The last mile in subduing disturbances is the most difficult to navigate, says S.Ananthanarayanan.

The quest for gravitational-waves, which arise from events far in deep space, calls for detecting the feeblest of signals that we encounter. And we need such quiet to make them out that noise control is the first challenge to overcome.

Gravitational-waves are detected by the effect they have is on the dimensions of space. The most sensitive arrangement to detect gravitational-waves, to date, hence uses interference of light when the length of a path of light, past which the gravitational-wave passes, is altered. The innate ‘grainy’ nature of the light source, however, limits sensitivity, as it could mask the variation of intensity caused by a gravitational-wave. Using a more powerful beam would overcome this effect, but it would increase the miniscule jitter that light imposes on mirrors, which are part of the apparatus. Controlling this disturbance, known as Quantum Radiation Pressure Noise, or QRPN, would hence be critical

Jonathan Cripe, Nancy Aggarwal, Robert Lanza, Adam Libson, Robinjeet Singh, Paula Heu, David Follman, Garrett D. Cole, Nergis Mavalvala and Thomas Corbitt, from Louisiana State University, MIT, the University of Vienna and Crystalline Mirror Solutions, an optics firm in Santa Barbara and Vienna, report in the journal, Nature, that they have created a device to measure, and perhaps lead to ways to mitigate this last mentioned effect.

The gravitational-wave is an effect that is predicted by Einstein’s General Theory of Relativity, which reinterprets the nature of gravity. Starting from the observation that the acceleration due to gravity is indistinguishable from any other acceleration, Einstein takes the help of the equivalence of mass and energy to connect the nature of mass with energy in space, and thence the force of gravity with curvature that a mass induces in the fabric of space. While it has been verified that the presence of a mass does bend the path of a beam of light, as if space is curved, a consequence of the theory is that accelerated masses should lose energy by radiation of gravity waves, just like acceleration of electric charges leads to electromagnetic waves.

Like electromagnetic waves create electric and magnetic fields where they pass, a gravitational-wave would cause spatial shrinking and stretching when it passes. The Laser Interferometer Gravitational-wave Observatory, or LIGO, consists of a pair of four kilometer-long channels, at right angles, through which a laser beam is split and then recombined. In case a gravitational-wave were to pass over LIGO, there would be differential changes in the dimensions of the two arms. Even very minute changes would show up as interference of the two halves of the split beam of light, when they combine.

The trouble is that there so many causes of minute changes in dimensions, with attendant interference of light, even when there is no gravitational-wave. For example, tremors in the earth, perhaps even traffic or heavy footfall, could trigger an interference pattern. To take care of this disturbance, the tubes of LIGO are very securely housed and then, there are two LIGO arrangements, one at Louisiana and the other at Washington, 3,002 kilometers apart, and an event is counted only if it occurs in both the LIGOs at once. But a more persistent cause of disturbance is that the laser source of the light is itself not continuous, but staccato, the manner of individual atoms in the laser material, which de-excite and emit photons.

We are all aware that when we toss a coin, in the long run, the number of heads and tails will be about the same. But in the short run, of just a few tries, there can be series of more head or more tails. It is the same with the laser. While the light output, on the average, is uniform, with a low power beam, where there are fewer atomic transitions, the emission of photons over a short period of time is not uniform. This non-uniformity, in LIGO, could be mistaken for a gravitational-wave!

One way of dealing with this problem is to use a more powerful laser beam, where there are billions of atom transitions every second. LIGO actually uses a 100 kW beam, which is quite powerful. But there is a limit to this recourse, as light has momentum, albeit very low. A powerful beam would hence materially impact the mirror off which the laser beam needs to be reflected. This effect on the mirrors of LIGO, which arises from the particle nature of light, is a very feeble, but definite, source of uncertainty in the intensity variations in the LIGO interference pattern.

As this effect, the QRPN mentioned earlier, is so feeble, there has been no way to study is features in the laboratory. This is because real life apparatus are subject to mechanical disturbances that create noise that is much more energetic than the subtle effect that we wish to study. The group writing in the journal describes a device and a method that deals with these limitations.

The device that they have created is miniature interferometer, not, 4 km long, but of the order of 1 cm, with components that are measured in microns. The heart of the device is what is called a Fabry-pérot cavity. The Fabry-Pérot arrangement is a pair of closely placed, parallel, partially transparent mirrors. When light of a single colour is admitted, at certain angles, the gap between the mirrors would be a whole number of wavelengths of light and reflected wavelets would reinforce or annihilate each other. An interference pattern is thus created and the pattern is a sensitive measure of space between the mirrors.

In the device now developed, one side of the Fabry-Pérot cavity is a curved mirror, while the other side is 70 micron reflector mounted on 55 micron lever, an elastic cantilever. The light entering and exiting the cavity is measured by photodetectors, which also control the intensity and phase of the light beam.

Just like the interference pattern of an optical, parallel mirror Fabry-Pérot interferometer can display the dimensions of the interferometer gap, the rise and fall of reflected intensity in the cantilever device represents the interplay of the mechanical vibration of the reflector mirror and the effect of the light pressure. The design minimises the disturbances due to changes of temperature and does not call for cooling to low temperatures before the jitter caused by light pressure can be observed.

The paper finds that their system shows QRPN affects at the frequencies from 2 kH to 100kH, a range that corresponds to frequencies of interest in gravitational-wave research. The system could thus serve as a platform to try out ways to reduce quantum noise, and improve the sensitivity of gravitational-wave detectors.

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