Gravitational radiation detection with laser interferometry

Gravitational-wave detection has been pursued relentlessly for over 40 years. With the imminent operation of a new generation of laser interferometers, it is expected that detections will become a common occurrence. The research into more ambitious detectors promises to allow the field to move beyond detection and into the realm of precision science using gravitational radiation. In this article, the state of art for the detectors is reviewed and an outlook for the coming decades is described.

Figure 1

Exaggerated example of the effect of a GW on a ring of test particles. The GW is coming from above, is “plus” polarized, and has a period $\tau$. As the wave passes, the ring is alternately stretched and compressed. This quadrupolar strain pattern matches well to the geometry of a Michelson interferometer.

Figure 2

Interferometer antenna response for ($+$) polarization (left), ($\times$) polarization (middle), and unpolarized waves (right).

Figure 3

Schematic of the initial LIGO interferometers. The input beam is phase modulated and then built up resonantly in the power recycling cavity. The phase modulation sidebands resonate only in the power recycling cavity. The light incident on the photodetector at the bottom of the diagram carries the GW signal.

Figure 4

The seismic vibration spectral densities shown for some of the relatively quiet sites of the current GW detector network. Also shown are two promising locations for future low-frequency detectors in the U.S.: the 4100 ft level of the Sanford Underground Lab and a surface site near El Paso, TX. The USGS New Low Noise Model (290) is included as a reference. All the spectra here [with the exception of Kamioka (47)] are estimated using Welch’s method but with median instead of mean averaging so as to better reject non-Gaussian transients.

Figure 5

Vibration isolation for the initial LIGO (169; 299), Virgo (51; 25; 15), TAMA (with SAS) (260), GEO600 (295; 186; 339), Advanced LIGO (9), KAGRA (335), and the Einstein telescope cases (149). In the KAGRA case, the mechanical links for cooling (included) are expected to limit the isolation performance above $\sim 1\mathrm{Hz}$ (348).

Figure 6

Estimate of the Newtonian gravity noise at the LIGO sites compared to the fundamental thermodynamic and quantum limits for Advanced LIGO. The dominant contribution is from surface waves on the nearby ground. Vibrations of the building walls and acoustics within the building are not very significant. The turbulence from wind outside of the building primarily couples through the vibration of the building walls and is therefore already included in this estimate.

Figure 7

Strain noise for the first generation detectors. TAMA300, GEO600, Virgo+, and Enhanced LIGO. Also shown (dashed) are the strain noise goals for the initial Virgo and LIGO detectors.

Figure 8

Noise budget of the LIGO Hanford 4 km detector during the fifth LIGO science run (S5) (7). The left plot shows mainly the noise sources that act as a force on the mirrors. The right plot shows noise sources that appear as a phase noise on the light. The known peaks in the measured strain data are indicated as ($p$) for power lines, ($c$) for calibration lines, ($s$) for the violin modes of the mirror suspension, and ($m$) for the mirror’s internal eigenmodes. The lighter unlabeled trace is a quadrature sum of all known noise sources and the darker unlabeled trace is the measured strain output of the interferometer. The discrepancy between these two traces remains unexplained but is suspected to be due to excess friction in the suspension wire attachments to the mirror. The dashed trace is the initial LIGO Science goal.

Figure 9

Advanced LIGO quadruple suspension. The final stage is a 40 kg mirror suspended by four laser-welded silica fibers.

Figure 10

(Top) Surface phase map (in units of nanometers) of one of the Advanced LIGO arm cavity mirrors after applying the high-reflectivity mirror coatings. From 402. (Bottom) Infrared image of an initial LIGO arm cavity mirror taken with the cavity locked, highlighting the abundance of point defects. The gray oval is the diffuse scatter from an auxiliary beam used for tracking the mirror angle. From 379.

Figure 11

Schematic of the Advanced LIGO interferometers. The output beam at the antisymmetric port is filtered by a rigid bow-tie cavity to remove the rf sidebands and the higher-order spatial modes that come from distortions in the optics.

Figure 12

Detector configurations to target particular astrophysical sources. The optimal tunings of the Advanced LIGO interferometer for (NS/NS) neutron star binary inspirals, (BH/BH) for intermediate mass black hole binary inspirals, and (pulsars) for narrow-band sources (such as pulsars) emitting gravitational radiation around 1 kHz are shown. The broadband configuration has the best overall sensitivity and is expected to be the easiest to operate.

Figure 13

Noise budget of the Advanced LIGO interferometers operating in a broadband configuration with the parameters of Table .

Figure 14

Relative power fluctuations after stabilization of a prototype laser system: (top curve) free running laser noise, (bottom curve) stabilized level (out of loop), and (dashed line) shot-noise limit. The goal for Advanced LIGO is $2\times {10}^{-9}/\sqrt{\mathrm{Hz}}$. From 240.

Figure 15

The common and differential angular modes of the Fabry-Pérot cavity mirrors are softened (bottom) and stiffened (top) by the radiation pressure torque.

Figure 16

Feedback loop diagram of the parametric instability process. The oscillation of one of the mirror’s mechanical eigenmodes scatters the resonant cavity mode into a higher-order transverse mode which resonates partially in the coupled optical cavities of the interferometer and returns to excite the mirror via radiation pressure.

Figure 17

Advanced LIGO vibration isolation platform: this double stage, in-vacuum platform provides active isolation from 0.5 to 30 Hz and passive isolation above $\sim 1\mathrm{Hz}$. The leaf springs around the outer edge of the image provide the vertical compliance. The copper coils near the center of the image are part of the coil-magnet actuators used in the active feedback. Inertial sensors in sealed pods are attached to the platforms to provide the readback signals in the isolation servos.

Figure 18

Comparison of strain noise estimates for the ground-based detectors. The LIGO-III trace refers to an upgrade of the Advanced LIGO detector including several of the ideas mentioned in Sec. 8.

Figure 19

Comparison of the equivalent strain noise levels of various quantum nondemolition schemes implemented on this LIGO-III concept. 10 dB squeezed light is injected in all cases. For the “Filter Cavity” trace, squeezed light is filtered with a 100 m cavity. For the “Variational” trace, the output of the interferometer is filtered by a 100 m filter cavity, and for the speed-meter case, the “Filter Cavity” configuration is modified by adding a 4 km speed-meter cavity.

Figure 20

Limiting noise sources for a potential third generation LIGO detector with 3 MW of arm cavity power, 10 dB of frequency dependent squeezed light injection, 140 kg Si mirrors with GaAs coatings operating cryogenically at 120 K, and $30\times$ subtraction of Newtonian gravity noise.

Figure 21

An example spiral array optimized for subtracting Newtonian noise due to surface waves for the LIGO-III concept shown in Fig. 20. The center of each sphere indicates the location of one seismometer and the size of the sphere is proportional to the coherence between the seismometer and the Newtonian gravitational perturbations on the test mass. Here the test mass is at (0, 0) and the laser beam direction is indicated by the arrow. From 142.

Figure 22

Comparison of strain noise estimates for future detectors: LISA, DECIGO, BBO, Basic AGIS, and ET (D). The LIGO sensitivity curves are included for reference.

Figure 23

DECIGO constellation concept. From 318.

Figure 24

Evolution in gravitational-wave detector sensitivity from 1965 into the near future. The minimum of the strain noise spectral density for the given detectors is plotted on the $y$ axis. The acoustic bar detectors are shown as squares and the laser interferometers as circles. Estimates for future detectors are stars.