Fig. 5
Sensitivity analysis of AC E-field (EAC) detection via modulation side-band magnitude detection and dependence on DC E-field (EDC). (a) EAC is varied between 1.535mV/cm to 15.35µV/cm for fAC at 150 Hz and 300 Hz. At fAC =150 Hz, measurements are conducted with and without a DC Stark field (blue line is with DC field, EDC =19.35mV/cm, which is close to the optimal point, see (b)). The DC field only slightly increases the signal-to-noise (SNR) ratio (improved sensitivity) at fAC =150 Hz (20.79 µVcm− 1Hz− 1/2 with DC field to 26.5 µVcm− 1Hz− 1/2 without the DC field). At a higher modulation frequency of fAC =300 Hz without the DC field, the noise-base reduction results in improved sensitivity to as high as 7.88 µVcm− 1Hz− 1/2. (b) The estimated SNR in dB at fAC =150 Hz as a function of EDC is shown for three AC field measurements (EAC of ~ 921µV/cm, ~ 445µV/cm, ~ 104µV/cm). SNR is maximized between EDC ~16–20 mV/cm, with corresponding improvements over zero bias of 4.39 dB, 6.76 dB, and 7.00 dB for the three data sets (mean of 6.05 dB). A resolution bandwidth of 10 Hz is used in all measurements. The SNR drop near EDC ~5–10 mV/cm arise from reduced OSC Q-factor and frequency pulling/re-locking, a behavior dependent on multiple operating parameters and will be investigated in future work. Data in Fig. 5a is available in Supplementary Dataset 3.
