated and corrected using excep-tionally accurate, absolute primary frequencystandards. Only seven highly accurate pri-mary frequency standards, located in fourcountries, are currently used to calibrate theinternational coordinated universal time(UTC) standard. The CRL-O1 opticallypumped primary frequency standard, devel-oped through cooperation between the CRLand the U.S. National Institute of Standardsand Technology (NIST) is one such standard.This particular device is capable of definingthe second with an uncertainty of 6×10-15[3][4].

2 Optically pumped primary fre-quency standard

Fig.1 shows a basic schematic diagram ofthe CRL-O1 optically pumped Cs atom pri-mary frequency standard. The CRL-O1 fea-tures numerous components, including acylinder beam tube, a vacuum pump, a laserlight source, a microwave synthesizer, and ameasurement and control computer unit. Thetotal system measures 1.2 m in height, 1 m indepth, and 3.2 m in width. The beam tube hasa symmetrical appearance, as shown in Fig.1.

Cs ovens are installed at both ends of thebeam tube. Cs atoms are heated to about100˚C in these ovens, and are made to enterthe beam tube in the form of a beam afterpassing through a narrow tube (a collimator,with a diameter of 3 mm and a length of 50mm). To absorb excessive Cs atoms, a cylin-der of carbon graphite is placed between thecollimator and the beam tube. The obtainedatomic beam irradiates approximately 108

atoms/sec at the site of detection.The Cs atom may be in one of two ground

states: one in which the total angular momen-tum quantum number F is 3, or one in whichthe quantum number is 4. Immediately fol-lowing emission from the ovens, these twostates of atoms are present in nearly equalamounts in the atomic beam, but by the opticalpumping effect of the laser light (opticalpumping light), all the atoms are driven intothe F=3 atomic energy state. If a microwaveis applied twice in succession through theRamsey cavity to the beam of atoms that havebeen driven completely to the F=3 state, Ram-sey resonance will take place. In this way, theprobability of the beam atoms being either inthe F=3 state or the F=4 state after passingthrough the cavity becomes highly dependentupon microwave frequency. A standard fre-quency measures the number of atoms in theF=4 state in the atomic beam and determinesthe microwave frequency at which the transi-tion to the F=4 state occurs most efficiently(i.e., the frequency of transition between thehyperfine levels). The obtained line width ofthe spectrum (Ramsey spectrum) depends onthe time of flight of the atomic beam betweenthe two interaction regions.

Since the quality of the microwave cavityis directly related to numerous factors con-tributing to frequency shift, this is the mostimportant characteristic of the standard. Sincemicrowave phase difference between the inter-action regions in two locations causes fre-quency shift, the cavity must be as symmetri-cal as possible in order to minimize suchphase difference. Moreover, if the resonancefrequency of the cavity deviates from the reso-

Journal of the National Institute of Information and Communications Technology Vol.50 Nos.1/2 2003

Schematic diagram of opticallypumped Cs atom primary frequencystandard

Fig.1

41

nance frequency of the atom, a frequency shiftwill be produced (referred to as a cavitypulling shift); therefore, it is also necessary tominimize this frequency difference. Further-more, since frequency shift is also caused byleakage of the microwave from the cavity andfrom the microwave supply component, extracare is required in the manufacture of theseparts. In the design of the cavity of the CRL-O1, close attention was paid to such frequencyshift factors. The cavity uses a U-shaped rec-tangular wave guide in which an H-plane isused in TE10 mode. The interaction region isdivided by a drift region 1.53 m in length intotwo interaction regions, each 23 mm in length.We adopted a DeMarchi cavity, featuring aring-type structure[5], substantially reducingfrequency shift arising from non-uniformphase distribution inside the cavity in theinteraction regions. The cavity has a hole 3mm in diameter through which the atomicbeam passes. The loaded Q value of the cavi-ty is about 400.

