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to-second harmonic ratio directly. A substantial effort was made to cope with this problem: a home-built high- voltage amplifier used in the first 13 runs was replaced by a commercial Trek 609B amplifier and a circuit con- trolling the DC-bias was upgraded. This allowed us to control the DC-bias and ˜ E$_{0}$ with mV-scale accuracy that would make the SNR to approach the shot-noise limit if this were the only source of the noise. As seen in Fig. 8, the last six measurements exhibit higher accuracy than the rest. These are the runs after the HV-system up- grade. However, the present SNR of ≈ 0 . 03 / √ τ (s) is worse by almost two orders of magnitude than the shot- noise limit. 

There are other fluctuations in the system parameters, such as light intensity fluctuations in the PBC, fluctua- tions of the spectral position of the PBC resonance with respect to the frequency reference, and noise in the de- tection system. All of them contribute to the noise in the first- and the second- harmonic signals but we found that such noise largely canceled in the ratio r$_{M}$ . 

However, there is a noise source, which is not canceled in the ratio. The following experiments demonstrated that this noise source is related to frequency excursions of the Fabry-P´ erot ´ etalon serving as the frequency ref- erence for the optical system. In these experiments the excitation light was frequency tuned to a wing of the atomic resonance, and the first- and second-harmonic sig- nals were recorded without scanning over the resonance. Then, the same was done when the spectral position was set at the peak of the resonance, and a change of the SNR for the harmonics ratio was determined. These experi- ments were performed using the upgraded HV-system. Results of the measurements are presented in Fig. 9. For 

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a shot-noise-limied signal, the SNR at the peak of the 

resonance is expected to be a factor of about √$_{2 higher}$ than at the wing due to larger signal. It was found, however, that the SNR went up by a factor of 4 by tun- ing from the wing to the peak of the resonance. This demonstrates that the main source of noise is not photon statistics but fluctuations in the spectral reference. In- deed, the frequency excursions at the wing of the spectral line produces substantially more intensity noise due to a steeper spectral slope than that at the peak, where the slope is nominally zero. It must be emphasized, that in the case of slow frequency excursions (compared to the E-field modulation period), the noise in the first- and the second-harmonic channels would be canceled in the ratio. However, fast excursions can generate noise in the signal ratio. 

The factors affecting the measurement accuracy men- tioned above have an impact on the statistical error of the result. The present systematic errors (summarized in Table IV) has nearly the same significance as the statis- tical one and also comprises a number of factors. 

One of the most significant factors is the uncertainty in the field-imperfection contributions, Eq. (21). This uncertainty is mostly due to statistical factors such as laser drifts, nevertheless, it provides an offset to the PV- parameter. Since the measurement of this contribution is actually the same measurement as the PV-effect, any improvements of the stability reduces the overall system- atic uncertainty. We would like to emphasize also that Eq. (21) represents a mean value of the imperfection con- tribution over numerous experiments averaging over pos- sible fluctuations of the field-imperfection contribution. These fluctuations may be partially responsible for the variance in the PV-parameter, and, thus, the statisti- cal uncertainty of its value. This fact demonstrates that the elimination of the field-imperfections is an essential requirement for improving the overall accuracy of the ex- periments. 

Another significant source of the systematic uncer- tainty is the uncertainty in the value of the electric field in the interaction region. While the voltage applied to the E-field plates and the correction electrodes is con- trolled precisely, the actual E-field value used in the PV parameter determination depends on the accuracy of the numerical modeling of the electric-field distribution in the particular geometry. There are two factors in the model contributing to the uncertainty: finite accuracy of mea- surements of the interaction region geometrical parame- ters, and the imperfect approximation of the geometry in the numerical simulation. 

However, while this systematic uncertainty plays a sig- nificant role for measurements of the PV parameter of a single isotope, for the isotope ratios this uncertainty will cancel (or will be substantially reduced), if the measure- ments observing different isotopes are performed without changing the E-field geometry. The same is true for the calibration parameter, C$_{0}$ , which also cancels in the iso- tope ratios. 

There are other, rather minor, factors contributing to 

