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 now, a direct laboratory observation of vacuum magnetic birefringence, an effect due to vacuum fluctuations, still needs confirmation. Indeed, the predicted birefringence of vacuum is $\Delta n = 4.0\times 10^{-24}$ @ 1~T. One of the key ingredients when designing a polarimeter capable of detecting such a small birefringence is a long optical path length within the magnetic field and a time dependent effect. To lengthen the optical path within the magnetic field a Fabry-Perot optical cavity is generally used with a finesse ranging from ${\cal F} \approx 10^4$ to ${\cal F} \approx7\times 10^5$. 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 a Cotton-Mouton and a Faraday effect 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 $10\;$Hz is $S_{\Delta{\cal D}}=6\times 10^{-19}\;$m$/\sqrt{\rm Hz}$, a value which we believe is consistent with an intrinsic thermal noise in the mirror coatings.