Many possible sources of stochastic GW background have been proposed, and several experiments have searched for it (see Maggiore 2000; Allen 1997 for reviews). Some of the proposed theoretical models are cosmological in nature, such as the amplifi- cation of quantum vacuum fluctuations during inflation (Grishchuk 1975, 1997; Starobinsky 1979), pre Y big bang models (Gasperini & Veneziano 1993, 2003; Buonanno et al. 1997), phase transitions ( Kosowsky et al. 1992; Apreda et al. 2002), and cosmic strings (Caldwell & Allen 1992; Damour & Vilenkin 2000, Damour & Vilenkin 2005). Others are astrophysical in nature, such as rotating neutron stars ( Regimbau & de Freitas Pacheco 2001), supernovae (Coward et al. 2002), or low-mass X-ray binaries (Cooray 2004).
was developed that is capable of meeting requirements for strength, thermal noise performance, and dimensional toler- ance for the next generation of gravitationalwave detector mirror suspensions. The ability to produce circular and rect- angular cross-section fibers was developed, as well as tapering along the length of the fiber. Two laser welding methods were investigated, allowing for smaller parts to be welded on the optical bench, and large suspensions such as those planned for Advanced LIGO, to be welded by delivering the beam to the weld locations using an articulated arm. The MIT-based machine has been used to build the monolithic suspension for the LASTI noise prototype and will soon be relocated to the Hanford LIGO site where it will be used to produce suspen- sion fibers for Advanced LIGO. The separate welding system for use on remote structures will be used for welding the sus- pensions close to the vacuum tanks at the Hanford and Liv- ingston LIGO sites. The machine at the Virgo site has been used to build a prototype suspension for the Virgo upgrade, and is now being used to produce the new suspensions for the interferometer at the site.
The principle of detecting gravitationalwave by using Michelson interferometers was first proposed by M. E. Gertenshtein and V. I. Pustoit in early 1960s  and G. E. Moss, etc. in 1970s . However, before Einstein put forward special relativity, A. A. Michel- son and E.W. Money spent decades to conduct experiments by using Michelson inter- ferometer, trying to find the absolute movement of the earth but failed at last. This re- sult led to the birth of Einstein’s special relativity. The explanation of special relativity for this zero result is based on the length contraction of interferometer. When one arm which moved in speed V contracted, another arm which was at rest was unchanged. The speed of light was considered invariable in the process so that no any shift of inter- ference fringes was observed.
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.
Abstract. A steerable low-noise source of illumination is described for shadow-sensors having a displacement sensitivity of ~ 100 picometres (rms)/√Hz, at 500 Hz, over a measuring span of at least ±0.5 mm. These sensors were designed to detect lateral ‘Violin-Mode’ resonances in the highly- tensioned fused-silica suspension fibres of the test-masses/mirrors for the Advanced LIGO (Laser Interferometer Gravitationalwave Observatory) gravitationalwave detectors. The shadow sensors—one intended for each of the four fibres in a suspension—comprised a source of Near InfraRed (NIR) radiation (emitter), and a differential shadow-displacement sensor (detector), these bracketing the fibre under test. The suspension fibres themselves were approximately 600 mm long by 0.4 mm in diameter, and, when illuminated from the side, they cast narrow, vertical, shadows onto their respective detectors—these being located at an effective distance of 50 fibre diameters behind the axes of the fibres themselves. The emitter described here was designed to compensate for a significant degree of mechanical drift or creep over time in the mean position of its suspension fibre. This was achieved by employing five adjacent columns of 8 × miniature NIR LEDs (λ = 890 nm), with one column being activated at a time. When used in conjunction with a ‘reverse Galilean’ telescope, the LED sources allowed the collimated beam from the emitter to be steered azimuthally in fine angular increments (0.65°), causing the fibre’s shadow to move laterally, in a step-wise manner, across the plane of its facing detector. Each step in shadow position was approximately 0.23 mm in size, and this allowed the fibre’s shadow to be re-centred, so as to bridge once again both elements of its photodiode detector—even if the fibre was off-centred by as much as ±0.5 mm. Re-centring allowed Violin-Mode vibrations of the fibre to be sensed once again as differential AC photocurrents, these flowing in anti-phase in the two elements of the ‘split- photodiode’ detector.
Sec. III describes the LLO and ALLEGRO experimen- tal arrangements, including the data acquisition and strain calibration for each instrument. Sec. IV describes the cross-correlation method and its application to the present situation. Sec. V describes the details of the post- processing methods and statistical interpretation of the cross-correlation results. Sec. VI describes the results of the cross-correlation measurement and the correspond- ing upper limit on the SGWB strength in the range 850– 950 Hz. Sec. VII describes the results of our analysis pipeline when applied to simulated signals injected both within the analysis software and in the hardware of the instruments themselves. Sec. VIII compares our results to those of previous experiments and to the sensitivities of other operating detector pairs. Sec. IX considers the prospects for future work.
