of interest, this yields a noise equivalent birefringence γ n = δn × √$_{4}$$_{τ}$ ≃ 1 × 10 − 16 $_{/}$√$_{Hz.}$ Let us now evaluate how far we are from the ultimate shot-noise limited sensitivity of our present apparatus: for an ideal optical coupling, the mean power impinging onto the reflection photodiode PR cw at resonance writes where P c is the optical power in the carrier and P s that in each sideband at frequency ν ± Ω / 2 π . This generates a statistical white noise with a power spectral density γ sn P = √$_{2}$$_{hνP}$ R cw , which is converted into frequency noise by the frequency regulation. The fre- quency noise spectral density γ sn ν is simply obtained by dividing γ sn P by the discriminator D , which yields One thus sees that the shot-noise limited sensitivity is inversely proportional to the cavity finesse F and roughly inversely proportional to the square root of the coupling efficiency, which is represented by P c in the above equation. For our present values P c = 10 mW, P s = 3 mW, Δ ν c ≃ 4 kHz, one finally obtains a shot-noise limited sensitivity γ sn ν ≃ 10 µ Hz $_{/}$√$_{Hz.}$ Converted into birefringence sensitivity, one obtains γ sn n ≃ 1 × 10 − 19 $_{/}$√$_{Hz}$$_{.}$ The sensitivity of our apparatus presently lies 3 orders of magnitude above this value. This estimation is not fully consistent with the spectrum analysis measurements (see Section III) which exhibit a noise spectral density only 15 dB above the shot-noise limit. This discrepancy is mainly due to an imperfect optical coupling, 3 to 10 times smaller than the ideal one, and to a finesse of 15000 instead of 50000 at the time of our measurements, due to mirror pollution and cavity misalignment. Indeed, both defects contribute to degrade the signal since the discriminator D is proportional to the coupling efficiency and to the finesse. Another noise source originates from the weakness of the voltages corresponding to the smallest frequency modulations we measured, in the mV range, hence very sensitive to environmental noise sources. 7 V. OUTLOOKS AND CONCLUSION P R cw = 2 P s + P c 4 , γ sn ν = √$_{hν}$ $_{2}$√$_{2}$ Δ ν FSR F √ P c / 4 + 2 P s P c P s .