4.3 Practical issues of ground-based interferometers

A detector with an arm length of 4 km responds to a gravitational wave with an amplitude of 10–21 with
δlgw ∼ hl ∼ 4 × 10 −18 m.

Light takes only about 10–5 s to go up and down one arm, much less than the typical period of gravitational waves of interest. Therefore, it is beneficial to arrange for the light to remain in an arm longer than this, say for 100 round trips. This increases its effective path length by 100 and hence the shift in the position of a given phase of the light beam will be of order 10–16 m. Most interferometers keep the light in the arms for this length of time by setting up optical cavities in the arms with low-transmissivity mirrors; these are called Fabry–Pérot cavities.

The main sources of noise against which a measurement must compete are:

  1. Ground vibration. External mechanical vibrations must be screened out. These are a problem for bar detectors, too, but are more serious for interferometers, not least because interferometers bounce light back and forth between the mirrors, and so each reflection introduces further vibrational noise. Suspension/isolation systems are based on pendulums. A pendulum is a good mechanical filter for frequencies above its natural frequency. By hanging the mirrors on pendulums of perhaps 0.5 m length, one achieves filtering above a few Hertz. Since the spectrum of ground noise falls at higher frequencies, this provides suitable isolation. But these systems can be very sophisticated; the GEO600 [144Jump To The Next Citation Point] detector has a three-stage pendulum and other vibration isolation components [293]. The most ambitious multi-stage isolation system has been developed for the Virgo detector [176Jump To The Next Citation Point].
  2. Thermal noise. Vibrations of the mirrors and of the suspending pendulum can mask gravitational waves. As with vibrational noise, this is increased by the bouncing of the light between the mirrors. Opposite to bars, interferometers perform measurements at frequencies far from the resonant frequency, where the amplitude of thermal vibration is largest. Thus, the pendulum suspensions have thermal noise at a few Hertz, so measurements will be made above 40 Hz in the first detectors. Internal vibrations of the mirrors have natural frequencies of several kHz, which sets an effective upper limit to the observing band. By ensuring that both kinds of oscillations have very high Q, one can confine most of the vibration energy to a small bandwidth around the resonant frequency, so that at the measurement frequencies the vibration amplitudes are extremely small. This allows interferometers to operate at room temperature. But mechanical Qs of 107 or higher are required, and this is technically demanding.

    Thermal effects produce other disturbances besides vibration. Some of the mirrors in interferometers are partly transmissive, as is the beam splitter. A small amount of light power is absorbed during transmission, which raises the temperature of the mirror and changes its index of refraction. The resulting “thermal lensing” can ruin the optical properties of the system, and random fluctuations in lensing caused by time-dependent thermal fluctuations (thermo-refractive noise) can appear at measurement frequencies. These effects can limit the amount of laser power that can be used in the detector. Other problems can arise from heating effects in the multiple-layer coatings that are applied to the reflective surfaces of mirrors.

  3. Shot noise. The photons that are used to do interferometry are quantized, and so they arrive at random and make random fluctuations in the light intensity that can look like a gravitational wave signal. The more photons one uses, the smoother the interference signal will be. As a random process, the error improves with the square root of the number N of photons. Using infrared light with a wavelength λ ∼ 1μm, one can expect to measure to an accuracy of
    √ --- δlshot ∼ λ∕(2π N ).

    To measure at a frequency f, one has to make at least 2f measurements per second, so one can accumulate photons for a time 1∕2f. With light power P, one gets N = P ∕(hc∕λ)∕(2f ) photons. In order that δl shot should be below 10–16 m, one needs high light power, far beyond the output of any continuous laser.

    Light-recycling techniques overcome this problem, by using light efficiently. An interferometer actually has two places where light leaves. One is where the interference is measured, the difference port. The other is the sum of the two return beams on the beam splitter, which goes back towards the input laser. Normally one makes sure that no light hits the interference sensor, so that only when a gravitational wave passes does a signal register there. This means that all the light normally returns toward the laser input, apart from small losses at the mirrors. Since mirrors are of good quality, only one part in 103 or less of the light is lost during a 1 ms storage time. By placing a power-recycling mirror in front of the laser, one can reflect this wasted light back in, allowing power to build up in the arms until the laser merely resupplies the mirror losses [150]. This can dramatically reduce the power requirement for the laser. The first interferometers work with laser powers of 5–10 W. Upgrades will use ten or more times this input power.

