Fig. 1: Algorithm base principle.
From: Ultra-high dynamic range quantum measurement retaining its sensitivity
a Since the measured signal (red dotted line) oscillates due to the rotating spin, the magnetic field B can be determined up to a certain range only. Example ranges are indicated by different colours, and the resulting magnetic field for each range given the measured signal (horizontal black dashed line) with blue crosses. b The conventional and most sensitive way to measure an AC field is given at the top left, with π/2-pulses of a Hahn-echo sequence at the beginning and end of the period, and the π-pulse halfway at the inflection point. The measured area A0 can be reduced by moving the π/2-pulses closer to the centre (top right A0/2, bottom left A0/4, bottom right A0/8). c The fraction of the maximum area A0 vs the fraction of the longest time delay between the π/2-pulses for DC (green dotted line) and AC (cyan line) fields. For DC, this is linear, while for AC, this depends on the area of a sinusoid, which resembles a line near the inflection point, thus the relation becomes quadratic for short time delays. The area and thus uncertainty/range can be changed continuously by changing this delay. d For smaller measured areas, the probed field decreases proportionally, as does the effective frequency. In a, the signal for area A0 was shown, while here, the signals for areas A0/2 and A0/4 are drawn in similar fashion, which are offset for clarity. Combining several measured areas reduces the potential fields (vertical grey dashed arrows), thus increasing the overall range. e After measuring the signal (horizontal green dotted line), with the known uncertainty of the signal (green line along the vertical axis), the probability distribution of the field (magenta line along the horizontal axis) follows via the sinusoidal relationship (red dotted sine-shaped line for area A0/2). f The measurement with the largest area A0 gives several similar peaks in the probability distribution (blue line). However, when combining measurements with different areas (magenta dashed line added A0/2, olive dotted line added A0/4 as well), the number of remaining peaks reduces, while the sharpness (thus uncertainty) remains similar to that of the first measurement.
