200 IRE TRANSACTIONS ON INSTRUMENTATION December

frequency shift in the double beam maser will be re- It may be concluded that the double-beam ammoniaduced by a factor maser with a system of automatic beam balancing and

nl- n22 cavity tuning will have a resettability of the order of( lOn2810-13 if the maser is magnetically well shielded. A rela-\fnl + n2/ tive short time stability of the order of 10-15 will be ob-

.. ~~~tainable in a favorable condition.where n1 and n2 are the effective intensities of the twobeams. For a value of nl:n2=2:3, the ratio is as small

as 0.04. ~~~~~~~~~~ACKNOWLEDGMENTas 0.04.Unfortunately, the observed effect of local magnetic The author expresses his thanks to N. Kohno for his

field is larger than those calculated from a simple theory, assistance in the operation of masers and to the mem-but it is still smaller than the effect in the hydrogen bers of the Tokyo Astronomical Observatory who fur-maser as shown in Table I. nished standard frequency signals.

N15H3 Double-Beam Maser as a PrimaryFrequency Standard*

JEAN DE PRINSt

Summary-Ammonia masers are studied concerning their use these two frequencies be brought into coincidence. It isas frequency standards. They oscillate on the J=K=3 inversion desirable that this characteristic frequency be equal toline of N'5H3. Single beam masers allow the realization of a frequency the natural frequency Po of the transition used.standard with a stability of 2-3.10-11, and an accuracy of about10-9. Experiments on double beam masers suggest that their use Since the oscillation conditions are relatively critical,makes it possible to obtain a stability of the order of 10-12 and an it is desirable that the maser oscillate on the most inten-accuracy better than 10-10. sive of the lines of the inversion spectrum of natural

ammonia N14H3, characterized by the quantum num-HE~~~~INETR ofteamnamsrhv ber J=K=3. Previous studies have shown that in this

l from the very first recognized its possibilities as afrequency standard t]. case the characteristic frequencies of the masers strongly

The frequency of a maser VM is in a good approxima- depend on the experimental conditions [31-[81. This isdue to the multiplicity of the line resulting from thetion related to the naturalfrequencyv Pofthe trela quadrupole interaction of the Ni4 nucleus of nuclear spinused, and to the frequency v, of the cavity by the rela-one Th uduoeculn cntn sgetrbtion 1 one. The quadrupole coupling constant iS greater bytion [2] about 3 kHz for the lower inversion state than for the

Pj - v0 Al P_vC -PO higher state [9].- = Qc-f(6) K (1) The result of this is that the line 3-3 of N14H3 is

formed by three components of different intensitieswhere QC is the quality factor of the cavity, Avl is the and separated in frequencies by 1.7 kHz and 0.6 kHz.line width, f(O) is a saturation factor. In principle, it is The intensity of these different components dependsthus possible to tune the frequency of the maser oscil- on the experimental conditions, and mainly on the statelator through the use of the Zeeman effect. If a mag- selector characteristics. The maser frequency oscilla-netic field is modifying Ai\, the cavity will be tuned tions, being an average of the frequencies of these com-(vc=v0) when the frequency PM of the maser is inde- ponents, will vary with the variations of their respec-pendent of the magnetic field applied to the cavity The tive intensities and consequently with the experimentalcorresponding maser frequency is defined as being the conditions. It is thus essential for the use of the maser"characteristic frequency" which differs from the as a frequency standard to utilize a single line.natural frequency iodue to secondary effects. The use of Onle solution is to use the 3-2 line of N14H3. For thisthe maser as a primary frequency standard requires that line the quadrupole interaction factor of the nitrogen

nucleus proportional to* Received August 17, 1962. Presented at the 1962 International

Conference on Precision Electromagnetic Measurements as Paper 7 3K2No. 7.2. 11-

t University of Brussels, Brussels, Belgium., J(J +1)

