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Dephasing processes significantly impact the performance of deterministicsingle-photon sources. Dephasing broadens the spectral line and suppresses theindistinguishability of the emitted photons, which is undesirable for manyapplications, primarily for quantum computing. We consider a light emitted by atwo-level system with a pulsed incoherent pump in the presence of the spectralfilter. The spectral filter allows control of the second-order autocorrelationfunction, indistinguishability, and quantum yield. We show that narrow spectralfilters can increase the indistinguishability of the emitted light whileundermining the quantum yield. The influence of the spectral filter on thesecond-order correlation function depends on the duration of the pump. When thepumping pulse is long compared to the lifetime of the two-level system, thenarrow spectral filters lead to a rapid increase in the second-orderautocorrelation function. In this limit, the statistics of the light from thetwo-level system inherit the statistics of the incoherent pump. In the case ofthe short duration of the pump pulse, it is possible to preserve single-photonproperties to some degree for the sub-lifetime width of the spectral filter.Moreover, when the light emitted by the single-photon source is used to controla quantum system, e.g., cavity, the single-photon properties of the lightmanifest themselves differently, depending on the response time of the quantumsystem. In particular, in the case of long response time, the spectral filterwith sub-lifetime width can provide the near-zero second-order autocorrelationfunction.

Controlling Purity, Indistinguishability and Quantum Yield of Incoherently Pumped Two-Level System by Spectral Filters