  4. Quantum effects. Shot noise is a quantum noise, and like all quantum noises there is a corresponding conjugate noise. As laser power is increased to reduce shot noise, the position sensing accuracy improves, and one eventually comes up against the Heisenberg uncertainty principle: the momentum transferred to the mirror by the measurement leads to a disturbance that can mask a gravitational wave. To reduce this backaction pressure fluctuation, scientists are experimenting with a variety of interferometer configurations that modify the quantum state of the light, by “squeezing” the Heisenberg uncertainty ellipse, in order to reduce the effect of this uncertainty on the variable being measured, at the expense of its (unmeasured) conjugate. The key point here is that we are using a quantum field (light) to measure an effectively classical quantity (gravitational wave amplitude), so we do not need to know everything about our quantum system: we just need to reduce the uncertainty in that part of the quantum field that responds to the gravitational wave at the readout of our interferometer. The best results on squeezing so far [371] have been obtained during preparations for the GEO-HF upgrade of the GEO600 detector [395Jump To The Next Citation Point]. These techniques may be needed for the second-generation advanced detectors and will certainly be needed for advances beyond that.
  5. Gravity gradient noise. One noise that cannot be screened out is that due to changes in the local Newtonian gravitational field on the timescale of the measurements. A gravitational wave detector will respond to tidal forces from local sources just as well as to gravitational waves. Environmental noise comes not only from man-made sources, but even more importantly from natural ones: seismic waves are accompanied by changes in the gravitational field, and changes in air pressure are accompanied by changes in air density. The spectrum falls steeply with increasing frequency, so for first-generation interferometers this will not be a problem, but it may limit the performance of more advanced detectors. And it is the primary reason that detecting gravitational waves in the low-frequency band below 1 Hz must be done in space.

4.3.1 Interferometers around the globe

The two largest interferometer projects are LIGO [304] and VIRGO [176]. LIGO has built three detectors at two sites. At Hanford, Washington, there is a 4 km and a 2 km detector in the same vacuum system. At Livingston, Louisiana, there is a single 4 km detector, oriented to be as nearly parallel to the Hanford detector as possible. After a series of “engineering” runs, which helped to debug the instruments, interspersed with several “science runs”, which helped to test and debug the data acquisition system and various analysis pipelines, LIGO reached its design sensitivity goal in the final months of 2005. In November 2005, LIGO began a two-year data-taking run, called S5, which acquired a year’s worth of triple coincidence data among the three LIGO detectors. S5 ended on 30 September 2007. Although interferometers are pretty stable detectors, environmental disturbances and instrumental malfunctions can cause them to lose lock during which the data quality will be either poor or ill defined. The typical duty cycle at one of the LIGO sites is about 80%, and hence about two years of operation was required to accumulate a year’s worth of triple coincident data. Up to date information on LIGO can be found on the project’s website [238]. A recent review of LIGO’s status is [305].

VIRGO finished commissioning its single 3-km detector at Cascina, near Pisa, in early 2007 and began taking data in coincidence with LIGO in May 2007, thus joining for the last part of S5. VIRGO is a collaboration among research laboratories in Italy and France, and its umbrella organization EGO looks after the operation of the site and planning for the future. There are websites for both VIRGO [380] and EGO [154]. A recent review of VIRGO’s status is [20].

A smaller 600-m detector, GEO600, has been operational near Hanover, Germany, since 2001 [144]. It is a collaboration among research groups principally in Germany and Britain. Although smaller, GEO600 has developed and installed second-generation technology (primarily in its suspensions, mirror materials and interferometer configuration) that help it achieve a higher sensitivity. GEO600 technology is being transferred to LIGO and VIRGO as part of their planned upgrades, described below. Full information about GEO can be found on its website [175]. A recent review of GEO600’s status is [396].

LIGO and GEO have worked together under the umbrella of the LIGO Scientific Collaboration (LSC) since the beginning of science data runs in 2001. The LSC contains dozens of groups from universities around the world, which contribute to data analysis and technology development. The two detector groups pool their data and analyze it jointly. The LSC has a website containing detailed information, and providing access to the publications and open-source software of the collaboration [239].