1962 De Prins: N15Hs Double-Beam Maser as a Primary Frequency Standard 201

is zero. The total number of molecules required to build is conditioned by the method of measurements. We needup an oscillation is unfortunately higher than for beam a mode with n = 0 or 1, and one which is not degenerated3-3 and this leads to serious inconveniences, as we shall with another mode (e.g., TEoll and TM111).see later. In particular, our experiments show that the For the tuning of the cavity, the magnetic field mustline width AP, increases linearly with the number of be orientated in the direction corresponding to the o-molecules used. components of the Zeeman effects. In our case twoA second solution which is preferable is to use the rectangular coils produce a magnetic field, the intensity

line 3-3 of the isotopic ammonia N15H3. The basic equa- of which is limited to one-oersted.tion (1) is valid only if the molecule undergoes an The focusing voltage and the number of molecules ininduced transition in a high-frequency field that is sta- the two beams can be independently adjusted in Ap-tionary. In practice this condition is not realized be- paratus No. 1, but the alignment of the cavity with thecause the energy emitted by the molecule is not uni- nozzles and the state selection is only roughly possible.formly distributed along the cavity [2 ]. The dissymetryresults from the divergence of the beam and from the Apparatus No. 2fact that the transition probability depends on the inter- This apparatus was specially designed so that anaction time of the molecule with the high-frequency field. alignment of the components within 0.1 mm is possible.This gives rise to a progressive wave component which Furthermore the construction ensures that the char-tends to equalize the energy distribution in the cavity. acteristics of the two beams are identical. Indeed, theThe frequency emitted by the molecules in the presence high voltage generator is the same for both state se-of this progressive wave will be displaced by the Doppler lectors, and the symmetrical construction of the am-effect. monia distribution system provides, on the two nozzles,As suggested by Shimoda, Wang, and Townes [2 ] the an identical number of molecules.

progressive wave appearing in the cavity can be greatly The components are identical to those used in Ap-reduced by symmetrizing the phenomena with the aid paratus No. 1 with the exception of the nozzles, whichof a second beam of opposite direction. It is to verify here have a diameter of 5 mm and are formed by chan-this hypothesis and to make the maser a primary fre- nels of 0.3 mm diameter and 5 mm long. The nozzlequency standard that we have constructed in the "La- directivity in Apparatus No. 2 is therefore about threeboratoire Suisse de Recherches Horlogeres" two experi- times smaller than in No. 1.mental prototypes of a double beam maser.

METHOD FOR THE MEASUREMENT OF THEDESCRIPTION OF THE APPARATUS CHARACTERISTIC FREQUENCY

Apparatus No. 1 The frequency of a quartz clock 1 MHz determinedAmmonia enriched to 95 per cent of N15H3 can be by a Cesium standard is compared to the maser fre-

commercially obtained. Since this product is expensive quency. The measurement is made in two stages.the maser has been built with the intent of recovering 1) The frequency of the maser is compared to that ofthe ammonia used during the measurements. an adjustable auxiliary 8.5 MHz quartz oscillator. ThisApparatus No. 1 permits the independent adjustment latter frequency is multiplied by 2681 so that a micro-

of the two beams entering the cavity. Each beam is wave reference signal is obtained of a frequency nearlyformed by a nozzle, fed from a stainless steel reservoir, equal to that of the maser. After superheterodyne de-and produces a beam of ammonia molecules which, tection and amplification, the beat frequency betweenpassing through a state selector, is enriched in mole- these two signals is measured by a frequency meter andcules in the higher inversion state by the action of an is graphically recorded.inhomogeneous electrostatic field. To determine the characteristic frequency, the tem-A "needle valve" regulates the debit of the N15H3 perature of the cavity is slightly changed so that the fre-

beam. The beam intensity of 1016 to 1018 molecules/sec quency of the cavity is slowly displaced through theis measured by the pressure before the nozzle. The noz- natural frequency Po. At the same time, a sawtoothzle (diameter 3.5 mm) is formed by an array of fine generator establishes in the cavity a magnetic fieldparallel channels (0.1 mm diameter, 5 mm long). The which varies linearly from 0 to 1 oersted at a repetitionstate selector uses a quadrupolar electric field and con- rate of 1 cps. The recording of the beat frequency im-sists of four cones of stainless steel, the axes of which mediately shows the passage through zero of the fre-converge toward the nozzle. A voltage up to 20 kv is quency modulation produced by the magnetic field, andapplied between neighboring cones. thus easily permits the determination of the characteris-The cavity of a maser must have a high quality factor tic frequency. The frequency of the auxiliary oscillator

and a good frequency stability. For this reason, we is thus known in comparison with that of the maser.chose a copper-plated brass cylindrical cavity, 17-cm 2) During the measurements described above, thelong, of mode TM010 without movable parts. frequency of the quartz oscillator 1 MHz is compared toA frequency adjustment is affected by varying the the frequency of the auxiliary oscillator by classical

temperature of the whole cavity. The choice of the mode rmethods using electronic counters.

