Displacement-noise-free gravitational-wave detection with a single Fabry-Perot cavity: A toy model

We propose a detuned Fabry-Perot cavity, pumped through both the mirrors, as a toy model of the gravitational-wave (GW) detector partially free from displacement noise of the test masses. It is demonstrated that the noise of cavity mirrors can be eliminated, but the one of lasers and detectors cannot. The isolation of the GW signal from displacement noise of the mirrors is achieved in a proper linear combination of the cavity output signals. The construction of such a linear combination is possible due to the difference between the reflected and transmitted output signals of detuned cavity. We demonstrate that in low-frequency region the obtained displacement-noise-free response signal is much stronger than the -limited sensitivity of displacement-noise-free interferometers recently proposed by S. Kawamura and Y. Chen. However, the loss of the resonant gain in the noise cancelation procedure results is the sensitivity limitation of our toy model by displacement noise of lasers and detectors.     

Displacement transformer in laser gravitational-wave detectors

We analyze the measurement of small variations of distance between the mirrors of long Fabry-Perot cavity (model of gravitational wave detector) applying optical variant of displacement transformer. We show that using optical rigidity and manipulating the parameters of displacement transformer we can overcome Standard Quantum Limit (SQL) sensitivity without increasing laser pumping. The scheme analyzed has an additional potential of changing the shape of sensitivity curve over a wide range.     

Demonstration of a recombined Fabry-Perot-Michelson interferometer with suspended mirrors

We describe preliminary experimental results concerning the operation of a 3 m arm-length Michelson interferometer with two Fabry-Perot cavities whose mirrors and beam splitter are suspended independently by wires. The reflected light beams from the two Fabry-Perot cavities are recombined to obtain interference at a photo-detector; this scheme is necessary for future power-recycled laser interferometers used to detect gravitational waves. The fundamental properties of the interferometer are presented, including the power spectral density of the displacement noise.     

An experimental demonstration of resonant sideband extraction for laser-interferometric gravitational wave detectors

Resonant sideband extraction is a new optical configuration for laser-interferometric gravitational wave detectors with Fabry-Perot cavities in the arms. It reduces the thermal load on the beam splitter and the coupling mirrors of the cavities and also allows one to adapt the frequency response of the detector to a variety of requirements. We report the first experimental demonstration using a table-top setup at a detuned operating point. An increase of sensitivity by 6 dB was observed for artificial signals at frequencies above the arm cavity bandwidth, and the overall transfer function agreed well with theoretical predictions.     

Noises in Detecting Relic Gravitational Wave

We analyse the three basic kinds of noises in detecting the relic gravitational wave （GW）, which are the noises caused by the thermal radiation in the detecting cavity and by the scattering of the Gaussian beam in the detecting cavity, and noise in the microwave radiometers. The analysis shows that a reasonable signal-to-noise ratio may be achieved for a detecting device with a suitable geometric structure only when the temperature of the environment is no more than T = 0.6 K, and the power of the radiation of the Gaussian beam is no less than P=10^5 W.     

Electromagnetic Response of High-Frequency Gravitational Waves by Coupling Open Resonant Cavity

We present a new detecting scheme of high-frequency gravitational waves （HFGWs） in the GHz band, the scheme consists of a high-quality-factor open microwave cavity, a static magnetic field passing through the cavity and an electromagnetic （EM） normal mode stored in the cavity. It is found that under the resonant condition first- and second-order perturbation EM effects have almost the same detecting sensitivity to the HFGWs in the GHz band （h ～10^-26, v～5GHz）, but the former contains more information from the HFGWs. We also provide a very brief review for possible improving way of the sensitivity. This scheme would be highly complementary to other schemes of detecting the HFGWs.     

Phase and Polarization State of High-Frequency Relic Gravitational Waves

The displaying condition of strength, phase and polarization states of high-frequency relic gravitational waves （HFRGWs） in electromagnetic （EM） detecting systems is studied. It is shown that the displaying condition depends not only on the sensitivity of EM detecting systems and the amplitudes of HFRGWs, but also on the phase, the polarization states of HFRGWs and their matching to the EM detecting systems. In order to display simultaneously the strength, phase and polarization states of the resonant ＂monochromatic component＂ of HFRGWs, an important necessary condition is the utilization of two or more different EM detectors.     

Possible Approach to Improve Sensitivity of a Michelson Interferometer

We propose a possible approach to achieve a 1/N sensitivity of Michelson interferometer by using a properly designed random phase modulation. Different from other approaches, the sensitivity improvement does not depend on increasing optical powers or utilizing the quantum properties of light. Moreover the requirements for optical losses and the quantum efficiencies of photodetection systems may be lower than the quantum approaches and the sensitivity improvement is independent of frequency in all the detection bands.     

Thermo-optical nonlinearities and stability conditions for high-finesse interferometers

A theoretical study of a Fabry–Perot cavity in presence of radiation pressure and photo-thermal effects is reported. We show that the competition between these nonlinearities leads to bistability or self-sustained oscillations also in absence of time-delays effects in the intracavity field buildup. In both regimes the stability domains are derived analytically. The results are relevant for extremely sensitive interferometric displacement measurements including quantum optics experiments and gravitational waves detection.     

Micro Extrinsic Fiber-Optic Fabry-Perot Interferometric Sensor Based on Erbium- and Boron-Doped Fibers

Micro extrinsic Fabry-Perot interferometers （MEFPIs）, with cavity lengths of up to ~ 9 μm and maximum fringe contrast of ~19 dB, are fabricated by chemically etching Er- and B-doped optical fibers and then splicing the etched fiber to a single-mode fiber, for the first time to the best of our knowledge. The strain and temperature responses of the MEFPI sensors are investigated experimentally. Good linearity and high sensitivity are achieved. Such a type of MEFPI sensor is cost-effective and suitable for mass production, indicating its great potential for a wide range of applications.     