VIRGO has signed an agreement with the LSC to pool data and analyze it jointly, thereby creating a single worldwide network of long-baseline gravitational wave detectors. VIRGO is not, however, a member of the LSC.

The LSC has already published many papers on the analysis of data acquired during its science runs, and many more can be expected. The results from these science runs, which will be discussed later, are already becoming astrophysically interesting. The LSC maintains a public repository of its papers and contributions to conference proceedings [245].

For instance, although the search for continuous waves from known pulsars has not found any definitive candidates, it has been possible to set stringent upper limits − 6 𝜖 ≤ few × 10 on the magnitude of the ellipticity of some of these systems [10Jump To The Next Citation Point]. In particular, in the case of the Crab pulsar, gravitational wave observations have begun to improve [12Jump To The Next Citation Point] the upper limit on the strength of radiation obtained by radio observations of the spin-down rate.

A yet smaller detector in Japan, TAMA300 [365], with 300 m arms, was the first large-scale interferometer to achieve continuous operation, at a sensitivity of about 10–19 – 10–20. TAMA is seen as a development prototype, and its sensitivity will be confined to higher frequencies (above ∼ 500 Hz). An ambitious follow-on detector called the Large-scale Cryogenic Gravitational-Wave Telescope (LCGT) is being planned in Japan, and, as its name suggests, it will be the first to use cooled mirrors to reduce the effects of thermal noise. TAMA [357] and the LCGT [233] have websites where one can get more information. A recent review of TAMA’s status is [131].

There are plans for a detector in Australia, and a small interferometer is operating in Western Australia [254]. The Australian Interferometric Gravitational Observatory (AIGO) [24] is a proposal of the Australian Consortium for Interferometric Gravitational Astronomy (ACIGA) [21]. The ACIGA collaboration is a member of the LSC and assists in mirror and interferometry development, but it is not yet clear whether and when a larger detector might be funded. From the point of view of extracting information from observations, it is very desirable to have large-scale detectors in Japan and Australia, because of their very long baselines to the USA and Europe. But the future funding of both LCGT and AIGO is not secure as of this writing (2008).

The initial sensitivity levels achieved by LIGO, VIRGO, and GEO are just the starting point. Detailed plans exist for upgrades for all three projects. In October 2007, both LIGO and VIRGO began upgrading to enhanced detectors, which should improve on LIGO’s S5 sensitivity by a factor of roughly two. These should come online in 2009. After a further observing run, called S6, the detectors will again shut down for a much more ambitious upgrade to advanced detectors, to operate around 2014. This will provide a further factor of five in sensitivity, and hence in range. Altogether the two upgrades will extend the volume of space that can be surveyed for gravitational waves by a factor of 1000, and this will make regular detections a virtual certainty. Advanced LIGO has a website giving the plans for the upgrade in the context of development from the initial sensitivity [22].

GEO600 will remain in science mode during the upgrade to enhanced detectors, just in case a nearby supernova or equally spectacular event should occur when the larger detectors are down. But, when the enhanced detectors begin operating, GEO will upgrade to GEO-HF [395], a modification designed to improve its sensitivity in the high-frequency region above 1 kHz, where its short arm length does not prevent it being competitive with the larger instruments. GEO is also a partner in the Advanced LIGO project, contributing high-power lasers and high-Q suspensions for controlling thermal noise.

Beyond that, scientists are now studying the technologies that may be needed for a further large step in sensitivity to third-generation detectors. This may involve cooling mirrors, using ultra-massive substrates of special materials, using purely nontransmissive optics, and even circumventing the quantum limit in interferometers, as has been studied for bars. The goal of third-generation detectors would be to be limited just by gravity-gradient noise and quantum effects. A design study for a concept called the “Einstein Telescope” started in Europe in 2008.

4.3.2 Very-high–frequency detectors

The gravitational wave spectrum above the detection band of conventional interferometers, say above 10 kHz, may not be empty, and stochastic gravitational waves from the Big Bang may be present up to megaHertz frequencies and beyond. It is exceedingly difficult to build sensitive detectors at these high frequencies, but two projects have made prototypes: a microwave-based detector that senses the change in polarization as the electromagnetic waves follow a waveguide circuit as a gravitational wave passes by [127Jump To The Next Citation Point], and a more conventional light-based interferometer [26].

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