202 IRE TRANSACTIONS ON INSTRUMENTATION December

The measurement of the characteristic frequency is state selector passes from 0 to 20 kv [3]. If we admit amade with a precision of 2.0-11. frequency variation proportional to the number of mole-

cules in the cavity, the effect of the high voltage varia-EXPERIMENTAL RESULTS tions in Apparatus No. 1 for a number of molecules

Effect of the Progressive Wave in the Cavity lower than 3.1017 mol s-' is less than 10-10 and thus notmeasurable.

The experiments made with Apparatus No. 1 bring The complete theoretical justification of this fre-out the effect of the progressive wave component in the quency variation is more difficult. In fact the measure-cavity. We have measured the frequency of the maser ments of line width show a broadening proportional toas a function of the number of molecules in one beam. the number of molecules, thus indicating that there areThe voltages of the two state selectors and the number interactions between the molecules in the cavity. Weof molecules in the other beam are kept constant. We would attribute to these interactions the frequency vari-observed the frequency variation of the maser predicted ations as a function of number of molecules.by the progressive wave theory [2 ]. The frequency goesthrough an extremum when the two beams are identical(Fig. 1). k21 - |----t .= N:6,2 1016Hmlls

22789421 705 -fdl____________

DOUBLE BEAM N 0 N=q2 1016x ~~~~~~N=1,35 11

22789421 700H 7 N7,1 1

710 10 15 20kV

Fig. 2-Frequency variations of double-beam maserwith experimental conditions.

N1 =9,2 1016 mol/s720 / V1 =v2 16k V

I Double beam N'1kHz *Double beam N!2

730L xlx10mat/s 22789421700-1 2 N

Fig. 1-Influence of traveling wave on maser frequency.

705-Influence of the Experimental Parameters on the Charac-teristic FrequencyThe frequency of the double beam maser is within the 710-

experimental errors independent of the voltage appliedon the state selector (Fig. 2). On the other hand the fre- 7N/3quency varies in function of the number of molecules N 1 2 3 4 5xlO mol/sin the beam, but not with the oscillation amplitude. In- Fig. 3-Frequency of the double-beam masers vsdeed this latter varies strongly with the voltage applied number of molecules in the beam.to the state selectors and the experiment shows that inthis case the frequency does not vary. kHzThe following results suggest a linear relation between 1°-10 Double beam N 1

the frequency and the number of molecules in the cavity, 22789421 700- Double beam N'2this number being proportional to N2'3: 1) A plot of fre-quency vs N213 gives a straight line within experimentalerror (Figs. 3, 4). 2) The difference in nozzle directivities 70produces different numbers of molecules in the cavityand thus different slopes, the ratio of which corresponds Yapproximately to the ratio of nozzle directivities. 3) For mmaser oscillation on the 3-2 N14H3 line, the influence of\the number of molecules should be 12 times larger due \ N 2/3to the larger threshold number of molecules required foroscillation. The experiment effectively gives this order of 2 3 4 Sx07o/magnitude. 4) The number of molecules in the cavity Fi.4reunyothdub-eamsrsvealtdvaries only by 2 per cent when the voltage applied to the number of molecules in the cavity.

1962 De Prins: N15H? Double-Beam Maser as a Primary Frequency Standard 20O

Stability and Accuracy of the Double-Beam Maser oscillator, which amounts to 2.10-11 for 0.2 sec measuring

1) Stability: The number of molecules in the beam time. Such fluctuations should be eliminated if the auxil-is easily measurable and reproducible within a few per iary quartz oscillator is replaced by a maser. Prelim-cent. This reproducibility ensures the reproducibility inary experiments have indicated a measurement preci-of the frequency to within a few units in 1012. One can sion of 4.10-12 (Fig. 5). A system using this techniquethus be certain that for a given apparatus the long-term is under construction at the University of Brussels.stability is also of a few 10-12.