Since our standard uses an H-plane cavity,the static magnetic field (C-field) used to pro-duce Zeeman splitting is parallel to the atomicbeam. A solenoid coil to generate the C-fieldis wound around an aluminum bobbin andcovers nearly the entire beam tube. This coilis covered with a three-fold magnetic shield.Magnetic shielding factors perpendicular toand parallel to the atomic beam direction areon the order of 106 and 103, respectively. Inorder to supplement reduced the magneticshielding factor in the parallel direction andalso to minimize the effects of geomagnetism,the beam tube is positioned in an east-westorientation. Moreover, the C-field is activelycontrolled to ensure generation of a constantmagnetic field.

An ion pump is used to regulate the beamtube to maintain a degree of vacuum equal toor less than 10-8 Torr (pumping speed of 20l/s). A constant temperature (approximately37˚C) is maintained using a nonmagneticheater and thermal insulation.

A microwave of 9.2 GHz corresponding tothe frequency of clock transition is obtained

by multiplying and synthesizing outputs ofvoltage control crystal oscillators (VCXO) of5 MHz, 100 MHz, 10.7 MHz. All the VCXOsare phase locked to a hydrogen maser actingas a standard oscillator and are linked to theoriginal signal for Japan Standard Time, desig-nated as "UTC (CRL)." The 10.7-MHz VCXOis phase locked to a DDS (Direct Digital Syn-thesizer) controlled by a PC, and is capable ofsweeping a range of about 360 kHz around acenter frequency of 9.2 GHz. Microwaveintensity can be set to an arbitrary intensitywith reduced fluctuation using a power servocircuit; this intensity then may be controlledby the PC. In order to determine the center ofthe atomic resonance line, slowly changingsquare-wave modulation is applied.

A 20-mW DBR laser (its frequency stabi-lized relative to a Cs absorption line using theFM sideband method) is used to excite theatom. The laser light is divided into twobeams: one for optical pumping, and the otherfor detection. In our standard, the opticalpumping light and the detection light are tunedto the transition from the F=4 ground state tothe F'=3 excited state as well as to the transi-tion from the F=4 state to the F'=5 excitedstate. The laser light is of linear polarizationand is irradiated to the atom from a directionperpendicular to the direction of travel. Theoptical pumping light that passes through thebeam tube is then reflected by a double-refrac-tion prism and is again irradiated to the atomicbeam. This reflected light is polarized perpen-dicular to the incident light, thus increasingthe efficiency of optical pumping. By thismethod, the atom is transformed from the F=4energy state to the F=3 state at almost 100%efficiency, without the atomic transition to thedark state normally generated by laser-lightirradiation. A spherical mirror and an ellip-soidal mirror are combined to form a mirrorfor collecting fluorescence from the atoms thathave interfered with the microwave, and thecollected light is extracted to the outside of thevacuum chamber by a light-pipe. The extract-ed fluorescence is converted to an electricalsignal using a high-sensitivity optical detector

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and an operational amplifier, and this signal isthen sent to the measurement and control com-puter through an AD converter.

3 Frequency shift and uncertainty

When the frequency of the clock transitionof the cesium atom is measured, various exte-rior perturbations are introduced; as a result,the measured frequency differs from the origi-nal frequency of the cesium atom. By defini-tion, however, the frequency of the clock tran-sition between the ground states of the cesiumatom must be determined in the absence ofany such perturbations. Therefore, in order todetermine the value for definition experimen-tally, the extent of the shift due to perturbation(referred to hereinafter as the frequency shiftquantity) must be estimated and the measure-ment value adjusted accordingly. The uncer-tainty of this estimation is also an importantparameter in the application of the primaryfrequency standard; the process of estimationand the associated uncertainty will be dis-cussed separately below[6][7].

