Fig. 2

Spectral reconstruction of control filter transfer functions. a A single-frequency perturbation, β _Ω(t) is applied to the control envelope Ω(t), which drives rotations about x. Measuring operational fidelity (see main text) for each system identification frequency, ω _sid, allows frequency-resolved reconstruction of F _Ω(ω). b Experimental reconstruction of DPSS filter functions for k = 1 and varying NW. Solid lines show the analytic \({\cal F}_{{\mathrm{av}}}\) calculated based on F _Ω(ω). Control envelopes (shown schematically as insets) have a duration of 1.1 ms with area normalized to π prior to sid perturbation, and measurements are averaged over 10 linearly sampled φ ∈ [0, 2π], with α = 0.5. Each phase realization is repeated 50 times to reduce the influence of photon shot noise. c–e Measured spectral response of flat-top vs. DPSS-modulated pulses implementing \({\Bbb I}\) for different k and NW. Shading indicates the target band [0, ω _B ]. We choose NW = k + 1 for each k, to conservatively maintain spectral concentration of the DPSS-modulated pulses while matching the number of zero crossings in comparable flat-top protocols. Markers represent experimental measurements and solid lines show the analytic \({\cal F}_{{\mathrm{av}}}\). Arrows highlight out-of-band sensitivity due to harmonics of the flat-top control. We employed large modulation depths (α = 0.95 for DPSS-modulated pulses, α = 0.85 for flat-top pulses) to amplify these signals. Measurement sensitivity floor ~0.5%. As the pulse area and duration are fixed, the target bands within which the DPSS-modulated pulses are contained are broader than the main peaks of the flat-top pulses