Any theory of gravity that avoids instantaneous action at a distance must feature some kind of gravitational waves. Even Newtonian gravity can be modified to account for propa- gation delays from massive bodies that are the sources of attraction. Gravity as we know it, however, is described by the general theory of relativity. In general relativity, spacetime is treated as a four-dimensional manifold with some intrinsic curvature. This curvature is generated by the presence of mass and energy. In the absence of forces, particles follow geodesic trajectories on this manifold. Quintessentially, “Space tells matter how to move;
While the use of higher classical laser input initially increases interferometer sensitivity, eventually the Michelson interferometer topology employed in existing detectors reaches the standard quantum limit preventing further enhancement. Efforts are being made to test the suitability of so-called quantum non-demolition (QND) technologies able to surpass this limit, one of which involves the use of a new interferometer topology altogether. An experi- ment to demonstrate a reduction in quantum radiation pressure noise in a QND-compatible Sagnac speed meter topology is underway in Glasgow, and we introduce novel techniques to control this suspended, audio-band interferometer to inform the technical design of fu- ture detectors wishing to measure beyond the standard quantum limit. In particular, the problem of controlling the interferometer at low frequencies is discussed. Due to the na- ture of the speed meter topology, the response of the interferometer vanishes towards zero frequency, while the interferometer’s noise does not. This creates a control problem at low frequencies where test mass perturbations arising from, for example, seismic and electronic noise, can lead to loss of interferometer sensitivity over the course of minutes to hours. We present a solution involving the blending of signals from different readout ports of the in- terferometer, facilitating measurements with almost arbitrary integration times.
similar to the corresponding curve for the UG detector. High-pass and low-pass (anti- aliasing) filters, with corner frequencies of 320 Hz and 4 kHz respectively, were applied to the data before it was recorded. Their effects are illustrated by the faint line in the figure. Noise peaks are evident at a frequency near 3.5 kHz. Their origin is known to lie in mechanical resonances within the detector. The typical 0 − 1.25 kHz h strain sensitivity of the MPQ detector during the experiment had a measured value around 3 × 10 − 17 . About midway through the experiment this sensitivity was observed to degrade by more than a factor of two due to loss of alignment of the laser beams in the vacuum tubes. In common with the observed behaviour of the UG sensitivity, there were also rare, transitory, periods when the sensitivity of the MPQ detector was poorer by more than a factor of five times its typical measured value.
Figure 11.10: Test cavity mode identification. The red lines indicate modes predicted by the FEA model shown in Fig. 11.9.
Finally, with the slight reduction in the high-frequency noise, it became clear that there were some apparent true displacement noise features hiding just beneath the broadband noise in the same band. To investigate these, a technique was devised by which the noise of each cavity could be compared independently to a quiet laser locked to a rigid reference cavity, typically used for a separate experiment. This technique is not ideal for the main measurement, since it does not take advantage of any mechanical common-mode suppression that exists between the two closely spaced cavities. Nevertheless, a broad feature around 3.2 kHz was revealed to in fact be a composite of four separate narrower features—two from each cavity—using this technique, as shown in Fig. 11.11.
The next step in the gravitational-wave science workflow after calibrating the data is searching the data for gravitational-wave signals. I performed a search on one month of Initial LIGO (iLIGO) data for sub-solar mass binary black hole systems. The motivation for this search was both astrophysical and computational. Not only could the search produce the first detection of gravitational waves or set new upper limits on the rate of sub-solar mass binary black hole mergers, but the search was also a proof-of-principle for an Advanced LIGO (aLIGO) binary neutron star (BNS) search. There are similarities in an iLIGO sub-solar mass binary search and an aLIGO BNS search in both the duration of signals in band and the number of templates required to appropriately populate the template bank. I used the gstlal inspiral search pipeline, which is poised as the leading low-latency compact binary coalescence search pipeline in aLIGO. While no gravitational waves were found in the iLIGO sub-solar mass binary search, we did find the search was sensitive out to about 4 Mpc, which is beyond our Local Group. This means we are now able to probe many other galaxy halos for primordial black hole systems, whereas microlensing experiments are limited to searching our own Galactic halo. We found that, upon tuning the pipeline appropriately, we were able to run the search with very reasonable computational resources. We determined that we would only require about 200 CPUs to produce results for a search with this type of computational burden in low- latency. Therefore, the low-latency search pipeline is ready for an aLIGO BNS search at design sensitivity.