2) Accuracy: If we accept the hypothesis of a linear Typic expimentfrequency variation as a function of the number ofmolecules, we can extrapolate the frequency to zeronumber of molecules in the cavity. The extrapolated llos.value is identical for the two double-beam masers. Thefrequency is 22,789,421,701 + 1 Hz in the A-1 scale (Cs |_ __l_l9,192,631,770 Hz). MeasurementTo evaluate the accuracy of the double-beam maser,

it is necessary to know to what extent the progressivewave has been eliminated. We can make the followingrough evaluations: In a single-beam maser, increasingthe high voltage applied to the state selector from 10 to 42.0 43. 44.00 46.0 Hz.20 kv gives an increase of the progressive wave effect by -about 40 per cent [3]. In the double-beam maser, the | Field 0,520e.corresponding increase is less than the measurementerror of 2.10-11 and we may estimate that the total Fig. 5-Frequency measurement with two masersmaximum progressive wave effect is lower than 10-10.

In spite of the uncertainty subsisting as to the true ACKNOWLEDGMENTcause of the frequency variation in terms of the numberof molecules, our results clearly establish that the accu- The author wishes to thank C. Menoud for his collab-racy of the double-beam maser exceeds 10-10. oration in the final experimentation, and P. Kartaschoff

for the construction of certain electronic devices. Dr.CONCLUSION G. Severne has kindly corrected the English text.

The essential qualities of an atomic frequency stand-ard are high signal-to-noise ratio, high operating fre- REFERENCESquency within the region where frequency multiplica- [11 J. P. Gordon, H. J. Zeiger, and C. H. Townes, "The maser newtion is possible, and relative insensitivity to external type of microwave amplifier, frequency standard and spectrome-

ter," Phys. Rev., vol. 99, pp. 1264-1274; August, 1955.parameters. All these qualities are fulfilled by the [2] K. Shimoda, P. C. Wang, and C. H. Townes, "Further aspect of

double-beam N'1H3 maser. the theory of the maser," Phys. Rev., vol. 102, pp. 1308-1321;Jujne, 1956.

The maser signal-to-noise ratio is high, and thus the [3] F. S. Barnes, "Operating Characteristics of an Ammonia Beamfrequency stability of the signal is excellent. The short Maser," PROC. IRE, vol. 47, pp. 2085-2098; December, 1959.

[4] J. C. Helmer, "Small signal analysis of molecular beam," J. A ppl.time stability of one maser was found to be 2.10-12 for Phys., vol. 30, pp. 118-120; January, 1959.a measuring time of 0.2 sec. Another advantage of the [5] A. M. Mitchell and E. Sandback, "Measurements of the fre-

ammonia maser is itsreatinsesitiquency of an ammonia maser in England and Australia," Nature,ammonia maser iS itS great insensitivity to the magnetic vol. 185, pp. 834-835; March, 1960.field. There only appears a second-order Zeeman effect [6] R. C. Mockler, J. Barnes, R. Beehler, H. Salazar, and L. Fey,

"The ammonia maser as an atomic frequency and time stand-which induces a fractional shift of the line center of ard," IRE TRANS. ON INSTRUMENTATION, Vol. I-7, pp. 201-202;roughly 2.10-15 H2 hertz where H is in oersteds. This is December, 1958.

[7] K. Shimoda, "Characteristics of the beam type maser," Part I:about 106 times less than the effect for atoms such as Cs, J. Phys. Soc. Japan, vol. 12, pp. 1006-1016; 1957; Part II:and about 1010 times smaller than for hydrogen. J. Phys. Soc. Japan, vol. 13, pp. 939-947; 1958.

[81 J. Bonanomi, J. De Prins, J. Hermann, and P. Kartaschoff,Our experiments show the interest of more precise "Stabilite d'etalons de frequence a NH3," Helv. Phys. Acta, vol.

measurement techniques. Actually, the precision is 30, pp. 288-290; 1955.[9] J. P. Gordon, "Hyperfine structure in the inversion spectrum of

limited by the fluctuation of the comparison quartz NH3," Phys. Rev., vol. 99, pp. 1253-1263; August, 1955.