Figure 1

Schematic of the experimental setup. Laser cooled Cs atoms are prepared in an all-glass vacuum cell centered within a plexiglas cube supporting the bias and rf coils. Microwave radiation is provided by two horn antennas. Stern-Gerlach analysis is performed by letting the atoms fall in a magnetic field gradient provided by the MOT coils and by inferring the magnetic populations from the time-dependent fluorescence excited by a probe beam and detected with a photodiode (PD).Reuse & Permissions

Figure 2

Implementation of the quantum state map $|4,4⟩\to (|3,3⟩+|3,-3⟩)/\sqrt{2}$. (a) Phase modulation waveform for the rf (top and middle) and $\mu \mathrm{w}$ (bottom) fields. (b) Numerical simulation of the evolving quantum state, shown as density matrices for the times indicated. Populations are shown as dark (red) tones and coherences (absolute values only) as light (blue) tones. Magnetic sublevels are ordered $\{|4,4⟩,\dots ,|4,-4⟩,|3,3⟩,\dots ,|3,-3⟩\}$ along the axes.Reuse & Permissions

Figure 3

(a) Stern-Gerlach analysis of magnetic sublevel populations, in the form of arrival time distributions at the probe beam. Each line is a separate measurement after a state map $|4,4⟩\to |F,m⟩$, as indicated. (b) Histogram of the fidelities for 32 nonrobust state maps of this form. (c) Histogram of the fidelities for 32 robust state maps of this form.Reuse & Permissions

Figure 4

(a) Randomized benchmarking data showing the overall fidelity for sequences of up to four state maps. Points are experimental data, and lines are fits of the form $\mathcal{F}(l)$, for robust (red circles) and nonrobust (black diamonds) control waveforms. Error bars are 1 standard deviation for the average over different state map sequences. The average fidelities per state map inferred from the fits are 99.11(5)% and 97.7(3)%, respectively. (b) Plot showing the correlation between benchmarking and standard fidelities. Each data point (${ϵ}_B$, ${ϵ}_S$) is obtained from a numerical simulation performed with a distinct set of values for the parameters in $H_C$. Solid and dashed lines correspond to ${ϵ}_S={ϵ}_B$, ${ϵ}_S=0.5{ϵ}_B$, and ${ϵ}_S=1.15{ϵ}_B$, respectively.Reuse & Permissions