Shot-noise-limited measurement of sub–parts-per-trillion birefringence phase shift in a high-finesse cavity

We report on a promising approach to high-sensitivity anisotropy measurements using a high-finesse cavity locked by optical feedback to a diode laser. We provide a simple and effective way to decouple the weak anisotropy of interest from the inherent mirror’s birefringence whose drift may be identified as the key limiting parameter in cavity-based techniques. We demonstrate a shot-noise-limited phase shift resolution previously inaccessible in an optical cavity, readily achieving the state-of-the-art level of $3\times {10}^{-13}$ rad.

Figure 1

Experimental setup. ECDL, Extended Cavity Diode Laser; APP, anamorphic prism pairs; BS, beam splitter; PZT, piezoelectric transducer; P, polarizer; PD, amplified photodiode; $\Sigma$, summation; $\int$, integrator stage.

Figure 2

Kerr phase-shift resolution as a function of the dc bias. Dashed line: photon-noise limited; thick line: technical noise; black dot: our experiment. $I_0$ is the cavity transmitted power, $S$ the photodiode responsivity, and $e$ the electron charge. Our parameters: $I_0=240\hspace{0.5em}\mu$W, $F=250\hspace{0.5em}000$, and $S=0.5$ A/W.

Figure 3

Nitrogen phase-shift distributions for 1 s measurements at four electric field levels: (a) $E=0$ V/m; (b) $E=1.3\times {10}^3$ V/m (only the Gaussian fit is shown); (c) $E=2.7\times {10}^3$ V/m; (d) $E=6.4\times {10}^3$ V/m.

Figure 4

Simultaneously measured Allan variance for (a) the Kerr phase shift induced in nitrogen by $E=9\times {10}^3$ V/m and (b) the phase shift induced by the HR mirror. Error bars are from the statistical errors from the calculation of the Allan variance, which have the usual property of growing at longer integration times.