Fig. 3: Fidelity (F1∣2) of preserving ion1 for state reset light at ion2 location.
a Excitation and decay mechanisms for the \({D}_{1}^{(11)}\) and \({D}_{1}^{(10)}\) transitions in 171Yb+ ion initialized in state \(\left\vert \uparrow \right\rangle\)29, for various polarizations (thick arrows representing π and thin arrows representing σ±). The \({D}_{1}^{(11)}\) transitions contribute to state reset via optical pumping, although any residual \({D}_{1}^{(10)}\) light (e.g., from frequency modulation via an electro-optic modulator29) may degrade F1∣2. b Calculated F1∣2 for the state reset process as a function of the ratio of the intensity of \({D}_{1}^{(11)}\) component I(11) to the total intensity I (where I = I(11) + I(10) with I(10) indicating \({D}_{1}^{(10)}\) component) and ratio of the intensity of π polarization Iπ to the total intensity I (where \(I={I}_{\pi }+{I}_{{\sigma }^{+}}+{I}_{{\sigma }^{-}}\) with equal intensities in σ+ and σ− polarizations) Here, F1∣2 is calculated using numerical simulations of the master equation (Supplementary Note 5) under the conditions of I2 = 1.25Isat and IX = 5 × 10−5. The red star marker indicates the parameters used to measure F1∣2 in (c). Additionally, the plot on the right (sharing the same vertical axes) shows an estimation of state reset times τop(ion2) as a function of Iπ/I for I(11)/I = 1. c F1∣2 vs d expressed in multiples of the beam waist w (case-B in Fig. 2b). Here, w = 1.50(5) μm is the Gaussian beam waist for the addressing beam. Error bars denote standard deviation in estimating F1∣2, using 20 bootstrapping repetitions from 200 measurements (Supplementary Note 7). The estimated infidelity (1-F1∣2) due to the inherent decoherence of the qubit in the absence of the probe light is < 3 × 10−5. For calibrating crosstalk IX, we measure F1∣2 for a probe beam with relative intensity attenuated to 7.2(2) × 10−5 addressing ion1 (triangle marker at d = 0). For comparison, F1∣2 is calculated (solid gray line) for a diffraction-limited (Numerical Aperture NA = 0.16) Gaussian beam of beam waist w = 1.50 μm. F1∣2 is > 99.9% for d ≥ 4w (see discussion). For these measurements, I2 = 1.25(16)Isat, Iπ/I = 0.86, I(11)/I = 1, τop = 9.73(7) μs.