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,
The organization of this paper is as follows. Section II reviews the properties and characterization of a SGWB. Section III describes the LLO and ALLEGRO experimen- tal arrangements, including the data acquisition and strain calibration for each instrument. Section IV describes the cross-correlation method and its application to the present situation. Section V describes the details of the postpro- cessing methods and statistical interpretation of the cross- correlation results. Section VI describes the results of the cross-correlation measurement and the corresponding upper limit on the SGWB strength in the range 850 – 950 Hz. Section VII describes the results of our analysis pipeline when applied to simulated signals injected both within the analysis software and in the hardware of the instruments themselves. Section VIII compares our results to those of previous experiments and to the sensitivities of other operating detector pairs. Section IX considers the prospects for future work.
One of the primary scientific requirements for LISA (the Laser Interferometer Space Antenna) is to map, in exquisite detail, the spacetime geometries of massive black holes (and, if they exist, other massive, compact bodies) by using the gravitational waves emitted by inspiraling white dwarfs, neutron stars, and small-mass black holes. This emission process has come to be called “Extreme Mass Ratio Inspiral” (EMRI, pronounced emm-ree). The possibility of making such maps from EMRI waves was discussed by Thorne in the early 1990s (e.g., in [1, 2]). In 1995 Ryan  laid the first detailed foundation for such mapping: he showed that, when the massive, central body is general-relativistic, axisymmetric, and reflection-symmetric, and when the orbiting object is in a near-equatorial, near-circular orbit in the vacuum region surrounding the body, the full details of the central body’s metric are encoded in (i) the phase evolution of the waves and also in (ii) the evolution of the frequencies (or phases) of wave modulation produced by orbital precession. Phinney  has given the name “bothrodesy” to the mapping of a black hole’s metric via EMRI waves, and bothrodesy has been identified, by the LISA International Science Team (LIST), as one of the prime goals for LISA . The initial phase of scoping out LISA’s data analysis challenges for EMRI waves is now underway [6, 7].
The Laser Interferometer Gravitational-Wave Observatory (LIGO) is designed to support successive generations of interferometricgravitational-wave detectors. LIGO’s first interferometers are now in operation , and the (negative) results of its first gravitational-wave searches have recently been submitted for publication . When they reach their design sensitivity (presumably next year), LIGO’s initial interferometers, together with their international partners, will reach out into the universe to distances where it is plausible, but not probable to detect gravitational waves . After a planned upgrade to advanced LIGO interferometers (planned to begin in 2007), wave detection will be quite probable . A baseline design for the advanced LIGO interferometers has recently been adopted , along with several options, not currently in the baseline, that merit further study and might be incorporated at a future date. This paper describes one of these options, which has been much discussed within the LIGO Scientific Community (LSC) but has not previously been presented in the published literature: the reshaping of the arm-cavity light beams so as to reduce thermoelastic noise.
Abstract. A low-noise source of illumination is described for shadow-sensors having a displacement sensitivity of (69 ± 13) picometres (rms)/√Hz, at 500 Hz, over a measuring span of ±0.1 mm. These sensors were designed to detect ‘Violin-Mode’ resonances in the suspension fibres of the test-masses/mirrors for the Advanced LIGO (Laser Interferometer Gravitationalwave Observatory) gravitationalwave detectors. The source of illumination (emitter) described here used a single column of 8 × miniature Near InfraRed LEDs (λ = 890 nm). These emitters cast the shadows of 400 µm diameter fused silica suspension fibres onto their complementary shadow- displacement detectors, located at a distance of 74 fibre diameters (29.6 mm) behind the axes of the fibres themselves. Violin-Mode vibrations of each fibre were sensed as differential AC photocurrents in the corresponding ‘split-photodiode’ detector. This paper describes the design, construction, noise analysis, and measures that were taken in the conception of the emitters, in order to produce high-contrast shadows at such distant detectors. In this way it proved possible to obtain, simultaneously, a very high transfer sensitivity to Violin-Mode vibration of the fibres, and a very low level of detection noise—close to the fundamental shot noise limit—whilst remaining within the constraints of this simple design of emitter. The shadow detector is described in an accompanying paper.
At 15:02 (GMT) on 02 March 1989 two prototype gravitationalwave detectors, one op- erated by the University of Glasgow (UG) and the other by the Max Planck Institute for Quantum Optics (MPQ), participated in a joint observing run over a period of 100 hours. The motivations for this run were twofold. First, to demonstrate the practicality of making long-term coincident observations with interferometers, and second to provide real data with all its inherent complexities for testing out a range of signal analysis pro- grams. This was the first time that two interferometers had been run in coincidence for such a length of time. The noise performances of the detectors during the run were poorer by more than a factor of ten times what the prototypes could achieve today. They might have been able to detect a nearby (1 kpc) gravitational collapse event in our Galaxy, the probability of which in any 100-hour period may be between 10 − 5
In space, Michelson type interferometry invariably involve large distances. The laser power received at the far end of the optical link is weak. To continue the optical path as required by TDIs, one needs to amplify it. The way of amplification is to track the optical phase of the incoming weak light with the local laser oscillator by optical phase-locking. At National Tsing Hua University, 2 pW weak-light homodyne phase-locking with 0.2 mW local oscillator has been demonstrated (Liao et al. [16, 17]). In JPL (Jet Propulsion Laboratory), Dick et al.  have achieved offset phase locking of local oscillator to 40 fW incoming laser light. More recently, Gerberding et al.  and Francis et al.  have phase-locked and tracked a 3.5 pW weak light signal and a 30 fW weak light signal respectively at reduced cycle slipping rate. For LISA, 85 pW weak-light phase locking is required. For ASTROD-GW, 100 fW weak-light phase locking is required. Hence, the weak level of these weak-light power requirements has achieved. In the future, the frequency-tracking, modulation-demodulation and coding-decoding needs development to make it a mature technology. This is also important for deep space CW (Continuous Wave) optical communication.