Improving the accuracy of these estimatescontinues to form a significant focus ofresearch. According to the guidelines of theInternational Committee of Weights and Mea-sures (BIPM = Bureau International des Poidset Mesures)[8], uncertainty can be divided intothat induced by statistical variation (type A)and that induced by systematic deviation inmeasured values (type B). From here throughsection 3.6 below we will describe type Buncertainty (type A uncertainty will be dis-cussed in section 3.8). All values listed beloware expressed in the order of magnitude of 10-15,and are obtained using the clock transition fre-quency to normalize the frequency width cor-responding to the estimated uncertainty.

3.1 Second-order Doppler shiftSince the microwave is applied perpendi-

cular to the travelling direction of the atom, itis not necessary to consider the first-orderDoppler shift. However, according to the the-ory of relativity, time viewed from the coordi-

nate system of a stationary observer differsfrom time within the coordinate system of thetraveling atom (atomic eigentime). The fre-quency shift quantity in this case is given by

Here, V denotes the velocity of an atomcluster, c the velocity of light, andνCs the clocktransition frequency of the cesium atom,9,192,631,770 Hz. This equation is for anatom cluster having a single velocity. Sincegenerally atom clusters feature a distributionof velocities, however, the weighted integralof the value determined by this equation willcorrespond to the frequency shift quantity forsuch an atom cluster. In this case, we mustdetermine the velocity distribution; this isdone by measuring Ramsey signals (usingseveral microwaves of different intensities)and then performing Fourier transformation onthese signals[9].

Type B uncertainty in the second-orderDoppler shift depends on the accuracy of thedetermination of velocity distribution. Thestatistical uncertainty accompanying theFourier transformation was 0.6. The uncer-tainty arising from potential instability of themicrowave power servo was 1.8. Therefore,overall uncertainty of the second-orderDoppler shift was estimated to be 2.

3.2 Quadratic Zeeman shiftZeeman shift refers to a change in the res-

onance energy of an atom resulting fromapplication of an external magnetic field. Theclock transition of the cesium atom is the tran-sition from a ground state in which F=4 andmF=0 to one in which F=3 and mF=0 (here-inafter referred to as a "0-0 transition" refer-ring to the mF values of the two ground states),where F denotes the total angular momentumquantum number, and mF denotes the magneticquantum number. In order to observe the fre-quency of this transition, a C-field is appliedto the microwave cavity of the standard insuch a way as to prevent transitions betweenother Zeeman sub-levels. The shift in the 0-0

Journal of the National Institute of Information and Communications Technology Vol.50 Nos.1/2 2003

43

transition frequency due to this magnetic fieldis the quadratic Zeeman shift. Here the shiftquantity is expressed by the following equation.

Here,νZ denotes the Zeeman Frequency, orthe difference between the frequency of the 0-0 transition and that of the 1-1 transition. Theuncertainty associated with this shift quantitydepends on the frequency stability of the servocircuit used to control the C-field. Since theaccuracy of the determination of the Zeemanfrequency in this circuit is 0.01 Hz or lower,the uncertainty is 0.2 or less.

3.3 Cavity pulling shiftThis shift is caused by the difference

(detuning) between the resonance frequencyof the microwave cavity and the atomic reso-nance frequency. This phenomenon occurswhen the resonance frequency of the cavitydeviates from that of the atom, resulting indeformation of the atomic resonance line andin an apparent shift in the frequency of the res-onance peak. The shift quantity in this casecan be expressed by the following equation.

Here,λdenotes detuning of the microwave,P represents transition probability,ωm is theamplitude of modulation, and b is the Rabifrequency. In this case, the quantity db/dλisdependent solely on the detuning between thecavity and the line width[10].

Since the cavity of the CRL-O1 is con-structed with great care, this shift is extremelysmall. System stability when the frequencywas stabilized to the center of the Rabi reso-nance frequency was found to be approxi-mately 2×10-11 for a period of 100 s. Byextrapolating this to a value corresponding toa full day of measurement (86,400 sec) andalso taking into account the frequency shiftdue to Ramsey resonance (this shift is approx-imately three orders of magnitude smaller thanthat of Rabi resonance), type B uncertainty

was estimated at 0.6.

