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Middlessex, England National Bureau of Standards, Boulder, Colorado Cesium Beam Atomic Time and Frequency Standards By R. E. BEEHLER, R. C. MOCKLER, and J. M. RICHARDSON ( ReceivedFebruary 23, 1965) With 10 Figures in the Text Abstract concept which underlies the operational realization of In recognition of the October 1964 declaration of the the unit. It remains to construct and operate the actual International Committee of Weights and Measures that the physical apparatus which makes the idealized concept physical measurement of time be based on a particular transi- tion between two hyperfine levels in the ground state of observable. At this point practical variations from cesium 133, a review of the characteri~tics of cesium beam ideality occur .We must then distinguish between the atomic frequency standards is presented; This article discusses ideal definition and the practical apparatus which the general requirements for frequency and time standards, physically embodies the definition. The qualities of the advantages offered by the atomic standard as compared to astronomical standards, various other atomic standards in apparatus are the subject of greatest study, and in our brief, the operating principles of cesium standards, measures discussion we shall elect to call the apparatus the of performance, error sources in cesium standards, character- "standard". The term standard, then, will imply an istics of several standards in current operation, comparison of apparatus based on a particular idealized concept, cesium standard!!, and atomic time standards derived from atomic frequency standards. namely the definition. It follows that the value provided by the standard Introduction may approach the value intended by definition to a greater or lesser degree. The degree to which any The Twelfth General Conference of Weights and prescribed observation of the standard approaches Measures, in October 1964, authorized the Internation- the definition may be termed the accuracy of the al Committee of Weights and Measures to designate standard with respect to the definition, or simply anatomic or molecular frequency to be used tempora- accuracy for short. rily for the physical measurement of time. The Inter- A standard of time is taken as a device which national Commitee declared that the transition to be generates an ordered, nearly continuous sequence of used is that between the hyperfine levels F = 4, mF = 0 and F = 3, mF = 0 of the ground state 281/2 states, or phases, which can be quantitatively identi- fied and correlated by observation with events -in of the atom of cesium 133, unperturbed by external short, a clock. In practice, clocks are often based on fields, and that the value 9, 192, 631, 770 Hz is assig- phenomena which recur with almost uniform period. ned to the frequency of this transition. The unit of time will then be proportional to the period A review of the characteristics of cesium beam of the clock upon which its definition is based. atomic frequency standards is therefore appropriate. Since time is a basic quantity in the Inter;national This article discusses the general requirements for System of Units, its standard should satisfy certain frequency and time standards, advantages offered by requirements deemed desirable for a standard of any the atomic standard as compared to astronomical standards, various other atomic standards in brief, quantity. Firstly, it must have continuity of operation, the operating principles of cesium standards, measures because of the impossibility of "storing" the unit of of performance, error sources in cesium standards, time as one "stores", say, the unit of mass. Only if the characteristics of several standards in current opera- unit is continuously generated and accumulated into tion, the comparison of cesium standards, and atomic its multiples is it possible to measure an arbitrary time standards derived from atomic frequency stand- interval whenever desired. The only acceptable alter- ards. native to continuity is the ability to re-establish the Requirements of Time Standards unit and its multiples whenever and wherever needed. The unit of the quantity time is the second. Before Secondly, as time progresses, the standard must this unit can be useful in measurement, we must give generate a unit which retains constant size with a definition of it in order to specify its magnitude. The respect to other acceptable measures of time. Of definition is an abstr~ction. It specifies the idealized course, a determinable and predictable variability in Vol.l R. E. BEEHLERet al. : Cesium Beam Atomic Time and Frequency Standards No.3 115 the period of the standard is permissible if corrections moon taken together with its theoretical relationship may be applied which lead to a constant unit. to the observed motion of the sun. The accuracy of Thirdly, accuracy of the standard should equal or this standard with respect to the definition is a few excel that of standards based on other possible defuri- parts in 109. tions. The requirement of accessibility at any place on Fourthly, the standard should be accessible to all earth and at any time is well satisfied by celestial who need it. If it is not directly accessible, its proper- standards. As refinements have been made, however, ties must be made available by indirect means such as it has been necessary to rely on a few well equipped calibration or broadcast. observatories to make and reduce the observations Fifthly, the characteristic period of the standard and to disseminate the results by appropriate means. should be convenient with respect to the operations The characteristic period of the celestial standard, which are to be performed on it. Time standaJ"ds give presently the tropical year, is inconveniently long. an observable phenomenon j (for example, angular Observations over a few years are necessary to attain position or voltage) nearly of the form j(t) = j precision comparable to the other factors which limit (t + 2 nn/(.0) where t is the time, (.0 is the nominal accuracy. Observations over centuries are necessary angular frequency of the standard, and n is an integer. for an exhaustive understanding of the standard. Necessary operations are averaging the period over Interpolation by auxilliary clocks is necessary bet- large values of n for precision, taking Fourier trans- ween observations of the celestial standards. forms for large n for analysis of the standard, and Astronomical standards provide epoch extremely generating multiples and submultiples of the period well. Their continuous operation precludes any lapse for measurement. It is convenient that (.0 be large so which would destroy the relationship of the present that these operations can be applied to conveniently epoch to the initial epoch. Their long characteristic small intervals as judged by a time characteristic of periods help avoid ambiguity of phase, even with man's work, such as his lifetime or the time in which infrequent observation. significant changes in techniques occur . Atomic frequency standards are based upon the Finally, because of the need to locate events on a frequency 'I' corresponding to a transition between continuous scale of time running from some arbitrary two atomic states separated in energy by L1E, accord- origin and common to all observers, the standard ing to the Bohr relation should also be capable of continuously accumulating h'l' = L1E , (1) the units. This process will give what is often called epoch. Epoch means the state, or phase, of the stand- where h~Planck's constant. Atomic standards have ard expressed in the measure of time, as referred to been developed in the past decade to the point that some arbitrary initial state. they satisfy the requirements of good time standards to a degree competitive with astronomical standards. Astronomical and Atomic Time Standards Continuity of operation has been achieved for Up to now, time standards based upon the obser- intervals of several years. In case of failure, it is pos- ved positions of celestial bodies undergoing known sible to re-establish the unit of time with confidence. or assumed motions have best satisfied the require- Constancy in the size of the unit based on an atomic ments discussed above. Two of the many possible definition may be strongly presumed to hold by the celestial "clocks" have major importance. These are nature of atomic energy levels. They are subject to the the rotation of the earth as manifested by the apparent laws of quantum mechanics and electrodynamics, diurnal motion of the stars, and the orbital motion of which enjoy a validity and permanence equal to that the earth, as manifested by the apparent orbital of the laws of dynamics underlying the astronomical motion of the sun. The apparent diurnal motion of the standards. In particular the levels are determined by sun, which also serves as an important clock, is a the interactions of relatively few elementary particles, combination of these phenomena.