S. P. Vyatchanin

Conversion of conventional gravitational-wave interferometers into quantum nondemolition interferometers by modifying their input and/or output optics

The LIGO-II gravitational-wave interferometers (ca. 2006–2008) are designed to have sensitivities near the standard quantum limit (SQL) in the vicinity of 100 Hz. This paper describes and analyzes possible designs for subsequent LIGO-III interferometers that can beat the SQL. These designs are identical to a conventional broad band interferometer (without signal recycling), except for new input and/or output optics. Three designs are analyzed: (i) a squeezed-input interferometer (conceived by Unruh based on earlier work of Caves) in which squeezed vacuum with frequency-dependent (FD) squeeze angle is injected into the interferometer’s dark port; (ii) a variational-output interferometer (conceived in a different form by Vyatchanin, Matsko and Zubova), in which homodyne detection with FD homodyne phase is performed on the output light; and (iii) a squeezed-variational interferometer with squeezed input and FD-homodyne output. It is shown that the FD squeezed-input light can be produced by sending ordinary squeezed light through two successive Fabry-Perot filter cavities before injection into the interferometer, and FD-homodyne detection can be achieved by sending the output light through two filter cavities before ordinary homodyne detection. With anticipated technology (power squeeze factor e-2R=0.1 for input squeezed vacuum and net fractional loss of signal power in arm cavities and output optical train e*=0.01) and using an input laser power Io in units of that required to reach the SQL (the planned LIGO-II power, ISQL), the three types of interferometer could beat the amplitude SQL at 100 Hz by the following amounts μ≡sqrt[Sh]/sqrt[ShSQL] and with the following corresponding increase V=1/μ3 in the volume of the universe that can be searched for a given noncosmological source: Squeezed input —μ≃sqrt[e-2R]≃0.3 and V≃1/0.33≃30 using Io/ISQL=1. Variational-output—μ≃e*1/4≃0.3 and V≃30 but only if the optics can handle a ten times larger power: Io/ISQL≃1/sqrt[e*]=10. Squeezed varational —μ=1.3(e-2Re*)1/4≃0.24 and V≃80 using Io/ISQL=1; and μ≃(e-2Re*)1/4≃0.18 and V≃180 using Io/ISQL=sqrt[e-2R/e*]≃3.2.

Parametric oscillatory instability in Fabry–Perot interferometer

Abstract We present an approximate analysis of a nonlinear effect of parametric oscillatory instability in Fabry–Perot (FP) interferometer. The basis for this effect is the excitation of the additional (Stokes) optical mode with frequency ω1 and of the mirrors elastic mode with frequency ωm when the optical energy stored in the FP resonator main mode with frequency ω0 exceeds the certain threshold and the frequencies are related as ω0≃ω1+ωm. This effect is undesirable in laser gravitational wave antennae because it may create a specific upper limit for the value of energy stored in FP resonator. In order to avoid it the detailed analysis of the mirrors elastic modes and FP resonator optical modes structure is necessary.

Thermo-refractive noise in gravitational wave antennae

Abstract Thermodynamical fluctuations of temperature in mirrors of gravitational wave antennae may be transformed into additional noise not only through thermal expansion coefficient [V.B. Braginsky, M.L. Gorodetsky, S.P. Vyatchanin, Phys. Lett. A 264 (1999) 1; cond-mat/9912139] but also through temperature dependence of refraction index. The intensity of this noise is comparable with other known noises at frequencies ∼1 kHz.Thermodynamical fluctuations of temperature in mirrors of gravitational wave antennae may be transformed into additional noise not only through thermal expansion coefficient but also through temperature dependence of refraction index. The intensity of this noise is comparable with other known noises and must be taken into account in future steps of the antennas.

