9 The systematic uncertainty comes from a sensitivity of the numerical model of the E-field, which is used for cal- culating the exaggerated fields in the interaction region, to an imperfect approximation of the electrode-system geometry. These experiments suggest that this field’s imperfection cannot mimic the PV-effect entirely, never- theless, it appears to be a major source of systematic un- certainty impacting the accuracy of the PV-asymmetry measurements. The most prominent contribution is given by a combined effect of the parasitic components of the electric field and the non-zero projection of the lead- ing magnetic field on the direction of the electric field: e$_{y}$ (˜ e$_{z}$/ 2 ˜ E$_{0}$ + ˜ b$_{x}$/B ). The PV-asymmetry parameter, ζ/β is obtained from the measured value of K 1 by compensat- ing for the influence of these magnetic- and electric-field imperfections, Eq. (21). There is another effect that cannot, by itself, mimic the PV-asymmetry, but needs to be taken into account for proper calibration. This effect is related to the E-field modulation implemented in the present experiment. The atoms are excited to the metastable state, 6s6p $^{3}$P$_{0}$ , by the light beam in the interaction region and then travel ∼ 20 cm until they are detected downstream in the probe region. Due to the spread in the time-of-flight between the interaction and probe regions, the phase mixing leads to a reduction of the signal modulation contrast at the probe region, and it depends on the signal-modulation frequency. Since the signal comprises two time-scales of interest, first- and second-harmonic of the E-field mod- ulation, the contrast reduction is different for the two. Therefore, the ratio of the signal modulation amplitudes, r$_{M}$ , on which we base the PV-asymmetry observation, appear altered in the probe region compared to what it would be at the interaction region. The amplitude com- bination, K , and, therefore, the PV-parameter, ζ/β , are similarly affected. In our data analysis, a correction co- efficient, C$_{0}$ , is introduced, which has been calculated theoretically: Under present experimental conditions, this coefficient, C$_{0}$ , is found to be 1.028(3), and the measured PV param- eter is corrected accordingly. Principles of its derivation are given in Appendix C. In Fig. 8, the PV interference parameter ζ/β is shown as determined in 19 separate runs ( ∼ 60 hours of integra- tion in total). Its mean value is 39(4)$_{stat.}$(3)$_{syst.}$ mV/cm, which is in agreement with the theoretical predictions [14, 15]. The value of the PV parameter was extracted using the expression given in the first column of Ta- ble II, taking into account the calibration correction C$_{0}$ . Thus, | ζ | = 8 . 7 ± 1 . 4 × 10 − 10 ea$_{0}$, which is the largest APV amplitude observed so far (here we used | β | = 2 . 24 +0 . 07 − 0 12 × 10 − 8 ea$_{0}$/(V/cm) [4, 7]). The sign of the PV interference parameter ζ/β is found by comparing the measurements with the theoretical The present measurement accuracy is not yet sufficient to observe the isotopic and hyperfine differences in the PV amplitude, which requires an accuracy better than ≈ 1% for PV amplitude in a single transition [17–19]. In the present apparatus the signal levels achieved values high enough to reach the signal-to-noise ratio (SNR) of 2 / √ τ (s) for the PV asymmetry if the noise were domi- nated by the fluorescence-photon shot-noise ( τ is the in- tegration time). This is good enough to reach the sub- percent accuracy in a few hours of integration. However, a number of additional factors limit the accuracy. One of the most important noise sources is the fluctua- tions of the modulating- and DC-field parameters during the experiment. The first- and the second-harmonic sig- nals depend differently on the modulating electric field amplitude, ˜ E$_{0}$ , and the DC-bias, thus, a noise in the electronics controlling the fields contaminates the first- model of the transition rates employing the field geome- try shown in Fig. 2. The direction and, thus, the signs of the electric and magnetic fields as well as the polarization angle θ were calibrated prior to the PV measurements. Special care was taken of detecting parasitic phase shifts in the lock-in amplifier. A signal from an arbitrary func- tion direct digital synthesis (DDS) generator simulating the output of the probe region photodetector was fed into the amplifier. The signal is comprised of a sum of two sinusoidal waveforms, one frequency doubled, attenu- ated, and phase shifted with respect to the other. Results of the signal parameters measurement from the lock-in, such as the first-to-second harmonic amplitude ratio, rel- ative phase shift and its sign, are compared to those used in the DDS generator to simulate the signal. The differ- ence in the measured and generated amplitude ratio is found to be below 0.01%, and the relative phase shift is detected within ± 1 . 5 $^{◦}$. No relative sign flips between the first- and second-harmonic amplitudes were detected. VII. ERROR BUDGET [ ζ β ] probe reg. = C$_{0}$ [ ζ β ] real . FIG. 8: (color online) The PV interference parameter ζ/β . Mean value: 39(4)$_{stat.}$(3)$_{syst.}$ mV/cm, | ζ | = 8 . 7 ± 1 . 4 × 10 − 10 ea$_{0}$.