Intrinsic mirror noise in Fabry–Perot based polarimeters: the case for the measurement of vacuum magnetic birefringence

Although experimental efforts have been active for about 30 years, a direct laboratory observation of vacuum magnetic birefringence, due to vacuum fluctuations, still needs confirmation: the predicted birefringence of vacuum is $$\Delta n = 4.0\times 10^{-24}$$ @ 1 T. Key ingredients of a polarimeter for detecting such a small birefringence are a long optical path within the magnetic field and a time dependent effect. To lengthen the optical path a Fabry–Perot is generally used with a finesse ranging from $${{\mathscr {F}}} \approx 10^4$$ to $${{\mathscr {F}}} \approx 7\times 10^5$$ . Interestingly, there is a difficulty in reaching the predicted shot noise limit of such polarimeters. We have measured the ellipticity and rotation noises along with Cotton-Mouton and Faraday effects as a function of the finesse of the cavity of the PVLAS polarimeter. The observations are consistent with the idea that the cavity mirrors generate a birefringence-dominated noise whose ellipticity is amplified by the cavity itself. The optical path difference sensitivity at $$10\;\hbox {Hz}$$ is $$S_{\Delta {{\mathscr {D}}}}=6\times 10^{-19}\;\hbox {m}/\sqrt{\mathrm{Hz}}$$ , a value which we believe is consistent with an intrinsic thermal noise in the mirror coatings. Our findings prove that the continuous efforts to increase the finesse of the cavity to improve the sensitivity has reached a limit.