Thermal noise in the interferometer mirrors is a significant challenge in LIGO’s development.
This thesis reviews the theory of test mass thermal noise and reports on several experiments con- ducted to understand this theory.
Experiments to measure the thermal expansion of mirror substrates and coatings use the pho- tothermal effect in a cross-polarized Fabry-Perot interferometer, with displacement sensitivity of 10 −15 m/rHz. Data are presented from 10 Hz to 4kHz on solid aluminum, and on sapphire, BK7, and fused silica, with and without commercial TiO 2 /SiO 2 dielectric mirror coatings. The substrate contribution to thermal expansion is compared to theories by Cerdonio et al.  and Braginsky, Vyatchanin, and Gorodetsky . New theoretical models are presented for estimating the coating contribution to the thermal expansion. These results can also provide insight into how heat flows between coatings and substrates relevant to predicting coating thermoelastic noise [26, 108].
where d is the detector separation. For the values used in the search (T seg = 60 sec), this error is less than 1%.
10.2.4 The Point Spread Function
The radiometer search described in section 10.2.3 is optimal for point sources, where optimality again means that it yields the maximum SNR for a given source strain H (f). This does not mean that it maximally avoids contamination with signal from other directions; there is significant co- variance between different sky locations. This can be seen in the point spread function (PSF), which is the result of this covariance. Figure 10.2 is an example of the point spread function, with five injected sources at different locations to illustrate how the PSF changes with sky location. This is computed by injecting a strong source at a chosen location into simulated data (noise), and calculating the radiometer response across the whole sky. The detailed structure of the PSF will vary with sky position and frequency of the source. Because the radiometer algorithm depends on sidereal variations in the antenna acceptance to provide direction discrimination, in theory the PSF should not vary with right ascension of the source, although it will vary with declination. Its angular size will in general be smaller for higher frequency sources. A lower limit can be placed on the size of the point spread function by assuming diffraction limited detection of the gravitational waves, which limits the resolving power of an instrument by the familiar formula,
promptly reflected beam and the cavity signal is weaker than optimal. Despite this, the signal was still high enough to establish the first stage of the coherent lock.
A new double-AOM scheme for coherent locking was first implemented on the VOPO2 .
The scheme is described theoretically in section 4.4.3. This scheme has the advantages that it does not require a second laser, reducing cost and control loop complexity. The second auxiliary laser is replaced with two AOMs, which up-shift and down-shift the frequency of a portion of the main laser beam. The difference between the two AOM frequencies is the CLF offset frequency – far enough from the squeezing as to not interact with it, but close enough to be within the cav- ity linewidth. This technique has been tried with a single AOM with poor results for squeezing experiments in the audio band due to zeroth order contamination entering the cavity and causing seeding at the fundamental squeezing wavelength. With two AOMs this becomes a second order problem, however care must be taken to implement proper electromagnetic shielding and ground- ing to prevent cross-talk between the two AOMs. Using two AOMs also allows for operation at higher shift frequency as the frequency offset between the carrier and the CLF is the difference between the two AOMs. Higher shift frequency gives a better spatial separation of zeroth (unshif- ted) and first order beams. Once properly shielded cables were installed between radio frequency signal generators and the AOMs, the scheme was found to be comparable to traditional coherent locking.
Using this method the fiber tolerances depend only on the stability of the laser and not on mechanics. However, this can only be achieved for very thin fibers, where the diam- eter is approximately the same as the wavelength of the in- cident laser light, and as such is not a suitable method for producing fibers of several hundred microns diameter. The lightguides described in Ref. 44 were made using a de- liberately asymmetric laser heating arrangement to produce an elliptical cross-section core. This anisotropy is required to preserve the state of polarization of the electromagnetic field as it propagates through the lightguide. With the sys- tem we describe here, we wish to achieve the opposite of this, to produce highly symmetric fibers. The fiber welding described in Ref. 45 was used to weld thin fibers without necks by heating from one side. To obtain a high strength joint the fibers used in gravitationalwave detector mirror suspen- sions are typically welded at the neck that has a diameter of 3 mm and must be heated from multiple directions.
