A General Approach to Optomechanical Parametric Instabilities

We present a simple feedback description of parametric instabilities which can be applied to a variety of optical systems. Parametric instabilities are of particular interest to the field of gravitational-wave interferometry where high mechanical quality factors and a large amount of stored optical power have the potential for instability. In our use of Advanced LIGO as an example application, we find that parametric instabilities, if left unaddressed, present a potential threat to the stability of high-power operation

Thermo-optic noise in coated mirrors for high-precision optical measurements

Thermal fluctuations in the coatings used to make high-reflectors are becoming significant noise sources in precision optical measurements and are particularly relevant to advanced gravitational wave detectors. There are two recognized sources of coating thermal noise, mechanical loss and thermal dissipation. Thermal dissipation causes thermal fluctuations in the coating which produce noise via the thermo-elastic and thermo-refractive mechanisms. We treat these mechanisms coherently, give a correction for finite coating thickness, and evaluate the implications for Advanced LIGO

Optimal configurations of filter cavity in future gravitational-wave detectors

Sensitivity of future laser interferometric gravitational-wave detectors can be improved using squeezed light with frequency-dependent squeeze angle and/or amplitude, which can be created using additional so-called filter cavities. Here we compare performances of several variants of this scheme, proposed during last years, assuming the case of a single relatively short (tens of meters) filter cavity suitable for implementation already during the life cycle of the second generation detectors, like Advanced LIGO. Using numerical optimization, we show that the phase filtering scheme proposed by Kimble et al [Phys.Rev.D 65, 022002 (2001)] looks as the best candidate for this scenario.Comment: 17 pages, 5 figure

Measurement of radiation-pressure-induced optomechanical dynamics in a suspended Fabry-Perot cavity

We report on experimental observation of radiation-pressure induced effects in a high-power optical cavity. These effects play an important role in next generation gravitational wave (GW) detectors, as well as in quantum non-demolition (QND) interferometers. We measure the properties of an optical spring, created by coupling of an intense laser field to the pendulum mode of a suspended mirror; and also the parametric instability (PI) that arises from the nonlinear coupling between acoustic modes of the cavity mirrors and the cavity optical mode. Specifically, we measure an optical rigidity of $K = 3 \times 10^4$ N/m, and PI value $R = 3$.Comment: 4 pages, 3 figure

Self-cooling of a movable mirror to the ground state using radiation pressure

We show that one can cool a micro-mechanical oscillator to its quantum ground state using radiation pressure in an appropriately detuned cavity (self-cooling). From a simple theory based on Heisenberg-Langevin equations we find that optimal self-cooling occurs in the good cavity regime, when the cavity bandwidth is smaller than the mechanical frequency, but still larger than the effective mechanical damping. In this case the intracavity field and the vibrational mechanical mode coherently exchange their fluctuations. We also present dynamical calculations which show how to access the mirror final temperature from the fluctuations of the field reflected by the cavity.Comment: 4 pages, 3 figure

Negative optical inertia for enhancing the sensitivity of future gravitational-wave detectors

We consider enhancing the sensitivity of future gravitational-wave detectors by using double optical spring. When the power, detuning and bandwidth of the two carriers are chosen appropriately, the effect of the double optical spring can be described as a "negative inertia", which cancels the positive inertia of the test masses and thus increases their response to gravitational waves. This allows us to surpass the free-mass Standard Quantum Limit (SQL) over a broad frequency band, through signal amplification, rather than noise cancelation, which has been the case for all broadband SQL-beating schemes so far considered for gravitational-wave detectors. The merit of such signal amplification schemes lies in the fact that they are less susceptible to optical losses than noise cancelation schemes. We show that it is feasible to demonstrate such an effect with the {\it Gingin High Optical Power Test Facility}, and it can eventually be implemented in future advanced GW detectors.Comment: 7 pages, 3 figure

Gravitational-wave confusion background from cosmological compact binaries: Implications for future terrestrial detectors

Increasing the sensitivity of a gravitational-wave (GW) detector improves our ability to measure the characteristics of detected sources. It also increases the number of weak signals that contribute to the data. Because GW detectors have nearly all-sky sensitivity, they can be subject to a confusion limit: Many sources which cannot be distinguished may be measured simultaneously, defining a stochastic noise floor to the sensitivity. For GW detectors operating at present and for their planned upgrades, the projected event rate is sufficiently low that we are far from the confusion-limited regime. However, some detectors currently under discussion may have large enough reach to binary inspiral that they enter the confusion-limited regime. In this paper, we examine the binary inspiral confusion limit for terrestrial detectors. We consider a broad range of inspiral rates in the literature, several planned advanced gravitational-wave detectors, and the highly advanced "Einstein Telescope" design. Though most advanced detectors will not be impacted by this limit, the Einstein Telescope with a very low frequency "seismic wall" may be subject to confusion noise. At a minimum, careful data analysis will be require to separate signals which will appear confused. This result should be borne in mind when designing highly advanced future instruments.Comment: 19 pages, 6 figures and 3 tables; accepted for publication in Phys. Rev.

Entanglement of macroscopic test masses and the Standard Quantum Limit in laser interferometry

We show that the generation of entanglement of two heavily macroscopic mirrors with masses of up to several kilograms are feasible with state of the art techniques of high-precision laser interferometry. The basis of such a demonstration would be a Michelson interferometer with suspended mirrors and simultaneous homodyne detections at both interferometer output ports. We present the connection between the generation of entanglement and the Standard Quantum Limit (SQL) for a free mass. The SQL is a well-known reference limit in operating interferometers for gravitational-wave detection and provides a measure of when macroscopic entanglement can be observed in the presence of realistic decoherence processes

Readout and Control of a Power-recycled Interferometric Gravitational-wave Antenna

Interferometric gravitational wave antennas are based on Michelson interferometers whose sensitivity to small differential length changes has been enhanced by adding multiple coupled optical resonators. The use of optical cavities is essential for reaching the required sensitivity, but sets challenges for the control system which must maintain the cavities near resonance. The goal for the strain sensitivity of the Laser Interferometer Gravitational-wave Observatory (LIGO) is 10^-21 rms, integrated over a 100 Hz bandwidth centered at 150 Hz. We present the major design features of the LIGO length and frequency sensing and control system which will hold the differential length to within 5 10^-14 m of the operating point. We also highlight the restrictions imposed by couplings of noise into the gravitational wave readout signal and the required immunity against them.Comment: Presentation at ICALEPCS 2001, San Jose, November 2001, (WECT003), 3 page

Sub-SQL Sensitivity via Optical Rigidity in Advanced LIGO Interferometer with Optical Losses

The ``optical springs'' regime of the signal-recycled configuration of laser interferometric gravitational-wave detectors is analyzed taking in account optical losses in the interferometer arm cavities. This regime allows to obtain sensitivity better than the Standard Quantum Limits both for a free test mass and for a conventional harmonic oscillator. The optical losses restrict the gain in sensitivity and achievable signal-to-noise ratio. Nevertheless, for parameters values planned for the Advanced LIGO gravitational-wave detector, this restriction is insignificant.Comment: 15 pages, 9 figure