Second‐Order Autocorrelation Function of Spectrally Filtered Light From an Incoherently Pumped Two‐Level System

Light with zero second‐order autocorrelation function, g(2)(0), emitted by single‐photon source (SPS), for example, two‐level system (TLS), is usually considered as being in a Fock state with one photon in a certain electromagnetic mode of free space. However, real SPSs have finite linewidths and excite all modes lying within the linewidth. It is shown that the zero value of g(2)(0) of light emitted by an incoherently pumped TLS is a consequence of the quantum interference of electromagnetic modes lying within the linewidth. Applying the quantum regression theorem for out‐of‐time‐ordered correlation functions, an analytical expression for g(2)(0) is obtained for the light emitted by a TLS and passed through a spectral filter. It is shown that narrowing the spectral width of the band‐pass filter inevitably leads to an increase in g(2)(0). g(2)(τ)$g^{(2)}(\tau )$ is found and it is demonstrated that certain spectral filters lead to its nonmonotonic time dependence. These results open up the possibility of controlling the statistics of the emitted light using a spectral filter, which can find applications in quantum communication and cryptography. A full analytical solution for the second‐order autocorrelation function g(2)(t) of light emitted by a single‐photon source and passed through a filter is presented. It is shown that the zero value of g(2)(0) is a consequence of quantum interference of electromagnetic modes at different frequencies. Narrowing filter spectral width leads to an increase in g(2)(0) and can result in nonmonotonic time dependence of g(2)(t).