We are looking for a stretching in space. The gravitational wave (gw) causes a strain in directions transverse to its direction of propagation. One direction will be stretched and the orthogonal direction contracted and then, half a period later, the first direction is contracted and the orthogonal stretched. Space can be thought of as a piece of cloth with a square weave being pulled in one direction and then the other.
The waves will appear as either a "chirp", a "burst", "periodic" or "stochastic". A chirp would occur as two massive bodies (neutron stars or black holes) inspiral and coalesce. The radiated wave will increase in amplitude and frequency with time. A burst accompanies the collapse of a supernova (if it is asymmetric) or the oscillation of a black hole event horizon after it swallows a star. The wave could also be periodic due to non-axisymmetric motion of a neutron star or the nuclear fluid on its surface. The final type of wave that could be detected is a stochastic or background wave. Such a background noise would support many Big Bang theories and allow us to probe to within 10^(-43)s of the Big Bang.
The interferometer (IFO) used is similar to the Michelson-type interferometer. Light from the laser is split at the beam splitter. Half of the light is reflected along one arm of the interferometer and half passes through another arm. In the standard interferometer, the rays are reflected back by mirrors at the end of the arms and they recombine. If the arms are exactly the same length, then the light will be exactly in phase when the beams recombine. If the length of the arms is different, then the length difference causes a phase difference in the light as it recombines and we get interference.
Here we see the IFO used in gw detection, greatly simplified. One difference between this and the Michelson interferometer is that there is no light entering the photodetector if the two arms are the same length. A phase change of 180 degrees is introduced into the beam that is reflected into the photodetector so that the two beams are totally out of phase and there is total destructive interference.
A couple of other changes are introduced to increase the sensitivity of the interferometer. We require that the intensity of the light that reaches the photodetector is significant but with the very weak gws, the changes in length along the arms is extremely small and the phase difference in the recombining beams is also extremely small. With such small changes, the interference will not produce a very strong signal.
The intensity of the signal depends on the interaction time of the wave with the light in the arms. The longer the light is traveling under the space-contracting or expanding influence, the greater the effect as long as the light is not present for longer than half the wave's period--otherwise, the contraction and expansion will cancel. Fortunately the period of a gw is on the order of a tenth of a second, which is a very long time scale when considering the motion of light. To increase the interaction time, the optical beams are folded within the arms (see "light storage arms" in diagram) which increases the length of the arms by a factor of 50.
The intensity is also increased by making the entire IFO a resonant optical storage cavity. A mirror (not shown in the diagram) is placed between the laser and the beam splitter allowing beams reflected back into the laser to be "recycled". This increases the power by a factor of 30.
This is a major consideration when trying to detect something so small amongst the many sources of noise that exist on Earth and in the experimental set-up. The noise can be divided into three groups- sensing noise, random force noise and quantum noise. Quantum noise is the fundamental limit of measuring and is so much smaller than the other two noise types that it will not be an issue for at least the first two generations of gw IFOs.
There is an error associated with Poisson statistics (random events such as the detection of photons in the photodetector). This is the shot noise limit and goes as 1/sqrt(n) where n is the number of photons. Increasing the number of photons would reduce the shot noise but introduces problems of its own, such as optical heating of mirrors and radiation pressure fluctuations. Other sensing noise sources include fluctuations in the laser frequency, the laser amplitude, and stabilization of the beam geometry. There could also be scattering of the laser beam by gas molecules, which is why the IFO is kept evacuated--but like all vacuums, it is imperfect.
This noise is due to the motion of the test masses--the mirrors. Between 10 and 100 Hz (in our region of interest) there is seismic noise. This includes the motion of the Earth's surface as driven by wind, water, human activity and earthquakes. At approximately 100Hz there is also thermal noise. Particles in the test masses and the wires hanging them move at random (Brownian motion), driven by thermal excitations. Another noise source, less significant for the first generation of IFOs but bound to come into consideration in the second generation, is due to fluctuations in gravity. Density of the earth and atmosphere will add noise along the arms. Fortunately, these errors are not linearly dependent with the length of the arms--by doubling the arm length you would be doubling the gw signal strength but not the errors and so making the arms longer is one way to reduce their significance. Since there are practical limits to the size of the IFOs on Earth, there are other methods of dealing with them. The IFO is isolated from the motions of the Earth by using springs and masses to reduce the seismic motion in much the same way as a car suspension.
A gw must appear in all IFOs (with the required sensitivity), otherwise it cannot be considered a gw. This is also true of the stochastic signal which will appear as a common noise in all the IFOs.
LIGO ran its "First Upper Limit Run," called S1, from 23rd August to 9th September 2002. The amount of time for "triple coincidences" (when all three interferometers agreed on signals) totalled 95.7 hours. Of this, 35.5 hours were useful--the rest were rejected for reasons such as poor calibration.
No gws were detected and from this an upper limit on the number of sources can be set. The S1 data indicates that there are at most 1.4 gw-burst causing events per day (any more and they believe that LIGO would have detected them) and 164 neutron star binary inspirals per year in one Milky Way-equivalent galaxy.
The second run S2 began on the 14th February 2003 and finished on 14th April 2003. It is ten times more sensitive and the results are expected soon.