Analysis of parametric oscillatory instability in signal recycled LIGO interferometer

We present the analysis of a nonlinear effect of parametric oscillatory instability in power recycled LIGO interferometer with Fabry-Perot cavities in the arms. The basis for this effect is the excitation of the additional Stokes optical mode and the mirror elastic mode when the optical energy stored in the main Fabry-Perot cavity mode exceeds the certain threshold. We demonstrate that in the resonance case the parametric oscillatory instability will take place at the energy stored in the cavity of about five orders smaller than one planned for LIGO-II interferometer. The presence of anti-Stokes modes can depress parametric oscillatory instability. However, it is very likely that the anti-Stokes modes will not compensate the parametric instability completely because of the existence of the mode combinations which interact with each other quite strongly.

Thermoelastic dissipation in inhomogeneous media: loss measurements and displacement noise in coated test masses for interferometric gravitational wave detectors

The displacement noise in the test-mass mirrors of interferometric gravitational wave detectors is proportional to their elastic dissipation at the observation frequencies. In this paper, we analyze one fundamental source of dissipation in thin coatings, thermoelastic damping associated with the dissimilar thermal and elastic properties of the film and the substrate. We obtain expressions for the thermoelastic dissipation factor necessary to interpret resonant loss measurements, and for the spectral density of displacement noise imposed on a Gaussian beam reflected from the face of a coated mass. The predicted size of these effects is large enough to affect the interpretation of loss measurements, and to influence design choices in advanced gravitational wave detectors.

Thermodynamical fluctuations in optical mirror coatings

Thermodynamical (TD) fluctuations of temperature in mirrors may produce surface fluctuations not only through thermal expansion in mirror body [Phys. Lett. A 264 (1999) 1] but also through thermal expansion in mirror coating. We analyze the last “surface” effect which can be larger than the first “volume” one due to larger thermal expansion coefficient of coating material and smaller effective volume. In particular, these fluctuations may be important in laser interferometric gravitational antennae.

Quantum variation measurement of a force

The quantum limit for the resolution of a small force using an optical transducer of a displacement with a coherent nonmodulated pump is proved to be less than the standard quantum limit if one measures the quadrature amplitude in the output wave, squeezed by the ponderomotive nonlinearity mechanism. This squeezing has a spectral dependence and we propose a procedure showing it.

A Squeezed state source using radiation pressure induced rigidity

We propose an experiment to extract ponderomotive squeezing from an interferometer with high circulating power and low mass mirrors. In this interferometer, optical resonances of the arm cavities are detuned from the laser frequency, creating a mechanical rigidity that dramatically suppresses displacement noises. After taking into account imperfection of optical elements, laser noise, and other technical noise consistent with existing laser and optical technologies and typical laboratory environments, we expect the output light from the interferometer to have measurable squeezing of 5 dB, with a frequency-independent squeeze angle for frequencies below 1 kHz. This squeeze source is well suited for injection into a gravitational-wave interferometer, leading to improved sensitivity from reduction in the quantum noise. Furthermore, this design provides an experimental test of quantum-limited radiation pressure effects, which have not previously been tested.

Observation of three-mode parametric instability

Three-mode parametric interactions occur in triply resonant optomechanical systems: Photons from an optical pump mode are coherently scattered to a high-order mode by mechanical motion of the cavity mirrors, and these modes resonantly interact via radiation pressure force when some conditions are met. They can either pump energy into acoustic modes, leading to parametric instability, or extract mechanical energy, leading to optomechanical cooling. Such effects are predicted to occur in long baseline advanced gravitational-wave detectors, possibly jeopardizing their stable operation. We have demonstrated both three-mode cooling and amplification in two different three-mode optomechanical systems. We report an observation of the three-mode parametric instability in a free-space Fabry-Perot cavity, with ring-up amplitude saturation.

Isolation of test masses in the advanced laser interferometric gravitational‐wave antennae

We analyze the experimental conditions required for the action of thermal, seismic, and excess noises on the test mass in the advanced LIGO experiment to be smaller than the uncertainty of the coordinate corresponding to the standard quantum limit. It is shown that the contribution of thermal noise can be made small enough if existing low‐dissipation materials are used for the suspension. On the other hand, the contribution of excess noise can be large and has to be examined thoroughly.