Fig. 3 | Nature Communications

Fig. 3

From: Ultra-long coherence times amongst room-temperature solid-state spins

Fig. 3

Alternating current (AC) magnetic field measurement. a Pulse sequence for a BAC measurement. It is a Hahn-echo sequence (see Fig. 2c) with a synchronised sinusoidal AC magnetic field, which changes its sign during the π-pulse. Hence, the final phase depends on the magnetic field amplitude. A total sequence for a measurement like b is given at the bottom, where the amplitude of the magnetic field is increased at each Hahn-echo sub-sequence. The final microwave π/2-pulse is along the y axis, so that, at BAC = 0 T, the gradient is at a maximum. b Single measurement to find the working points that have the maximum gradient (100,000 iterations, data with blue crosses, sinusoidal fit with red line). The working point indicated with an orange circle is an example, the dashed arrows show how a measured intensity translates to a magnetic field amplitude. c Theoretical sensitivity vs the time period of the magnetic field derived from the T2 data (see Supplementary Note 5), giving an optimum period τoptimum (=1/fB,optimum) of 1.2 ms. The inner-magenta/outer-purple dotted vertical lines mark the range of periods for which the difference with the optimum sensitivity remains within 2%/10%, respectively. d Histogram of the repeatedly measured Hahn-echo intensity at working point BAC = 0 T to determine the uncertainty σ1. For the vertical axis of b and the horizontal axis of d, the same units and scale are used (since the same analysis method is applied), so they cancel when computing δBmin. e Logarithmic plot of δBmin vs Tmeas (data with blue crosses, fit to δBmin = η/Tmeas with red line, \(\eta = 9.1_{ - 0.3}^{ + 0.3}\) nT Hz−1/2)

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