Pseudomode approach to Fano effect in dissipative cavity quantum electrodynamics

TL;DR

The paper addresses Fano interference in dissipative cavity QED by leveraging the pseudomode approach to rederive a Born–Markov quantum master equation and to extract the system–environment spectral function. It shows that the spectral function $J(\omega)$ comprises a constant background term $J_0$ and a non-Lorentzian component that yields the Fano profile, with the constant term ensuring the master equation can be written in Lindblad form. The authors derive explicit parameter correspondences ($J_0=\gamma/(2\pi)$, $\Re z_1=\omega_C$, $\Im z_1=-\kappa/2$, $\mu=g$, $\nu=\gamma_F/2$) and provide the full form of $2\pi J(\omega)$, including its Fano representation $2\pi J(\epsilon)=\gamma|\epsilon+q|^2/(\epsilon^2+1)$ for strong interference ($\eta=1$). They further validate the spectral function via Fano diagonalization in a common-environment setup, demonstrating the non-Markovian origin of Fano interference. Overall, the work offers a unified, Markovian-embedding framework to describe Fano effects in single-mode cavity QED and clarifies the role of memory effects in shaping interference phenomena.

Abstract

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.

Figures (2)

• Figure 1: Setups of the present study. (a) Initial setup for the pseudomode approach (Secs. \ref{['sec:setup']} and \ref{['sec:pseudomode_approach']}), which consists of an atom (two-level system) interacting with a reservoir (continuum of states). In this setup, the atom is the system of interest. (b) Setup after the Markovian embedding, which consists of the atom and a cavity (auxiliary system) interacting with a reservoir. In this setup, the atom and the cavity are the system of interest. The dotted lines represent interactions between the systems. Even after the Markovian embedding, we retain the atom--reservoir interaction that induces a Markovian dissipation for the atom. In Sec. \ref{['sec:Fano_diagonalization']}, we perform the inverse transformation, from (b) to (a), using Fano diagonalization.
• Figure 2: Spectral function $J(\epsilon)$, plotted against the reduced detuning $\epsilon = 2 (\omega - \omega_{\mathrm{C}}) / \kappa$. The solid, dashed, and dotted curves correspond to the cases of $(\eta, |q|) = (1, 2)$, $(0, 2)$, and $(1, 0)$, respectively. We set $\Delta \phi = 0$.