Fig. 3

Sensing techniques and spectrum reconstruction with DPSS-modulated pulses. a Measurements (markers) and expected average fidelity \({\cal F}_{{\mathrm{av}}}\) (solid lines) for spectral response of band-shifted first-order DPSS filter functions with COS modulation. Modulation depth for system identification measurements was α = 0.5. The pulse shapes are shown as insets for each modulation frequency. b Band-shifted SSB modulated DPSS, using the same modulation frequencies as a. c Protocol for three axes measurements to reconstruct the amplitude filter function \(\left( {{\cal S}_{{\mathrm{target}}}} \right)\) in the presence of white dephasing noise with a root-mean-square amplitude of 5Ω _x , where Ω _x is the maximum Rabi frequency of the control. Rotations around the x and y axes allow preparation and readout along all three axes of the Bloch sphere. Projective measurements onto x, y, and z (black markers and lines), expected fidelity under amplitude noise only (red line), and fidelity reconstructed from the three projective measurements (red markers). System identification measurements were all taken with α = 0.75. d Reconstruction of an applied amplitude noise spectrum (shaded comb teeth) using adaptive and Bayesian multitaper estimation (see text). Inset shows all shifted F _Ω(ω) for k = 1. Here, ω _s ranges from 1.4 to 10.0 kHz in steps of 1.1 kHz. Horizontal scale bar indicates target bandwidth of each measurement