Bernard, P

Gemme, G

Parodi, R

Picasso, Emilio

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Particle Accelerators, Vol. 61, pp. [343-350]/79-86Reprints available directly from the publisherPhotocopying permitted by license only© 1998 OPA (Overseas Publishers Association) N.V.Published by license underthe Gordon and Breach SciencePublishers imprint.Printed in India.COUPLED SUPERCONDUCTINGCAVITIES FOR THE DETECTIONOF WEAK FORCESPH. BERNARD a , G. GEMME b , R. PARODI b ,*and E. PICASSO Ca CERN, CH-1211, Geneva 23, Switzerland; bINFN, via Dodecaneso,33, 1-16146, Genova, Italy; cScuola Normale Superiore,Piazza dei Cavalieri, 7, 1-56126, Pisa, Italy(Received in final form 15 January 1998)The detection of weak forces acting on macroscopic bodies often entails the measurementof extremely small displacements of these bodies or their boundaries. This is the case in theattempts to detect gravitational waves or in the search for possible new long rangeinteractions. In 1978, Pegoraro et al. 3 suggested that superconducting coupled cavitiescould be used as a sensitive detector of gravitational effects, through the direct coupling ofthe gravitational wave with the electromagnetic field stored inside the cavities. Thedetector sensitivity is linearly dependent on the quality factor of the cavities and on thesquare root of the stored energy; for this reason the cavities are made out of super-conducting material. In 1984, Reece et al. 5 constructed such a detector in the 10 GHzfrequency range. They achieved a sensitivity to fractional deformations of the order8x/x = 4.10- 18, with a quality factor Q= 2.108 and a stored energy U = 2.10-4 J. Ourproposal is to repeat the Reece, Rainer and Melissinos (RRM) experiment, pushing thecavity quality factor into the 1010 range and the stored energy into the 1J range, in order toincrease the detector sensitivity by a factor of 103, thus reaching a sensitivity to frac-tional deformations of the order of 10-21 . If these results could be obtained, this detectorwould be an interesting candidate for the detection of gravitational waves or in the searchof long range interactions of weak intensity.Keywords: Superconductivity; Radiofrequency; Cavities; Weak forces; Detector*Corresponding author. Tel.: 39-10-3536326. Fax: 39-10-313358.E-mail: PARODI@GE.INFN.IT.[343]/79[344]/801 INTRODUCTIONPH. BERNARD et al.The detection of weak forces acting on macroscopic bodies often entailsthe measurement of extremely small displacements of these bodies ortheir boundaries. This is the case in the attempts to detect gravitationalwaves! or in the search for possible new long range interactions.2In 1978, Pegoraro et al. 3 suggested that superconducting coupledcavities could be used as a sensitive detector of gravitational effects,through the direct coupling of the gravitational wave with the electro-magnetic field stored inside the cavities.3This system is an example of a parametric converter, i.e. of a devicewhich converts energy from a reference frequency to a signal at a dif-ferent frequency as a consequence of the time variation of a parameterof the system. An interesting aspect of the proposed detector is that itwill respond to gravitational perturbations through their direct cou-pling to the electromagnetic field. 3 From· this point of view the timedependent gravitational potential hJ-ll/ modulates the energy storedin the cavity and one need not consider the motion of the cavitywalls. The detector sensitivity is linearly dependent on the quality factorof the cavities; for this reason the cavities are made out of super-conducting material.The proposed detector consists of two cylindrical rf supercon-ducting cavities coupled together. A system made of two coupledresonators shows a frequency spectrum with two energy levels (orresonant frequencies) for each energy level of the single resonator.Just to make a simple mechanical analogue this system is roughlyequivalent to a system of two pendulums coupled together by aspring, as shown in Figure 1; the two oscillating modes of theFIGURE 1 Simple mechanical analogue of the parametric converter.COUPLED SUPERCONDUCTING CAVITIES [345]/81system being the symmetric and antisymmetric modes of