The modeling techniques of the second-order correlation function g(2)(τ) for a quantum emitter

The numerical techniques required to prove the single-photon emission from any type of quantum emitter (QE) after being coupled to any nanostructure are presented in this paper. The Purcell effect modifies the emission characteristics of QEs, such as color centers in nanodiamonds, for example, nitrogen-vacancy (NV) centers, silicon vacancy (SiV) centers, and so forth, or semiconductor quantum dots. Our numerical approach is based on the unique QEs' experimental photophysics parameters and numerical analysis software, which are MATLAB and Quantum Toolbox in Python (QuTiP). Our results show a comparable g((2)) (tau) behavior between our proposed numerical model and the other two experimental results for the QE before and after coupling to a plasmonic waveguide with subwavelength dimensions. Our proposed method is essential to prove the single-photon emission of modeled single-photon source (SPS) in an on-chip polarization-dependent quantum key distribution system (QKD).