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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 

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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. 

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- 

## VII. ERROR BUDGET 

