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VOLUME 2 y NUMBER 3 PHYSICAL REVIEW LETTERS FEBRUARY 1, 1959case P(z) =z '+z ' and (6) becomes

((gp +k ) QP I&& (jap k =0.The same approximation would have been ob-tained (in the limit u,k/tc1) for an arbitrary fas may be seen by expanding the denominator of(4) in powers of v, . The four solutions of (9) are(u =+{-'[&o '+k'+ {((u '+k')'+4u, '(u 'k') 'P'The solution z4, obtained by taking minus signsin both choices, is negative imaginary, showingthe existence and rate of growth of self-excitedwaves, This solution is valid only when s,k/v1which. implies uogas becomes evident fromthe approximate expression

(u, = - iu, (opk/((op'+ k')~'A more detailed study of (6) shows that for largevalues of k one obtains damped waves.The author is indebted to Dr. B.D. Fried formany valuable discussions of these matters.~0. Buneman, Phys. Rev. Lett. 1, 8 (1958).M. Rosenbluth: Recent Theoretical Developments

in Plasma Stability, paper presented Nov. 1958 at theSan Diego Meeting of the Fluid Dynamics Division ofthe American Physical Society.3N. G. Van Kampen, Physics 22, 641 (1957). Thisreference contains a comprehensive review of previousliterature.

SOLID STATE INFRAREDQUANTUM COUNTERS*

N. BloembergenHarvard University,Cambridge, Massachusetts,(Received December 29, 1958)

Since maser operation is based on stimulatedemission of radiation, masers have an inherentlimiting noise temperature of hv/k due to spon-taneous emission. '~' Weber' has called atten-tion to the fact that it is possible to constructquantum- mechanical amplifiers without sponta-neous emission noise. In fact, this is the usualstate of affairs for x-ray or y-counters. Thisnote describes how a solid counter for infraredor millimeter wave quanta might be constructedin principle.Consider a crystal containing ions which,among others, have the energy levels shown inFig. l. Salts of the rare earths and other tran-

OPTICAL PUMP)i I

IIIIIIIIIIIIIcE4

hF4PHOTO-MULTIPLIFR

IR quontum E2A/Vi~I

hv2I )& kTFIG. 1. Infrared quantum counter. Several ions oftransition group elements have appropriate energy lev-el diagrams: hv2&=15000 cm, hv32=10 && 10cmsition group ions, which may be embedded asimpurities in host lattices, offer examples ofthis situation. '~ ~ The distance between theground level and level E, is such that k py2&)kT.If, for example, hv-100 cm ' and T-2'K, onlythe ground state is populated. Intense light atthe optical frequency v is not absorbed, becauselevel E, is empty. Whenever an incident infra-red quantum h p is absorbed, the light will in-duce a second transition to Eprovided its in-tensity produces transitions at a faster rate thanthe radiationless decay or spontaneous emissionfrom level E, back to the ground state.Spontaneous emission from E, to E, will pro-duce resonance radiation. The system will berepumped, and several quanta hv may be re-emitted for each incident quantum hv2y It willbe difficult to detect these quanta h v in thepresence of the intense pumping flux, althoughone may use discrimination in polarization anddirection of propagation. %hen radiation due tospontaneous emission from level E, to E, is ableto leave the crystal, quanta hv may be counteddirectly. If this radiation is self-absorbed, afourth level will provide an effective discrimina-tion in frequency. The fluorescent quanta hv, 4may be counted with a photomultiplier and asuitable filter.A variation of this scheme is that E, is anoccupied deep impurity level, E, is an emptyimpurity level, and E, represents the conductionband. The incident quantum hv triggers aphotoconductive avalanche in the semiconductornear absolute zero of temperature.It is illuminating to point out the relationship

with optical pumping methods proposed by84

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V()LUME 2y NUMBER PHYSICAL REVIEW LETTERS I'FEBRUARY 1, 1959I-/2 '/2 2 P( 2

be useful even if it falls short by many orders ofmagnitude of its ultimate potential.

