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Quantum interference on the transmission spectrum of a timed Dicke state in an open cavity

The transmission spectrum of a two-atom timed Dicke state is investigated in an open optical cavity. In the proposed system, two identical atoms are excited by an external single photon field. In this process, the excited atoms grasp different excitation phases for their different spatial positions. For identical coupling strength of atoms and cavity, the excitation phases get coupled via cavity and vacuum fields, and they finally induce cosine-type quantum interference on the two splitting peaks of the spectrum. However, when one of the atoms is decoupled with the cavity, the excitation phases cannot get coupled directly via the cavity but must be mediated by the vacuum fields, which leads to opposite quantum interference effects on the two splitting peaks. In addition, we find that the real and virtual vacuum-mediated excitation phase couplings generate different quantum interferences. The real vacuum-meditated coupling induces sine-type quantum interference, while it becomes cosine-type for the virtual vacuum-mediated coupling. Our study clarifies the mechanism of quantum interference in the two-atom timed Dicke state and provides a feasible scheme for investigating the effect of vacuum-mediated excitation phase coupling.