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First Generation Interferometers

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IntroductionLong Baseline InterferometryThe Interferometer Noise FloorStatus of the Interferometer ProjectsTAMA300GEO600LIGOVirgoAIGOConclusionsReferencesFirst Generation InterferometersBarry C. BarishCalifornia Institute of TechnologyPasadena, CA 91125Abstract. The status and plans for the first generation long baseline suspended massinterferometers TAMA, GEO, LIGO and Virgo are presented, as well as the expectedperformances. INTRODUCTIONThe effect of the propagating gravitational wave is to deform space in aquadrupolar form. The characteristics of the deformation are indicated in Fig. 1.FIGURE 1. The effect of gravitational waves for one polarization is shown at the top on a ring of freeparticles. The circle alternately elongates vertically while squashing horizontally and vice versa withthe frequency of the gravitational wave. The detection technique of interferometry being employed inthe new generation of detectors is indicated in the lower figure. The interferometer measures thedifference in distance in two perpendicular directions, which if sensitive enough could detect thepassage of a gravitational wave For an astrophysical source, one can estimate the frequency of the emittedgravitational wave. An upper limit on the gravitational wave source frequency can beestimated from the Schwarzshild radius 2GM/c2 of the radiated object. We do notexpect strong emission for periods shorter than the light travel time 4GM/c3 aroundits circumference. From this we can estimate the maximum frequency as about 104 Hzfor a solar mass object. Of course, the frequency can be much lower as illustrated bythe 8 hour period of PSR1916+13, which is emitting gravitational radiation.Frequencies in the higher frequency range 1Hz < f < 104 Hz are potentially reachableusing detectors on the earth’s surface, while the lower frequencies require putting aninstrument into space. The physics goals of the terrestrial detectors and the LISAspace mission are complementary, much like different frequency bands are used inobservational astronomy for electromagnetic radiationThe strength of a gravitational wave signal depends crucially on the quadrupolemoment of the source. We can roughly estimate how large the effect could be fromastrophysical sources. If we denote the quadrupole moment of the mass distribution ofa source by Q, a dimensional argument, along with the assumption that gravitationalradiation couples to the quadrupole moment yields:rccEGrcQGhsymmnonkin22.4)/(~~ (1)where G is the gravitational constant and .symmnonkinE is the non-symmetrical part ofthe kinetic energy. For the purpose of estimation, let us consider the case where one solar mass is inthe form of non-symmetric kinetic energy. Then, at a distance of the Virgo cluster weestimate a strain of h ~ 10-21. This is a good guide to the largest signals that might beobserved. At larger distances or for sources with a smaller quadrupole component thesignal will be weakerLONG BASELINE INTERFEROMETRYA Michelson interferometer operating between freely suspended masses is ideallysuited to detect the antisymmetric (compression along one dimension and expansionalong an orthogonal one) distortions of space induced by the gravitational waves aswas illustrated in figure 1. Other optical configurations or interferometer schemes,like a Sagnac, might also be used and could have advantages, but the presentgeneration of interferometers discussed here are of the Michelson type. The simplest configuration, a white light (equal arm) Michelson interferometeris instructive in visualizing many of the concepts. In such a system the twointerferometer arms are identical in length and in the light storage time. Light broughtto the beam splitter is divided evenly between the two arms of the interferometer. Thelight is transmitted through the splitter to reach one arm and reflected by the splitter toreach the other arm. The light traverses the arms and is returned to the splitter by thedistant arm mirrors. The roles of reflection and transmission are interchanged on thisreturn and, furthermore, due to the Fresnel laws of E & M the return reflection isaccompanied by a sign reversal of the optical electric field. When the optical electricfields that have come from the two arms are recombined at the beam splitter, thebeams that were treated to a reflection (transmission) followed by a transmission(reflection) emerge at the antisymmetric port of the beam splitter while those that havebeen treated to successive reflections (transmissions) will emerge at the symmetricport. In a simple Michelson configuration the detector is placed at the antisymmetricport and the light source at the symmetric port. If the beam geometry is such as tohave a single phase over the propagating wavefront (an idealized uniphase plane wavehas this property as does the Gaussian wavefront in the lowest order spatial mode of alaser), then, providing the arms are equal in length (or their difference in length is amultiple of 1/2 the light wavelength), the entire field at the antisymmetric port will bedark. The destructive interference over the entire beam wavefront is complete and allthe light will constructively recombine at the symmetric port. The interferometer actslike a light valve sending light to the antisymmetric or symmetric port depending onthe path length difference in the arms. If the system is balanced so that no light appears at the antisymmetric port, thegravitational wave passing though the interferometer will disturb the balance andcause light to fall on the photodetector at the dark port. This is the basis of thedetection of gravitational waves in a suspended mass interferometer. In order to obtainthe required sensitivity, the arms of the interferometer must be long.FIGURE 2. Folded optical configurations for interferometer. The arrangement on the left is called adelay line interferometer and the one on the right using a resonant cavity is a Fabry Perotinterferometer. The GEO600 interferometer is a delay line interferometer, while the all the other longbaseline interferometers use Fabry


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