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Pseudomode approach to Fano effect in dissipative cavity quantum electrodynamics

We study the Fano effect in dissipative cavity quantum electrodynamics, which originates from the interference between the emitter's direct radiation and that mediated by a cavity mode. Starting from a two-level system coupled to a structured reservoir, we show that a quantum master equation previously derived within the Born-Markov approximation can be rederived by introducing a single auxiliary mode via pseudomode approach. We identify the corresponding spectral function of the system--environment interaction and demonstrate that it consists of a constant and a non-Lorentzian contribution forming the Fano profile. The constant term is shown to be essential for obtaining a Lindblad master equation and is directly related to the rate associated with this Fano interference. Furthermore, by applying Fano diagonalization to a common-environment setup including an explicit cavity mode, we independently derive the same spectral function in the strongest-interference regime. Our results establish a unified framework for describing the Fano effect in single-mode cavity QED systems and clarify its non-Markovian origin encoded in the spectral function.