3.4 End-to-end cavity phase shiftThis shift is peculiar to a Ramsey type

cavity with two resonance regions. If thephase of the microwave differs between theoccurrence of the first and second resonance,the peak of the Ramsey signal is shifted. Thisshift can be reversed and thus corrected byreversing the direction of the atom beam usedin measurement. However, if trajectories ofthe beams at both resonances do not perfectlycoincide, distributed cavity phase shift occurs,limiting the accuracy of the correction. How-ever, since we have adopted a ring-type cavity,the shift quantity is structurally minimized.This shift quantity can be expressed by thefollowing equation.

Here,φdenotes the phase differencebetween the cavities; this value is determinedfrom measurement data. E denotes the timerequired for the cesium atom to pass throughthe two cavities; this value is related to thevelocity distribution of the atom cluster. Theuncertainty of the resonance frequency in thiscase can be expressed by

Here, E and E' denote different values of Ein accordance with the different directions ofthe atomic beam. The equation shows that theuncertainty is dependent on the accuracy ofthe determination of phase difference and ofthe velocity distribution. In this case we esti-mated uncertainty to be 0.2 or less.

3.5 Blackbody radiation shiftThis shift originates from pumping of a

non-resonant atom by background blackbodyradiation. This shift can be interpreted as anAC Stark effect, with a theoretical equationgiven by

FUKUDA Kyoya et al.

44

In this case, the measurement error of the tem-perature inside the standard determines theuncertainty of the frequency. Roughly esti-mating the temperature-induced measurementerror to be 2˚C, we assumed an uncertaintyvalue of 0.5.

3.6 Gravitational shiftThis shift is induced by the earth's gravita-

tional field. Since the frequency of TAI is cur-rently defined as a value on an assumed geoidsurface, measured frequency must be correct-ed accordingly. A theoretical equation for thiscorrection is given by

where h denotes height from the geoid sur-face. Error in this measurement of height rep-resents an additional factor determining uncer-tainty. Experimental results indicated thatsuch error was on the order of several tens ofcentimeters. This corresponds to uncertaintyof 0.1 or less.

3.7 Other frequency shiftsFactors other than those described above

also contribute to frequency shift, some ofwhich will be discussed later. However, theeffects of most such factors were deemed suf-ficiently small in the present evaluation of theaccuracy of the CRL-O1; only potentiallynon-negligible factors were considered.(1) Light shift

This is a phenomenon in which the atomabsorbs the laser light used for optical pump-ing or detection and emits fluorescence to thebeam axis, resulting in a change in the energyof the atom due to the optical Stark effect.(2) Distributed cavity phase shift

This shift is generated by variation in thephase distribution of the microwave in thehole through which the atomic beam in themicrowave cavity passes. This shift alsoaffects the measurement of the end-to-endcavity phase shift described above. This shiftbecomes significant with conventional cavitystructures that rely on reflection at the waveguide terminations. The cavity we use fea-

tures ring-shaped terminations, as shown inFig.1, to minimize this shift.(3) Collisional shift

This frequency shift is generated by thecollisions between the atoms.

In reality, if such collision were to occur,causing the phase of the ground state to varyduring the atom's trajectory, the Ramsey signalitself would disappear; therefore, this shiftwould not result in phase variation.

It is conceivable that factors other than thethree discussed above may cause frequencyshift; however, it is presumed that the totalextent of such shift―including shift inducedby the three factors discussed above―will besmall. The major factors contributing to fre-quency shift remain those discussed in sec-tions 3.1 through 3.6. We should note, how-ever, that this assessment is considered toapply to measurement using the opticallypumped primary frequency standard; withatomic fountain primary frequency standards(expected to be used widely in the future)other factors may emerge for evaluation. Fur-thermore, as measurement accuracy isimproved, even more factors will come tolight. In the current case, shift caused byunidentified factors deemed negligible interms of our equipment (uncorrected biases)was assumed to be 0, with uncertainty (typeB) estimated as 3.2 or less.

