Extended Data Fig. 5: Spin ensemble simulations.
From: Detecting spins by their fluorescence with a microwave photon counter
a, Measured (blue dots) and simulated (orange solid line) electromagnetic field amplitude at the output of the spin cavity as a function of the time T from the π/2 pulse of an echo sequence. The echo appears as a slight increase of the field amplitude at twice the separation between the π/2 and π pulse (inset). The spin spectral density \({\rho }_{{\rm{spin}}}\) is the only free parameter of the simulation, accordance with the experimental data is achieved for \({\rho }_{{\rm{s}}{\rm{p}}{\rm{i}}{\rm{n}}}=14.6{{\rm{s}}{\rm{p}}{\rm{i}}{\rm{n}}{\rm{s}}{\rm{k}}{\rm{H}}{\rm{z}}}^{-1}\). b, Simulated time evolution of \(\langle {S}_{{\rm{z}}}\rangle \) during an echo sequence, using the same pulse parameters as in the experiment. c, Simulation of the time evolution of \(\langle {S}_{{\rm{z}}}\rangle \) during a π-pulse with the same parameters of the experiment of photo-detected incoherent relaxation. A spin density \({\rho }_{{\rm{s}}{\rm{p}}{\rm{i}}{\rm{n}}}=12{{\rm{s}}{\rm{p}}{\rm{i}}{\rm{n}}{\rm{s}}{\rm{k}}{\rm{H}}{\rm{z}}}^{-1}\) was adjusted so that the ratio between the variation of \(\langle {S}_{z}\rangle \) at echo time (b) and upon the π pulse excitation (c) reproduces the experimental ratio \({C}_{{\rm{spin}}}/({\eta }_{{\rm{duty}}}{c}_{{\rm{e}}})\).
