Fast iterative, adaptive frequency sensing scheme of a two-level system (theory)

In this work we propose an iterative, adaptive sensing protocol based on Ramsey interferometry of a two-level system. Our scheme allows one to estimate unknown frequencies with a high precision from short, finite signals. It avoids several issues related to processing of decaying signals and reduces the experimental overhead related to sampling. The scheme takes advantage of the so-called Magnus based corrections to speed up and achieve high fidelity preparation of the ideal sensing state. Additionally, it utilizes several signal processing techniques to get rid of spectral leakage and scalloping losses which hinder correct frequency estimation significantly. Combining these two techniques with an iterative procedure based on enhancing the Ramsey sequence, systematic errors are mitigated while estimating frequencies from Fourier transforms. IAS compares favorably to methods that allow one to extend the coherence time of the system, e.g., CPMG, as it allows one to determine with high accuracy the frequency on a much shorter time scale.