The effort to directly detect gravitational waves started in the 1960s when Joseph Weber con- structed resonant bars and attempted to read out the excitations of the bars by gravitational-wave bursts . Since the last decade, an array of kilometer scale, laser interferometer gravitational- wave detectors have been constructed, and put into operation. Among these are the detectors of the Laser Interferometer Gravitational-wave Observatory (LIGO) , VIRGO , GEO600  and TAMA300 . A first round of observations at the initial detectors’ design sensitivity has been per- formed since 2007, but no detections has been made. The absence of detections is compatible with astrophysical estimates of event rate at the strength accessible to these detectors. As planned, LIGO and VIRGO are now being upgraded into second-generation detectors, while the KAGRA detector in Japan are being constructed . These second-generation detectors will have a sensitivity roughly 10 times the initial detectors—and will thereby reach out 10 times farther into the universe. While the second-generation detectors are being constructed, third-generation detectors are being planned. Those detectors will have even better sensitivity, and therefore make possible a fruitful observational program of gravitational-wave astronomy. In Chapters 2 and 3 of this thesis, I will discuss coating Brownian noise, the dominant noise source of advanced LIGO in its most sensitive band of 40 Hz – 200 Hz. In Chapter 2, we assumes coating materials to be homogeneous and isotropic, and calcu- lates the level of bulk and shear fluctuations, accounting for light penetration into the coating layers; Chapter 3 evaluates the feasibility of using a higher-order Laguerre-Gauss optical mode to mitigate thermal noise.
site selection and suspension requirements, and optical design plans for ET. The optical design, like the current generation of detectors, would be based on dual-recycled Michelson interferometers with Fabry-Perot arm cavities, however the observatory would be formed from 3 identical, nested detectors forming an equilateral triangle, as shown in figure 4.1. The 60 ◦ angle between the arms means that each detector would be equally sensitive to both polarisations of gravitational waves, while co-locating three detectors in this manner would allow the Einstein Telescope to localise events. Each detector would consist of two interferometers, designed to be sensitive to different signal frequencies (referred to as ET-HF and ET-LF for the high- and low-frequency interferome- ters respectively). To reduce seismic noise, the observatory would be 100-200 m underground. To reduce radiation pressure noise, the mirror masses would be increased by a factor of 50. At high frequencies, sensitivity is shot noise limited, so a high circulating power of 3 MW was proposed for ET-HF. A higher order LG 33 optical mode for the carrier field was also proposed, to reduce the resulting coating thermal noise. In ET-LF, thermal noise would be reduced by cryogenically cooling the optics, necessitating a change in the material of the optics and therefore a change in laser wavelength. Both the ET-HF and ET-LF interferometers would employ frequency-dependent squeezing to overcome the Standard Quantum Limit set by the combined effects of quantum radi- ation pressure and shot noises.
Extensions to the shunt resistors that increases the volume without changing the electrical resistance are called cooling fins.
The experiments to measure the effective temperature of shunt resistors as a func- tion of the dissipated power and cooling fin size were performed in a dilution a re- frigerator in Leiden. The scheme of the experiment is shown on figure 3.15. The shunt resistor R d is biased by a low-pass filtered(C LP = 1 µF , R LP = 760 kΩ) cur- rent source I b . The power, dissipated on a resistor is P = I b V , where V is the voltage drop across the resistor, measured by a room temperature voltmeter, connected in a four-terminal scheme. The temperature of the resistor is evaluated by measurement of its Johnson noise with a SQUID. A decoupling capacitor C D is used to high pass filter the resistor noise, so the intrinsic noise of the SQUID can also be measured. The temperature of the thermal bath was calculated from the resistor noise with I b = 0 A.
choice was made in order to avoid the possibility of interference, however remote, with the optical sensing of the gravitationalwave interferometers. Instead, steady, unmodulated, low- intensity illuminating beams in the Near InfraRed were chosen, where such wavelengths would be well-matched to silicon photodiode-based shadow-sensors. Early work, employing NIR Laser-diodes as the sources of illumination, highlighted the need to avoid fringing effects at the borders of the fibres’ shadows, which otherwise could compromised the shadow-displacement sensitivity of the (necessarily) narrow split-photodiode detectors used. It was decided, therefore, that incoherent sources in the form of NIR LED-based emitters should be used to illuminate the suspension fibres.
