Fig. 2: AQM characterization scheme.
a (Top) Ramsey interferometric protocol (Supplementary Note 2) to measure qubit coherence time \({T}_{2}^{*}\) when the incoherent probe beam is applied for time T at a distance d. (Bottom) Ramsey fringes in normalized fluorescence originating from the detuning between the microwave source and the qubit frequency. \({T}_{2}^{*}\) is extracted from the decay in Ramsey fringe contrast. Here, the background-subtracted fluorescence counts are measured during the global detection step and are normalized with respect to the counts from \(\left\vert \uparrow \right\rangle\). The data shown here are for a single ion (N = 1) illuminated with the state-detection probe light (I = 1.25(16)Isat, waist w = 1.50(5) μm) at a distance of d = 6.0(3)w = 9.0(4) μm and Ramsey detuning of 10 kHz. Error bars indicate standard error from 200 experimental repetitions. Intensity crosstalk IX is estimated from numerical simulations of the master equation from the measured \({T}_{2}^{*}\). We find, using numerical simulations solving the master equation of the system (dashed line, Supplementary Note 5), that the intensity cross-talk, IX = 3.4(6) × 10−5 for this data. b Comparison of Ramsey fringe decay profiles between case-A: an ion located at the probe beam focus (N = 2), and case-B: no ion at probe beam focus (N = 1). Data points represent Ramsey fringe contrast measured over two fringes, and the fits are exponential decay with \({T}_{2}^{*}\) as a fitting parameter. The Ramsey fringe contrast is normalized with the contrast measured at T = 0. Error bars denote standard deviation in estimating Ramsey fringe contrast, using 20 bootstrapping repetitions from 200 measurements (Supplementary Note 7). The shaded region indicates fluctuations of experimental settings over periodic calibration of the probe beam location with respect to ion2 (Supplementary Note 4E) for case-A. \({T}_{2}^{*}\) values measured for case-A and case-B lie within the error bounds, indicating that the decoherence is limited by the intensity crosstalk and not by inter-ion scattering.