themechanical system.If we store some energy in the lower energy mode, the interaction ofthe gravitational wave with the electromagnetic field stored insidethe cavities transfers some energy from the lower to the higher modewhen the frequency difference of the two modes is equal to the wavefrequency.4For a gravitational wave of amplitude h, the energy transfer ~Uis proportional to h2Q2 U, where Q is the electromagnetic qualityfactor and U is the electromagnetic energy stored in the lowerenergy mode. Using the former relation we find the following equationwhich gives the minimum measurable amplitude in terms of cavityproperties:h. ~J6.Uminmm ex: Q u' (1)where ~Umin is the mInImum measurable energy transfer. FromEq. (1) it is clear that to obtain the best detector sensitivity a cavitywith large quality factor and large stored energy is needed.2 STATE OF THE ARTA parametric converter of the type proposed in Ref. [3] has been builtand used as a harmonic mechanical motion transducer in 1984 byReece, Rainer and Melissinos (RRM).5 In this experiment two cylin-drical niobium cavities have been built (see Figure 2), driven in the TEollmode at the frequency fo ~ 10 GHz, with a frequency split of the tworesonant modes ~f~ 1MHz. The quality factor of the two resonantcavities was Q == 2 . 108 and the stored energy in the lower modeU~2·10-4J.In order to measure the sensitivity limit of the detector, one of itswalls was excited by a harmonic perturbation (by a piezoelectric) at afrequency equal to the mode splitting. The results showed a sensitivityto relative deformations 8x/x~ 10-18, which corresponds to a wallabsolute displacement 8x ~ 10-17 cm.[346]/82zJ-yxPH. BERNARD et aleFIGURE 2 Schematic view of two coupled cylindrical cavities.3 PROPOSALThese results, even if of great interest, do not allow the use of the devicefor the detection of gravitational waves or weak forces. To reach thisgoal the detector sensitivity should be increased at least by three ordersof magnitude, approaching 8x/x';::j 10-21 limit, similar to the expectedsensitivity of the Weber-like detectors.We think that keeping the conceptual design of the RRM experimentunaltered, several aspects of it can be improved.At a first stage one can choose to work at a somewhat lower fre-quency taking advantage of the frequency dependence of the surfaceresistance of superconductors. We remind that the unloaded cavityCOUPLED SUPERCONDUCTING CAVITIESquality factor is given by the relation:rQo = Rs'[347]/83(2)where r is a geometrical factor which for a cylindrical cavity with itsdiameter equal to its length, in the TEoll mode, is equal to 780 nand Rsis the material surface resistance. The surface resistance itself is madeup of two contributions:R s == RBCS + Rres · (3)Since the BCS surface resistance for temperatures lower than half ofthe superconductor critical temperature follows approximately a tem-perature and frequency dependence given byW1.7 [~(T)]R cx-exp ---s T kT ' (4)one can gain something choosing to work at lower frequencies. Forexample the theoretical surface resistance of niobium at 10 GHz and1.5 K is 2.5· 10-8 n which gives a quality factor Qo == 3 . 1010. FromEq. (4) one can guess that at 3 GHz the BCS surface resistance shouldbe RBCS == 3 .10-9 n and the theoretical quality factor Qo == 2 .1011 .Obviously one has to consider the residual contribution to the surfaceresistance, which is in general the dominant one. To lower the residualresistance contribution, niobium surface treatments are critical. In thelast decade however a great deal of progress has been made in this fielddue to several large scale applications of rf superconductivity whichpushed the development of the technology of surface preparations andobtained very interesting results. A recent experimental result obtainedat CERN, showed that it was possible to store in a mono-cell coppercavity, sputter coated with a niobium film, operated in the TEoll modeat 966MHz, an energy exceeding 10J, at Q~ 101°.6 The maximumsurface magnetic field amplitude obtained in this cavity was 38 mT, andthe BCS and residual surface resistances at 4.2 K were 192 and 47 nnrespectively.From the experimental set-up point of view, the major differencebetween