Application of stochastic resonance in gravitational-wave interferometer

Abstract

We investigate novel approach, which improves the sensitivity of gravitational wave (GW) interferometer due to stochastic resonance (SR) phenomenon, performing in additional nonlinear cavity (NC). The NC is installed in the output of interferometer before photodetector, so that optical signal emerging interferometer incidents on the NC and passes through it. Under appropriate circumstances a specific transformation of noisy signal inside the NC takes place, which results in the increase of output signal-to-noise ratio (SNR). As a result optical noisy signal of interferometer becomes less noisy after passing through the NC. The improvement of SNR is especially effective in bistable NC for wideband (several hundreds Hz) detection, when chirp GW signal is detected. Then output SNR is increased up to ~ 0.5 and SNR gain reaches amounts ~ 10. When detection bandwidth is narrowed, the influence of SR mechanism gradually disappears, and SNR gain tends to 1. SNR gain also tends to 1 when the NC is gradually transformed to linear cavity. Proposed enhancement of SNR due to the SR is not dependent of noise type, which is prevalent in interferometer. Particularly proposed approach is the only one, which is capable to increase SNR at given amplitude of displacement noise. In present paper we study application of SR in GW interferometer for improving the sensitivity. PACSTo employ the SR phenomenon one needs to have nonlinear system, where noisy signal would be transformed and improved. Earlier in [9] we have considered this problem however, proposed configuration of interferometer was not suitable for experiments. In [9] we suggested to insert optical nonlinear medium in interferometer arm cavities, to change them to nonlinear cavities and to trigger the SR. But such scheme has the drawbacks: (i) because of high power circulating in arm cavities it would be difficult to maintain nonlinear medium in stable state (ii) it would be difficult to provide identical nonlinear parameters for two arm cavities. The scheme suffered also from the necessity to use a special white-light-cavity to relax tight requirements to laser frequency stability.Here we consider another, simpler configuration where an additional nonlinear cavity (NC) is installed in interferometer output before photodetector. A sketch of proposed configuration is shown in Fig. 1. The function of the NC is to improve SNR of passing through it noisy signal by the SR mechanism. This scheme is easy to realize in all existing ground based interferometers.We present in this paper the results of theoretical study of such interferometer. The main motivation of this work was to attract the attention of GW interferometery experts to the SR,

Optimal Noise Benefits in Neyman–Pearson and Inequality-Constrained Statistical Signal Detection

“…and ( 17) Define ( 18) and (19) Rewrite the Lagrangian (6) as (20) Then ( 8) becomes and because strict inequality in (23) implies that there exists an such that because of ( 24)-( 25)…”

“…So we present an algorithm that uses Theorems 1 and 2 and successive approximations to find a near-optimal SR noise from a finite set of noise realizations . The algorithm takes as input , , in ( 9)- (19), and the respective detection and false alarm probabilities and in . The algorithm first searches for a constant noise from the set if the inequality holds.…”

Gravitational wave detection: stochastic resonance method with matched filtering

“…The possible use of SR in connection with gravitational wave detection [15][16][17][18][19][20][21][22], was suggested since the infancy of SR [23]. The application of the stochastic resonance to gravitational wave detection includes two aspects, one is the relation to the data analysis [15], and the other is the detector itself [24,25]. As to the data analysis, all previous researches use Fourier transformation method to study the SR. At present the data analysis method used in gravitational wave detection such as the science run data of LIGO [26] is the matched filtering method.…”

Observation of optomechanical multistability in a high-Qtorsion balance oscillator

“…Applying a slowly changing force to the oscillator, we observe "hopping"between neighboring trapping states, either unidirectional in a staircase-like manner, or bidirectional between two or more states, also showing hysteresis behavior. Finally, with such a multistable system, it becomes possible to investigate another interesting effect, namely the stochastic resonance between neighboring trapping states [14,15,16]. Exploiting this technique, it appears feasible to further enhance the signal-to-noise ratio (SNR) in similar systems, even for gravitational wave detection [16].…”

“…Exploiting this effect, it is possible to enhance the SNR in the detection of small harmonic signals in bistable oscillators by adding noise to the system. As was recently proposed [16], a typical application for this technique can be found in the read-out interferometer unit of gravitational wave detectors where radiation pressure and cavity effects are non-negligible.…”