Measurement of Density Inhomogeneity for Glass Pendulum

The density inhomogeneity of a glass pendulum is determined by an optical interference method. The relative variations of the densities over a volume with sizes of 5 × 5×5 mm^3 are （0.64 ± 0.97） × 10^-5 and （0.99 ± 0.92） × 10^-5 for the K9 glass and silica glass pendulum, respectively. These variations of densities contributing to the relative uncertainties of the Newtonian gravitational constant G are 0.20 ppm and 0.21 ppm in our experiment on measurement of G.     

Evolution of high-frequency gravitational waves in some cosmological models

We investigate Isaacson’s high-frequency gravitational waves which propagate in some relevant cosmological models, in particular the FRW spacetimes. Their time evolution in Fourier space is explicitly obtained for various metric forms of (anti-)de Sitter universe. Behaviour of high-frequency waves in the anisotropic Kasner spacetime is also described.     

Negative and Superluminal Group Velocity Propagation with Narrow Pulse in a Coaxial Photonic Crystal

We investigate the propagation of electric signal along a spatially periodic impedance mismatched transmission line group. Anomalous dispersion is caused by the periodically mismatched impedance structure and a forbidden band appears near 8 MHz in transmission. The group velocity of the amplitude-modulated signal is augmented up to infinity, even -3.89c （c the speed of light in vacuum） in the forbidden region with the amplitude of the modulated signal increasing. When the carrier sinusoid signal is modulated in amplitude by the modulating sinusoid signal, of which the peak is superimposed with a narrow pulse at fivefold frequency, the superluminal group velocity also occurs. The experiment failed to show whether the propagation velocity of narrow pulse exceeds c or not.     

Test mass ring dampers with minimum thermal noise

Advanced laser interferometers gravitational wave detectors may need to substantially reduce the Q-factor of test mass normal modes to eliminate parametric instability. In this Letter we investigate various ring damper configurations for two different laser beam geometries. We show that there is a well-defined location near the mid point of a test mass where the thermal noise degradation from the ring damper is minimised. A Q-factor reduction by a factor of 5 can be obtained for at least 30% of the investigated normal modes at the cost of a 1% increase in thermal noise as seen by a 5 cm diameter incident laser beam. Ring dampers can be up to about 10 mm wide while maintaining minimum thermal noise effect contribution. Of the remaining modes, 30% are very weakly damped.     

Cosmological Gravitational Wave in de Sitter Spacetime

Since there is always an incorrect sign in the mass of the graviton in the so-called perturbation expansion approximation of de Sitter spacetime, the existence of a gravitational wave from the metric perturbation of de Sitter spacetime is doubtful. We try to take another way to start from the assumption that the cosmological gravitation wave equation should be both general covariant and conformal invariant. It is found that the so-called conformal gravitation is no longer part of the metric field and it has an effective mass of mg=√R/6=√2A/3 with the correct sign in de Sitter spacetime, though its intrinsic mass remains zero.     

Wave dynamics of a six-dimensional black hole localized on a tensional three-brane

We study the quasinormal modes and the late-time tail behavior of scalar perturbation in the background of a black hole localized on a tensional three-brane in a world with two large extra dimensions. We find that finite brane tension modifies the standard results in the wave dynamics for the case of a black hole on a brane with completely negligible tension. We argue that the wave dynamics contains the imprint of the extra dimensions.     

Quasinormal Modes of Electromagnetic Perturbation around a Stringy Black Hole

We investigate the electromagnetic perturbation around a stringy black hole. A second-order differential equation is obtained for the perturbation. The variation of the effective potential with r is presented. The complex frequencies of the quasinormal modes of electromagnetic perturbation around a stringy black hole are computed by the third Wentzel-Kramers-Brillouin （WKB） approximation. The results show that the parameters resulted from the compactification of higher dimensions can influence the quasinormal complex frequencies, and the Maxwell field around a stringy black hole damps more slowly than that around a Schwarzschild black hole.     

Berry phase in a bipartite system with general subsystem–subsystem couplings

The Berry phase in a bipartite system described by the XXZ model is studied in this Letter. We calculate the Berry phase acquired by the bipartite system as well as the geometric phase gained by each subsystem. The results show that as the coupling constants tend to infinity all geometric phases go to zero, this confirms the prediction given by us previously [X.X. Yi, L.C. Wang, T.Y. Zheng, Phys. Rev. Lett. 92 (2004) 150406] for bipartite systems with a specific subsystem–subsystem coupling.     

Intensity and frequency noise characteristics of two coherently-added injection-locked Nd:YAG lasers

Coherent addition of two injection-locked Nd:YAG lasers has been performed. A maximum output power of 4.4 W and addition efficiency of 0.94 was achieved, which is the highest power-coupling efficiency ever reported. It was shown experimentally that the frequency and intensity noise level of the coherently-added laser are the same as those of a single injection-locked laser. In particular, no additional intensity noise was observed above the relaxation oscillation frequency of the slave laser, which is suitable for use as the light source for a future gravitational wave detector. The frequency noise of the coherently-added laser was suppressed to 1×10^-4 Hz/ by controlling that of the master laser, and the intensity noise was also suppressed to 1×10^-8 / by controlling the intensity of pump lasers used for the slave lasers. Received: 11 April 2001 / Revised version: 20 June 2001 / Published online: 19 September 2001