3.8 Type A uncertaintyIn the evaluation of accuracy, measure-

ment is performed for ten days (one day forone data point) to determine the frequency dif-ference between the hydrogen maser and theCRL-O1. We arrive at an accuracy value bysubtracting all of the above-mentioned shiftquantities from daily measured values. Sinceeach daily measurement value collected fea-tures dispersion, the standard deviation of thedaily measurement data is calculated anddivided by the square root of the degree offreedom of measurement to obtain a value fortype A uncertainty.

In the evaluation of the CRL-O1, accuracycan be seen in terms of (a) the stability of the

Journal of the National Institute of Information and Communications Technology Vol.50 Nos.1/2 2003

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CRL-O1 itself, (b) the stability of a reference,and (c) other stabilities. The stability of actualmeasurement is the sum of these stability val-ues, which is given by the equations (8), (9).

and

Here, n denotes the number of frequencymeasurements and Ri denotes the measuredvalue from which the frequency shift quanti-ties (determined for the respective measure-ments) were subtracted. We used a Russianhydrogen maser (Oscilloquartz SA, CH1-75)as a reference; the stability of this reference,evaluated by Allan variance, was as follows:2×10-13 for measurement with a sampling timeof 1 sec, 2×10-15 for a measurement of 10,000sec, and 1×10-14 for a measurement of 10 days.

On the other hand, the stability of theCRL-O1 itself is always evaluated in terms ofa single second with reference to the hydrogenmaser, and one-day stability is estimatedbased on this value, which is given by the fol-lowing equation.

Here, Si denotes the estimated stability foreach measurement. The value obtained fromthis evaluation must be considered as a theo-retical minimum value of type A uncertainty.However, in a finite data set obtained over thecourse of 10 days of measurement,σr mayoccasionally be less than this minimum value.In such cases, we would use notσr butσs forthe evaluation of type A uncertainty. There-fore, type A uncertainty uA is expressed by thefollowing equation.

However, ifσr >σs, thenσj =σr, and ifσr <σs, thenσj =σs.

3.9 Total combined uncertaintyThe main uncertainties mentioned in our

report to the BIPM consist of the type A andtype B uncertainties described above. Thesquare root of the sum of the squares of theabove-mentioned uncertainties (both type Aand type B) plus all other uncertainties―suchas the uncertainty of the link between the UTC(CRL) (the time system managed by the CRL)and the hydrogen maser, the uncertainty of thelink between the UTC (CRL) and TAI (Inter-national Atomic Time)―forms a total com-bined uncertainty that is publicized in the Cir-cular T.

4 Bulletin report to BIPM

These measurement results are summa-rized as follows, and together comprise theaccuracy evaluation of the CRL-O1 as report-ed to BIPM.

(1) Frequency difference between the defi-nition value and the UTC (CRL) value, deter-mined by subtracting the frequency shift quan-tities described in sections 3.1 through 3.6from the measured frequency value

(2) Frequency shift quantities, their type Buncertainties and type A uncertainties, and theuncertainty of the link between CRL-O1 andUTC (CRL)

(3) As auxiliary data, the differencebetween the frequency determined using thehydrogen maser and that determined usingUTC (CRL)A portion of the latest report we have submit-ted is shown in Table 1. Each frequency shiftquantity is calculated by the above-mentionedtheoretical equation using actual measurementvalues. For type A uncertainty, a value of 5×10-15 was obtained. This is one of the betteraccuracy values obtained over 10 days of eval-uation results.

In Table 1, type B uncertainty of the end-to-end cavity phase shift is 0.8. The uncer-tainty values described in section 3.4 reflectresults obtained based on a detailed evaluationconducted after issuance of this report.

