Dalgacık temelli işlem sonrası tekniklerin katı hal kuantum ölçümleme uygulamaları için geliştirilmesi

Spin manifolds of defect centers formed in semiconductor hosts having extended coherence times and optical accessibility are ideal candidates for quantum infor- mation and high-precision quantum sensing applications. For such platforms the quantum state can be compromised due to hyperfine-mediated couplings with the environmental nuclear spin bath (NSB) and the photon shot noise (PSN) entailed to the optical spin readout. The primary aim of this thesis is to employ well-established wavelet analysis techniques for exploring underlying quantum processes as well as suppressing classical and quantum noises. First, I investi- gate the NSB behavior with synchrosqueezed wavelet transform which reveals the time-frequency dynamics simultaneously, and hence locations and orienta- tions of spinful nuclei relative to the central spin. Next, I tailor a wavelet-based approach, which I name as the template margin thresholding (TMT) method, to combat PSN for negatively-charged nitrogen-vacancy centers (NV−) in diamond. Unlike the conventional frequency-based filters, TMT has an unfair advantage as it facilitates on-resonant frequency band denoising of the photoluminescence (PL) acquired. I show that the wavelet-based denoising can enhance the signal- to-noise ratio by an order of magnitude as I computationally demonstrate on NV-center magnetometry. However, the TMT-method starts to lose its advan- tage for high-time-budget applications due to inferior scaling with respect to the standard quantum limit, which is remedied by modifying TMT into a different framework.