Eigenmode evolution in an atom-cavity system

An atom-cavity composite formed by one atom coupled to a single high-Q mode of a cavity is one of the essential systems in the study of cavity quantum electrodynamics, with applications in quantum information processing. This system is also of a considerable interest for the study of non-Hermitian Hamiltonian and quasi-eigenmode topology such as the existence of an exceptional point; the atom-cavity coupling with atomic and cavity decays are precisely described by a 2-by-2 non-Hermitian Hamiltonian. In order to observe quasi-eigenmode evolution, which is needed for demonstrating the existence of an exceptional point, it is necessary to control the atom-cavity coupling constant over a wide range covering from the strong coupling to the weak coupling regime. We have devised a method for varying the coupling constant between one cold rubidium atom and a high-Q mode of a Fabry-Perot by both controlling the polarization of a probe laser and employing a different Hermite-Gaussian mode of cavity. We have observed a transition from level crossing to avoided crossing as the atom-cavity coupling constant increases. As a result, we could observe a singular point or the exceptional point in the quasi-eigenmode topology, at which we observed the cavity transmission on resonance exhibiting discontinuous derivatives with respect to the atom-cavity coupling constant.