Introduction

All laser interferometers rely on measuring the strain in space caused by a gravitational wave, sensitivities of the order of 10–22 over millisecond timescales being required to allow a good probability of detection.

In principle the strain as monitored by the change in separation of two test masses hung as pendulums can be measured against the wavelength of light from a stable source, but the degree of wavelength or frequency stability required of the source is unreasonably high. It is much more conceivable to measure the distance between test masses along an arm with respect to the distance between similar masses along a perpendicular arm. This is particularly appropriate since the interaction of a gravitational wave is quadrupole in nature and so can cause an opposite sign of length change in the two arms. The measurement of a differential length change of this type when performed by interferometry puts much less demand in principle on the frequency stability of the illuminating laser light – since a Michelson interferometer is insensitive to changes in the wavelength of the light used if the path lengths are equal. However, in practice a fairly high degree of frequency stability is required. In the case of optical delay lines in the arms of a Michelson interferometer this is a result of the difficulty in achieving equal path lengths and of some light being scattered back early without completing the full number of reflections (Billing et al, 1983).

Principle of measurement

Gravitational waves manifest themselves as a variation of the metric of space-time. From an experimental point of view this can be considered as a time-dependent strain in space, which can be observed optically by registering the travel time of light between free test masses. Such experiments were first proposed by Gertsenshtein and Pustovoit (1963) and investigated in more detail by Weiss (1972) and Forward (1978). The corresponding arrangements are broadband in nature, as the effect of a gravitational wave onto the propagation of light between essentially free test masses is to be observed. No frequency is preferred, unless the storage time of the light inside the interferometer becomes comparable to the periods of the signals to be observed. Resonances of the test masses, for instance, are unwanted side-effects in this context. Since the strain in space introduced by gravitational waves has opposite signs in two directions perpendicular to each other, an ideal instrument is a Michelson interferometer (figure 11.1a). The signal at its output is a function of the path difference between the two arms. The beamsplitter and the mirrors serve as test masses. A gravitational wave with optimal polarization and direction of propagation would be incident perpendicularly on to the plane of the interferometer, making one arm shrink and the other one grow during half of a period; for the next half cycle the signs change.

This book is about gravitational radiation detectors. It is about experimental physics: the physics of extremely sensitive instruments designed to detect the infinitesimal time varying strains in spacetime which are gravitational waves.

For half a century most physicists considered the detection of gravitational waves to be an impossibility, but 30 years ago Joseph Weber first outlined possible means of detection, and followed this by a lonely pioneering decade of instrument development. About 20 years ago a range of new technologies appeared on the horizon, and we have now seen two decades of advance in a variety of areas, often driven by the needs of gravitational radiation detection. Looked at as a whole these represent a spectacular advance in technological capability, and now it is possible to look forward to a future when gravitational astronomy will plug a major gap in our knowledge of the universe.

The first area of intense effort was in the development of improved resonant bar antennas. This led to the development and understanding of systems and materials with ultralow acoustic loss, and ultralow electromagnetic loss. The development of low loss microwave cavities led to new technologies for vibration transducers and frequency standards. The need for sensitive amplifiers was met by the development of greatly improved superconducting quantum interference devices (SQUIDs) and cryogenic gallium arsenide field effect transistor amplifiers. The understanding of quantum mechanical limitations to measurement led to the development of techniques called variously squeezing, quantum nondemolition and back action evasion.

Introduction

The gravitational wave detection technique discussed here is a long-baseline nearly-free-mass technique, devised initially with the aim of obtaining high gravity-wave sensitivity with minimum practicable cost. The distinctive part of the technique is the use as sensors of a pair of optical cavities formed between mirrors attached to test masses defining two perpendicular baselines, illuminated by an external laser source. To introduce the basic concept it may be useful to summarize the train of ideas which led up to it.

Experience and analyses in the early 1970s of resonant-bar gravity-wave detectors indicated that, although it is in principle possible to achieve by this technique the high sensitivity likely to be required for detection of expected astronomical sources, the small energy exchange with the gravitational wave leads to increasingly difficult experimental problems as sensitivity is improved. Alternative techniques using free test masses at large separations, monitored by optical or microwave methods, can sample much larger baselines and make relatively less serious any thermal, seismic, and amplifier noise, as well as the uncertaintyprinciple quantum limit for the test masses. Measurement of the small relative displacements involved, which might correspond at 1 kHz to strains of order one part in 1021 or less in a 1 kHz bandwidth, is however a serious challenge for interferometers of any kind. If a simple Michelson interferometer were used the photon shot noise limit would demand an impracticably high light flux. One way of improving sensitivity was proposed by R.

Introduction to recycling

All the long baseline interferometers for the detection of gravitational radiation which are presently being studied are based on the construction of a large, Michelson-like interferometer with an armlength of 1 to 4 km, containing some kind of gravito-optic transducer in each arm. In order to improve the shot-noise limited sensitivity, all these interferometers will use high-power lasers, in conjunction with so-called light recycling techniques. The basic idea of recycling was proposed by R. W. P. Drever (1983): it consists in building a resonant optical cavity which contains the interferometer, so that, if the losses are low and if the cavity is kept on resonance with the incoming monochromatic light, there is a power build-up which results in a reduction of the shot noise. This can be realized in different ways, depending on the geometry of the gravito-optic transducer (delay line or Fabry-Perot).

A general theory of recycling interferometers was recently developed and published (Vinet et al, 1988) and the Garching (Schnupp, 1987) and Orsay (Man, 1987) groups have obtained the first experimental verifications of the efficiency of this technique. In this chapter, we first remind the reader of the main ideas and results of the theory, which is fully expressed in Vinet et al. (1988). We then describe today's experimental achievements, and we end up with a short discussion of possible future improvements.

Space, time, and gravitation

GENERAL RELATIVITY is Einstein's theory of gravitation. It is not only a theory of gravity: it is a theory of the structure of space and time, and hence a theory of the dynamics of the universe in its entirety. The theory is a vast edifice of pure geometry, indisputably elegant, and of great mathematical interest.

When general relativity emerged in its definitive form in November 1915, and became more widely known the following year with the publication of Einstein's famous exposé Die Grundlage der allgemeinen Relativitätstheorie in Annalen der Physik, the notions it propounded constituted a unique, revolutionary contribution to the progress of science. The story of its rapid, dramatic confirmation by the bending-of-light measurements associated with the eclipse of 1919 is thrilling part of the scientific history. The theory was quickly accepted as physically correct—but at the same time acquired a reputation for formidable mathematical complexity. So much so that it is said that when an American newspaper reporter asked Sir Arthur Eddington (the celebrated astronomer who had led the successful solar eclipse expedition) whether it was true that only three people in the world really understood general relativity, Eddington swiftly replied, “Ah, yes—but who's the third?”