our proposal and the RRM experiment will be in the signaldetection arrangement. While they used the signal reflected from[348]/84 PH. BERNARD et al.cavity either to phase lock the signal generator to the symmetric cavityfrequency, or to detect the converted signal at the antisymmetricfrequency, we plan to use the signal transmitted through the cavity todo these, jobs. With this arrangement we should improve system selec-tivity, or, in other words, we should have a lower contribution of thesymmetric mode at the higher, antisymmetric, frequency, lowering theoverall noise level in the system and increasing sensitivity.A further improvement in system sensitivity should be obtainedby choosing to work with spherical cavities, as shown in Figure 3,instead of cylindrical resonators. With spherical cavities one shouldgain on two sides:• on a first side the geometrical factor of a spherical cavity is higherthan the geometrical factor of a cylindrical one; this means that forequal surface characteristics (equal Rs) the quality factor of a spher-ical cavity will be higher;• field configuration is more favourable in a spherical cavity andshould be much easier to build the coupled cavity system with thecoupling hole in the higher field region.Nevertheless we plan not to build a spherical resonator until a full set oftests have been made on the cylindrical one.On the electronics side a large amount of microwave devices (lownoise amplifiers, filters, etc.) have been developed, mainly for applica-tions in telecommunication networks. These devices should allow toreduce the contribution of electronics to the noise in the experimentby at least one order of magnitude. Just to make a comparison, whileRRM used an rf low noise amplifier with a noise figure N f == 4.7 dB,nowadays low noise amplifiers with N f as low as 0.8 dB are commer-cially avaliable. A further gain could be obtained using a cold pre-amplifier. In this way the minimum detectable energy is lowered by theratio of the equivalent temperatures of the preamplifiers, which is, inthe ideal case, the ratio between room temperature and the operatingtemperature of the electronics.4 CONCLUSIONSWe plan to develop our work in a two-year period, starting with thecharacterization of a cavity prototype, made of copper, in the first halfCOUPLED SUPERCONDUCTING CAVITIES [349]/85z~X YFIGURE 3 Schematic view of two coupled spherical cavities.of 1998, to begin final system optimization and characterization in thesecond half of 1999.Based on the considerations made in the previous sections our pro-posal is to repeat the RRM experiment increasing the detector sensi-tivity by at least three orders of magnitude, reaching the 8x/x ~ 10-21limit. If these results could be obtained, this detector would be aninteresting candidate for the detection of gravitational waves or in thesearch of long range interactions of weak intensity.[350]/86ReferencesPH. BERNARD et al.[1] J. Weber, Phys. Rev. 117 (1960), 306; Nature 240 (1972), 28; Phys. Rev. Lett. 31(1973), 779.[2] G. Feinberg and J. Sucher, Phys. Rev. D 20 (1979), 1717; J.E. Moody and F. Wilczek,Phys. Rev. D 30 (1984), 130.[3] F. Pegoraro, E. Picasso and L.A. Radicati, J. Phys. llA (1978), 1949; F. Pegoraro,L.A. Radicati, Ph. Bernard and E. Picasso, Phys. Lett. 68A (1978), 165.[4] If we consider the interaction between a gravitational wave and the electromagneticfield stored inside a resonant cavity, the system parameter which drives the transi-tion between the energy levels is the permeability tensor E, whose components arefunctions of the metric and, for a monochromatic gravitational wave, are sinusoidalfunctions of time. Furthermore it must be taken into account that in order to interactwith the gravitational wave the electromagnetic field must have a quadrupole moment;this result can be achieved choosing with care the geometry of the coupled cavitiessystem.[5] C.E. Reece, P.J. Reiner and A.C. Melissinos, Phys. Lett. 104A (1984),341; Nucl. Instr.Meth. A 245 (1986), 299.[6] M. Bazan, Ph. Bernard, C. Dalmas and W. Weingarten, CERN SL-Note 97-64RF(1997).

Coupled superconducting cavities for the detection of weak forces

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