Exceptional-point-engineered dispersive readout of a driven three-level atom weakly interacting with coupled cavities in non-Markovian environments

In this paper we study the dispersive readout of a driven three-level atom weakly interacting with a passive cavity that couples to an active cavity. The system excluding the three-level atom exhibits a parity-time ($\mathcal{P}\mathcal{T}$) symmetric phase transition at the exceptional point (EP), which originates from the balance between dissipation of the passive cavity and gain of the active cavity. The perturbation to the passive cavity induced by the three-level atom can be amplified near the EP, where the eigenvalues of the effective Hamiltonian have significant differences when the three-level atom is in the excited, metastable, and ground states, respectively. Applying the modified Laplace transformation and input-output theory near the EP, we can realize the dispersive readout of the three-level atom weakly interacting with coupled cavities, which can be characterized through the different distributions of the transmission spectrum of the passive cavity and the ratio of the active cavity excitation number to the input photon number corresponding to the different levels of the three-level atom. Moreover, we generalize the dispersive readout method to the non-Markovian regime, which is in good agreement with that obtained by the Markovian approximation. We find that the non-Markovian effects of the environment backacting on the system dynamics can lead to the enhancement of the dispersive readout for the three-level atom, which is revealed by the excitation backflow generated in the interaction between the passive cavity and environment. The dispersive readout proposed is conducive to understanding the influences of $\mathcal{P}\mathcal{T}$ symmetry and the non-Markovian effect on dispersive readout, which offers the possibility of an alternative field of possible applications for quantum information and quantum communication.