Noise estimate of pendular Fabry-Perot through reflectivity change

Abstract

A key issue in developing pendular Fabry-Perot interferometers as very accurate displacement measurement devices, is the noise level. The Fabry-Perot pendulums are the most promising device to detect gravitational waves, and therefore the background and the internal noise should be accurately measured and reduced. In fact terminal masses generates additional internal noise mainly due to thermal fluctuations and vibrations. We propose to exploit the reflectivity change, that occurs in some special points, to monitor the pendulums free oscillations and possibly estimate the noise level. We find that in spite of long transients, it is an effective method for noise estimate. We also prove that to only retain the sequence of escapes, rather than the whole time dependent dynamics, entails the main characteristics of the phenomenon. Escape times could also be relevant for future gravitational wave detector developments.

Switching times in Fabry-Perot measurements

“…To test the electromagnetic mirrors performances and the noise effective temperature [8], [9], we propose to measure the escape time from a minimum, instead of the full trajectory. In analogy with research in Josephson junctions dynamics [10] where escapes have been employed to characterize Poissonian [11] or non Gaussian noise sources [12], escape times can be also used to characterize thermal noise intensity on pendular Fabry-Perot [13]. In this work we propose to extend the application of escape times analysis to the case where a signal is embedded in noise.…”

Interplay between detection strategies and stochastic resonance properties

“…(again T s = 2π/ω). It has been shown that the resulting unknown-initial-phase detector for H > 10 has nearly the same performance as (19), which applies to the coherent (known initial phase) case [4], and it is comparable to the performances of the noncoherent correlator (standard optimum benchmark detector for signals with unknown initial phase). On the other hand, the SSC-SRD is computationally extremely cheap, in that it only requires binary and/or integer arithmetics.…”

“…As preeminent examples where the optimal strategy is not feasible, we can mention the cases where the full trajectory S(t) is difficult to retrieve (as in very sensitive Fabry-Perot pendulums for gravitational waves detection [18,19]), or it is just not available for measurements (as in Josephson junctions, for the quantum mechanical nature of the dynamical variable [20][21][22]). …”

“…In practice, one is often frustrated in the application of LRT optimal technique and employs suboptimal strategies where SR based signal detection enhancement can genuinely occur. As preeminent examples where the optimal strategy is not feasible, we can mention the cases where the full trajectory S(t) is difficult to retrieve (as in very sensitive Fabry-Perot pendulums for gravitational waves detection [18,19]), or it is just not available for measurements (as in Josephson junctions, for the quantum mechanical nature of the dynamical variable [20][21][22]). In some other cases [23] the recorded signal is far too long to be analyzed with optimal methods, and the LRT is de facto not applicable.…”

“…P.Addesso et al / Commun Nonlinear Sci Numer Simulat 30 (2016) [15][16][17][18][19][20][21][22][23][24][25][26][27][28][29][30][31] …”