Fig.2 shows a plot of the difference

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between the measured frequencies of CRL-O1optically pumped primary frequency stan-dards, those of other research organizations,and International Atomic Time (TAI); thesedifferences are shown on the vertical axis,with year/month/day of measurement (in unitsof modified Julian day: MJD) on the horizon-tal axis. In the figure, data denoted by the Cir-cular T is a value based on multiple data itemsfor all of the primary frequency standards,including the magnetic-selection type standardand the atomic fountain type standard.

Based on the diagram, we can concludethat the CRL-O1 is the most accurate deviceamong all current optically pumped primarystandards for definition of the second. How-ever, in recent years, the advent of the atomicfountain type primary frequency standard hasconsiderably reduced the uncertainty associat-ed with the definition process. The uncertain-ty of the PTB's atomic fountain type standard(the PTB-CSF1) is approximately 2.0 to 2.5.The NIST atomic fountain type standard(NIST-F1) has reported uncertainty of about1.5 to 2.0. The CRL-O1 primarily featurestype A uncertainty. With increasing amountsof measurement data type A uncertainty can befurther reduced. However, since the frequen-cy drift of the hydrogen maser currently usedas the reference in the measurement periodaffects the shift quantity of the measured fre-quency, some correction will be required. Thecalculated average value of the frequency dif-ferences between the multiple commercial Csclocks and the UTC official announcementvalue becomes as small as 10×10-15 to 20×10-15

in terms of variation width; therefore, thisaverage can be used to correct frequency vari-ation of the hydrogen maser for the period ofevaluation. In this case we can perform cor-rection based on a drift trend that is predictedbased on past frequency variation data. Then,for the evaluation of reference standard accu-racy, a reference signal may be used that hasbeen adjusted according to the predicted trendusing a frequency offset generator.

5 Conclusions

In collaboration with the NIST, the CRLhas developed the CRL-O1 optically pumpedprimary frequency standard. We have report-ed on the results of accuracy evaluations con-ducted since April 2000, contributing in theprocess to the high accuracy of InternationalAtomic Time. The accuracy evaluation resultsfor the CRL-O1 agree well with BIPM values.A system for minimizing the frequency drift ofthe hydrogen maser used as the reference inthe accuracy evaluation is now under con-

Journal of the National Institute of Information and Communications Technology Vol.50 Nos.1/2 2003

Results of accuracy evaluation ofthe CRL-O1

Table 1

Comparison of measurement results ofthe optically pumped primary fre-quency standards of CRL-O1 andthose of other research organizations

Fig.2

47

struction, and we believe that type A uncer-tainty can be further reduced through long-term measurements. We are currently prepar-ing a paper dealing with the CRL-O1 accuracyevaluation; the paper is intended to report onthe details of the device, measurement results,a method of evaluating shift quantities anduncertainties, and more.[11].

Acknowledgments

We are thankful to Dr. R. Drullinger andmembers of the NIST Time and FrequencyDivision, who supported us with helpful dis-cussions and opinions in the course of thedevelopment of the CRL-O1 and in the corre-sponding evaluations of accuracy.

Appendix

Here we will describe Ramsey resonance.In a Ramsey system, atoms and microwavesinteract in two separate regions, and a reso-nance signal is observed. The two interactionregions have the same structure. There aretwo types of cavities: with one, the directionof travel of the atomic beam is perpendicularto the direction of the microwave magneticfield in the interaction regions (E-bend type);with the other, the direction of travel of theatomic beam is parallel to the direction of themicrowave magnetic field (H-bend type). AnH-bend type cavity is used in the CRL-O1.

Analysis is straightforward with a singleinteraction region; when a weak C-field isapplied to the atom and multiple Zeeman sub-levels in the ground state can be sufficientlyseparated, the atom can be treated using thetwo-level model. The resonance of the atomand the microwave in a single interactionregion is referred to as Rabi resonance. Theresonance-spectrum line width is inverselyproportional to the period of interactionbetween the atom and the microwave.

