How the mass of a scalar field influences Resonance Casimir-Polder interaction in Schwarzschild spacetime

Abstract: \emph{Resonance Casimir-Polder interaction(RCPI)} occurs in nature when one or more atoms are in their excited states and the exchange of real photon is involved between them due to vacuum fluctuations of the quantum fields. In recent times, many attempts have been made to show that the curved spacetime such as the \emph{de-Sitter spacetime} can be separated from a \emph{thermal Minkowski spacetime} using \emph{RCPI}. Motivated from these ideas, here we study the \emph{RCPI} between two atoms that interact with a massive scalar field in Schwarzschild spacetime provided the atoms are placed in the near-horizon region. Subsequently, we use the tool of the \emph{open quantum system} and calculate the Lamb shift of the atomic energy level of the entangled states. We show that the behavior of \emph{RCPI} modifies depending on the mass of the scalar field. In the high mass limit, the interaction becomes short-range and eventually disappears beyond a characteristic length scale of $1/m$, where $m$ is the mass of the scalar field.