One of the most exciting potential sources of gravitational waves (GWs) for low-frequency, space-based GW detectors such as the proposed Laser Interferometer Space Antenna (LISA) is the inspiral of compact objects into massive black holes in the centers of galaxies. The detection of waves from such “extreme mass ratio inspiral” systems (EMRIs) and extraction of information from those waves require template waveforms. The systems’ extreme mass ratio guarantees that their waveforms can be determined accurately using black hole perturbation theory. Such calcu- lations are computationally very expensive. There is a pressing need for families of approximate waveforms that can be generated cheaply and quickly but which still capture the main features of true waveforms. In this paper, we introduce a family of such “kludge” waveforms and describe ways to generate them. Different kinds of “kludges” have already been used to scope out data analysis issues for LISA. The models we study here are based on computing a particle’s inspi- ral trajectory in Boyer-Lindquist coordinates, and subsequent identification of these coordinates with flat space spherical polar coordinates. A gravitational waveform may then be computed from the multipole moments of the trajectory in these coordinates, using well known solutions of the linearised gravitational perturbation equations in flat spacetime. We compute waveforms using a standard slow-motion quadrupole formula, a quadrupole/octupole formula, and a fast-motion, weak-field formula originally developed by Press. We assess these approximations by comparing to accurate waveforms obtained by solving the Teukolsky equation in the adiabatic limit (neglect- ing GW backreaction). We find that the kludge waveforms do extremely well at approximating the true gravitational waveform, having overlaps with the Teukolsky waveforms of 95% or higher over most of the parameter space for which comparisons can currently be made. Indeed, we find these kludges to be of such high quality (despite their ease of calculation) that it is possible they may play some role in the actual search of LISA data for EMRIs.
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. PACS numbers: 04.80.Nn, 95.55.Ym, 95.75.Kk, 07.60.Ly, 03.65.Ta, 42.50.Lc
body of research has focused on increasing this “ Q f product” for a wide range of mechanical systems. If Q were truly a frequency-independent quantity—as in the “structural damping” model as described by Saulson —then moving to higher eigenfrequencies would lead to an immediate improvement. In the opposite direction, there are many experiments that would benefit from the use of low- frequency (sub-kHz) resonators. A number of bulk structures have been found to exhibit extremely high Q in this frequency range [133, 134]; unfortunately, such systems tend to have relatively large (gram- to kg-scale) effective masses, making them unsuitable for typical optomechanics experiments. The realization of sub-microgram effective masses requires the use of nanofabricated resonators. In practice, excess damping from surface effects , phonon tunneling loss  or intrinsic mechanisms such as thermoelastic  and Akhiezer damping  limits the achievable Q and thus the Q f product in these devices. In addition, we add the further requirement that the desired system exhibit excellent optical quality (i.e., high reflectivity owing to low scatter loss and absorption), which limits the resonator options considerably, especially in light of the fact that typical dielectric materials used to create multi-layer optical coatings (e.g., SiO 2 /Ta 2 O 5 )
In Chapter 3, I describe an instrument designed to measure the photothermal effect in an in- terferometer. In experiments with this instrument, I examine samples of sapphire, BK7, and fused silica, with and without high-reflectivity dielectric mirrors. To ensure that they have similar optical absorptivity and reflectivity, all the samples are coated with a thin layer of gold. To measure their photothermal response, two laser beams with orthogonal polarizations resonate in a Fabry-Perot cavity made from a sample and a reference mirror. One laser beam has its intensity modulated to heat the sample, while the second beam measures the length change of the cavity due to thermal expansion of the sample. The modulation frequency is varied from 10 Hz to 4 kHz to map out
The mechanical design of the VOPO followed other ultra-stable in-vacuum experiments in- cluding the aLIGO OMC  and LISA optical bench testbeds , where low resonance fre- quency tombstone optics are adhered to a stable glass breadboard base. While the LISA testbed tombstone optics have one face optically coated and act as the optical elements themselves, the VOPO cavity has the necessary complexity of curved mirrors and PZT actuators. Two of the VOPO cavity mirrors are curved to focus the beam through the crystal, and at least one mirror requires a piezo-electric transducer (PZT) to control the cavity length. While curved tombstones may be possible their development would be costly. For the initial VOPO build, half inch optics are adhered to the tombstones using degassed epoxy (MasterBond EP30-2). Finite element ana- lysis completed by the LIGO OMC group of a tombstone with attached PZT and mirror gives a 10 kHz resonant frequency. A CAD rendering of the VOPO is shown in figure 6.2.