  Dephasing processes significantly impact the performance of deterministic
single-photon sources. Dephasing broadens the spectral line and suppresses the
indistinguishability of the emitted photons, which is undesirable for many
applications, primarily for quantum computing. We consider a light emitted by a
two-level system with a pulsed incoherent pump in the presence of the spectral
filter. The spectral filter allows control of the second-order autocorrelation
function, indistinguishability, and quantum yield. We show that narrow spectral
filters can increase the indistinguishability of the emitted light while
undermining the quantum yield. The influence of the spectral filter on the
second-order correlation function depends on the duration of the pump. When the
pumping pulse is long compared to the lifetime of the two-level system, the
narrow spectral filters lead to a rapid increase in the second-order
autocorrelation function. In this limit, the statistics of the light from the
two-level system inherit the statistics of the incoherent pump. In the case of
the short duration of the pump pulse, it is possible to preserve single-photon
properties 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 control
a quantum system, e.g., cavity, the single-photon properties of the light
manifest themselves differently, depending on the response time of the quantum
system. In particular, in the case of long response time, the spectral filter
with sub-lifetime width can provide the near-zero second-order autocorrelation
function.