from the original one or the NGO/eLISA, we call it LISA (2.5 Gm or new LISA in case of possible ambiguity. Quoting from the proposal :
The observatory will be based on three arms with six active laser links, between three identical spacecraft in a triangular formation separated by 2.5 million km. Continuously operating heterodyne laser interferometers measure with pm Hz 1/2 sensitivity in both directions along each arm, using well-stabilized lasers at 1064 nm delivering 2 W of power to the optical system. Using technology proven in LISA Pathfinder, the Interferometry Measurement System is using optical benches in each spacecraft constructed from an ultra- low expansion glass-ceramic to minimize optical path length changes due to temperature fluctuations. 30 cm telescopes transmit and receive the laser light to and from the other spacecraft. Three independent interferometric combinations of the light travel time between the test masses are possible, allowing, in data processing on the ground, the synthesis of two virtual Michelson interferometers plus a third null-
The promise of this band has been known for quite some time, and has motivated several proposed missions to measure GWs at these frequencies. From the late 1990s until early 2011, the focus was LISA, the Laser Interferometer Space Antenna. LISA was proposed as a joint ESA–NASA mission, consisting of a three- spacecraft constellation orbiting the sun in an equilateral triangle with sides of 5 × 10 6 km. Each spacecraft was to be placed into an orbit such that the constellation orbited the sun once per year, lagging the Earth by 20 ° , and inclined 60 ° with respect to the ecliptic. By measuring the separation between drag-free proof masses in the spacecraft using phase-locked laser transponders with picometer accuracy, LISA would have achieved sufficient sensitivity to measure a rich spectrum of sources in this band over a multiyear mission lifetime. See Ref.  and references therein for detailed discussion.
Experimenters, since then and in four continents, have been engaged in these re- searches without stopping using sophisticated cryogenic versions of Weber resonant an- tennas, or by building giant detectors based on laser interferometry.
These researchers are heirs of two great experimental traditions. One is the tradition of the precision mechanical experiments, exempliﬁed by the work of Cavendish, Eotvos, Dicke, Braginski. At the heart of any experiment on gravitational waves there are masses isolated from the external noise, in conditions as similar to the ones of ideal bodies in free fall as possible. The other tradition is the one of precision optical measurements, started with Michelson, and supported by the developers of lasers and by the pioneers of microwave technology.
32 University of Birmingham, Birmingham B15 2TT, United Kingdom
33 University of Washington, Seattle, WA 98195, USA (Dated: February 14, 2017)
Quantum fluctuations in the phase and amplitude quadratures of light set limitations on the sensitivity of modern optical instruments. The sensitivity of the interferometricgravitationalwave detectors, such as the Advanced Laser Interferometer Gravitationalwave Observatory (LIGO), is limited by quantum shot noise, quantum radiation pressure noise, and a set of classical noises. We show how the quantum properties of light can be used to distinguish these noises using correlation techniques. Particularly, in the first part of the paper we show estimations of the coating thermal noise and gas phase noise, hidden below the quantum shot noise in the Advanced LIGO sensitivity curve. We also make projections on the observatory sensitivity during the next science runs. In the second part of the paper we discuss the correlation technique that reveals the quantum radiation pressure noise from the background of classical noises and shot noise. We apply this technique to the Advanced LIGO data, collected during the first science run, and experimentally estimate the quantum correlations and quantum radiation pressure noise in the interferometer for the first time.
by a system of sensors and actuators, intended to compensate for drifts in, and excitations of, the suspension .
The lateral eigenmodes, or ‘Violin-Modes,’ of the vertically orientated silica suspension fibres are transverse mechanical resonant modes in which all parts of the fibre oscillate with the same frequency. They can be excited by earthquakes, sudden relaxations of mechanical stress, etc. Once excited, the fibres can transfer this vibrational energy to the suspended test masses, such that the masses themselves will oscillate slightly, back and forth. Moreover, with the tension in each fibre being 98 kg m s −2 , the fundamental modal frequencies are of order 500 Hz, such that they (and their harmonics) may transfer this vibrational energy to their suspended test-masses along the line of the beam-axis, at frequencies lying within the gravitationalwave detection bandwidth. Once excited, the fibres’ ring- down time under vacuum, i.e. the consequential interferometer dead-time, is measured in days, because of their high Q values