Scaling law in signal recycled laser-interferometer gravitational-wave detectors

By mapping the signal-recycling (SR) optical configuration to a three-mirror cavity, and then to a single detuned cavity, we express the SR optomechanical dynamics, input-output relation, and noise spectral density in terms of only three characteristic parameters: the (free) optical resonant frequency and decay time of the entire interferometer, and the laser power circulating in the arm cavities. These parameters, and therefore the properties of the interferometer, are invariant under an appropriate scaling of SR-mirror reflectivity, SR detuning, arm-cavity storage time, and input power at the beam splitter. Moreover, so far the quantum-mechanical description of laser-interferometer gravitational-wave detectors, including radiation-pressure effects, has been obtained only at linear order in the transmissivity of arm-cavity internal mirrors. We relax this assumption and discuss how the noise spectral densities change.

[1]  J. Mason,et al.  Signal extraction and optical design for an advanced gravitational-wave interferometer. , 2003, Applied optics.

[2]  M. Rakhmanov.  Dynamics of laser interferometric gravitational wave detectors , 2000 .

[3]  Radiation pressure induced instabilities in laser interferometric detectors of gravitational waves , 2000, gr-qc/0011099.

[4]  Vinet,et al.  Optimization of long-baseline optical interferometers for gravitational-wave detection. , 1988, Physical review. D, Particles and fields.

[5]  G. Heinzel.  Advanced optical techniques for laser-interferometric gravitational-wave detectors , 1999 .

[6]  M. Gorodetsky,et al.  Optical bars in gravitational wave antennas , 1997 .

[7]  LSC White Paper on Detector Research and Development 1 SUMMARY AND INTRODUCTION , 2022 .

[8]  Joshua R. Smith,et al.  LIGO: the Laser Interferometer Gravitational-Wave Observatory , 1992, Science.

[9]  B. J. Meers,et al.  Recycling in laser-interferometric gravitational-wave detectors. , 1988, Physical review. D, Particles and fields.

[10]  Harald Lück,et al.  The GEO600 project , 1997 .

[11]  Vladimir B. Braginsky,et al.  Quantum Measurement , 1992 .

[12]  Schumaker,et al.  New formalism for two-photon quantum optics. I. Quadrature phases and squeezed states. , 1985, Physical review. A, General physics.

[13]  V. Braginsky,et al.  Low noise rigidity in quantum measurements , 1999 .

[14]  E. Phinney,et al.  AN OVERVIEW OF GRAVITATIONAL-WAVE SOURCES , 2022 .

[15]  Yanbei Chen,et al.  Practical speed meter designs for quantum nondemolition gravitational-wave interferometers , 2002, gr-qc/0208049.

[16]  Yanbei Chen,et al.  Quantum noise in second generation, signal recycled laser interferometric gravitational wave detectors , 2001 .

[17]  Laser-interferometer gravitational-wave optical-spring detectors , 2002, gr-qc/0201063.

[18]  Andrey B. Matsko,et al.  Conversion of conventional gravitational-wave interferometers into quantum nondemolition interferometers by modifying their input and/or output optics , 2001 .

[19]  Demonstration of detuned dual recycling at the Garching 30 m laser interferometer , 2000, gr-qc/0006026.

[20]  Stable operation of a 300-m laser interferometer with sufficient sensitivity to detect gravitational-wave events within our galaxy. , 2001, Physical review letters.

[21]  P. Purdue.  Analysis of a quantum nondemolition speed-meter interferometer , 2002 .

[22]  Deruelle,et al.  Pendular Fabry-Pérot cavities as a paradigm for the dynamics of systems with delays. , 1988, Physical review. A, General physics.

[23]  Quantum theory of fluctuations in a cold damped accelerometer , 1999, quant-ph/9904073.

[24]  P. Meystre,et al.  Optical bistability and mirror confinement induced by radiation pressure , 1983 .

[25]  Macdonald,et al.  Potential radiation-pressure-induced instabilities in cavity interferometers. , 1989, Physical review. A, General physics.

[26]  V. Braginsky,et al.  The analysis of table-top quantum measurement with macroscopic masses , 2001 .

[27]  E. Wright,et al.  Theory of radiation-pressure-driven interferometers , 1985 .

[28]  Marco Lops,et al.  The Virgo interferometer , 1997 .

[29]  Schumaker,et al.  New formalism for two-photon quantum optics. II. Mathematical foundation and compact notation. , 1985, Physical review. A, General physics.

[30]  F. Schutz.  in The Detection of Gravitational waves , 1991 .

[31]  Yanbei Chen,et al.  Quantum noise in laser-interferometer gravitational-wave detectors with a heterodyne readout scheme , 2003 .

[32]  Yanbei Chen,et al.  Signal recycled laser-interferometer gravitational-wave detectors as optical springs , 2002 .

[33]  A. Rüdiger,et al.  Resonant sideband extraction: a new configuration for interferometric gravitational wave detectors , 1993 .

[34]  Carlton M. Caves,et al.  Detection of gravitational waves , 2000 .