Analysis is complex, however, with twointeraction regions. In this case two interac-tion regions each of a length l are separated bya space of length L. No microwave is present

in the space between the two regions; this isreferred to as the drift space. Consider a casein which the static magnetic field of the driftspace is equal to the C-field of the interactionregions, and the atomic beam of a singlevelocity v passes through the two interactionregions and the drift space. The resonancebetween the atom and the microwave at thismoment is referred to as the Ramsey reso-nance, and its transition probability P2 is givenby the following equation[12].

where b =μBB/η,μB : Bohr magneton, B:microwave magnetic-field strength,η: Plankconstant, Ω = ,Ω0 =ω-ω0,ω: micro-wave frequency,ω0 : resonance frequency ofthe atom, T = L/v : time required for the atom-ic beam to pass through the drift space,τ=L/v : time required for the atomic beam to passthrough the single interaction region.

The transition probability P2(τ) is depend-ent on the microwave intensity. It reacheslocal maximum at Ω0 = 0, namely ω = ω0,and takes the highest value of 1 at bτ=π/2.The equation (A.1) indicates that with increas-ing T, the transition probability becomes moresensitive to the microwave frequencyωand anarrower resonance spectrum can be obtained.

The spectrum component generated byeach Rabi resonance in the two interactionregions is called the Rabi pedestal, and isexpressed by the following equation.

This is obtained by averaging the high-fre-quency component of the transition probabili-ty of the Ramsey resonance. The observedspectrum becomes a superposition of the Rabipedestal P3 and the Ramsey resonance spec-trum P2. In the foregoing example, only thecase in which the atomic beam has a singlevelocity v was considered; however, an actualatomic beam features velocity distribution.

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The most probable velocity of the atomicbeam used for the optically pumped standardis approximately 260 m/s, and the full width athalf maximum of the velocity distribution isapproximately 120 m/s. Therefore, theobserved resonance signal becomes a superpo-sition of resonance signals of atoms with vari-ous velocities, and consequently distinct maxi-mum and minimum points in the Ramsey res-onance (Ramsey fringe) are observed only inthe near vicinity of the resonance frequency ofthe atom.

In the atomic fountain type frequencystandard, the atomic speed is minimized bylaser cooling technology. The atomic beamused for microwave resonance has an averagevelocity of approximately 1 m/s and the widthof the velocity distribution is a few cm/s orless. Therefore, as shown in the present sec-tion 3-2-2, "Atomic fountain type frequencystandard," a spectrum narrower than that ofthe optically pumped frequency standard isobtained and the Ramsey fringe is observedover the entire Rabi pedestal.

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49FUKUDA Kyoya et al.

FUKUDA Kyoya

Senior Researcher, Atomic Frequency Standards Group, Applied Researchand Standards Division

Frequency Standard, Laser Spec-troscopy

HASEGAWA Atsushi, Ph. D.

Senior Researcher, Quantum Informa-tion Technology Group, Basic andAdvanced Research Division

Non-linear Laser Spectroscopy

ITO Hiroyuki, Ph. D.

Researcher, Atomic Frequency Stan-dards Group, Applied Research andStandards Division

Atomic Frequency Standards

KUMAGAI Motohiro, Ph. D.

Researcher, Atomic Frequency Stan-dards Group, Applied Research andStandards Division

Atomic Standard, Laser Physics

KAJITA Masatoshi, Dr. Sci.

Senior Researcher, Atomic Frequency Standards Group, Applied Researchand Standards Division

Quantum Electronics, Atom & Molecu-lar Physics

KOTAKE Noboru

Researcher, Japan Standard TimeGroup, Applied Research and Stan-dards Division

Time and Frequency Standard

HOSOKAWA Mizuhiko, Ph. D.

Leader, Atomic Frequency StandardsGroup, Applied Research and Stan-dards Division

Atomic Frequency Standards, SpaceTime Measurements

MORIKAWA Takao

Research Supervisor, Applied Researchand Standards Division