I/2+ /2I 2Q

/2

FIG. 2. Optical pumping between 8&&2 and Pfg 2doublets (reference 5). o+ pumping produces a maserat hv2&, the ground-state splitting. cr pumping pro-duces a quantum counter at hv2&.

Kastler' and with three-level masers. 'y' Con-sider the cr and o+ transitions between the S~,and 'Pz, states shown in Fig. 2. It makes nodifference whether these transitions are sepa-rated by the sense of circular polarization' orby the Zeeman frequency splitting. ' If the o+transition is pumped, one obtains maser actionin the ground-state doublet. If the o transitionis pumped, one prepares a quantum counter. Toeliminate thermal noise in this counter and keepall particles in the ground state Eeither freeatoms in a beam or a crystal near absolute zeroof temperature should be used.The condition on the intensity for optical pump-ing is the same to achieve maser action or quan-tum counting. Using the parlance of magneticresonance, one has to approach saturation of theoptical absorption coefficient at the pumpingfrequency. The optically induced transitionsmust have a faster rate than the competing re-laxation mechanisms between levels E, and E,.In favorable cases it appears possible to producethe required optical intensities.For the quantum counter, details of the decayfrom level E, are not important, provided ra-diationless transitions are not dominant. For

the maser action, one requires a decay to levelE, at the faster rate than the relaxation ratefrom E, to E,. It is evident that in either casemore than one optical transition may be pumped.Although the prospect of reaching a quantumefficiency of 100% or even 10% appears remote,the type of infrared detector proposed here may

First communicated at the Symposium on NewTechniques in Microwave and Radio-frequency Physics,National Academy of Sciences, Washington, D. C. ,April, 1958 (unpublished).~Gordon, Zeiger, and Townes, Phys. Rev. 99, 1264(1955);R. V. Pound, Ann. Phys. 1, 24 (1957);M. W.Muller, Phys. Rev. 108, 8 (1957);M. W. P. Strand-berg, Phys. Rev. 106, 617 (1957); Shimoda, Takahasi,and Townes, J. Phys. Soc. Japan 12, 686 (1957).J. Weber, Phys. Rev. 108, 537 (1957).3G. H. Dieke and L. Heroux, Phys. Rev. 103, 1227(1956);G. H. Dieke and L. Leopold, J. Opt. Soc. Am.47, 944 (1957).4S. Sugano and Y. Tanabe, J. Phys. Soc. Japan 13,880 (1958);S. Sugano and I. Tsujikawa, J. Phys. Soc.Japan 13, 899 (1958).~A. Kastler, Proc. Phys. Soc. London A67, 853(1954); J. Opt. Soc. Am. 47, 460 (1957).~N. G. Basov and A. M. Prokhorov, J. Exptl. Theo-ret. Phys. U. S.S.R. 27, 431 (1954).~N. Bloembergen, Phys. Rev. 104, 324 (1956).H. Bucka, Z. Physik 141, 49 (955).

EXTENDED FINE STRUCTURE OF E X-RAYABSORPTION EDGES IN PERMINVARR, D. Burbank and R. D. HeidenreichBell Telephone Laboratories,Murray Hill, New Jersey(Received December 15, 1958; revisedmanuscript received January 12, 1959)

In other communications, ' ' the structuralorigin and mechanism of the magnetic annealingof soft, magnetic alloys have been investigated.It has been found that the ability of soft, mag-netic alloys containing Fe, Co, and Ni to exhibitmagnetic annealing properties is due to oxygenpresent as an impurity. Single crystals with anoxygen content of 0.001-0.002% respond to fieldheat treatment. Single crystals with an oxygencontent of 0.0001% fail to respond to field heattreatment.It is well known that x-ray spectra, both inemission and absorption, are sensitive to thestate of chemical combination of the elementsunder study. Thus there is a possibility that astudy of the x-ray spectra of Fe, Co, and Ni insoft, magnetic alloys might yield information onhow the metal atoms are associated with the oxy-gen impurity.The extended One structure of the E x-ray ab-

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