Interactions of cosmic axions with Rydberg atoms in resonant cavities via the Primakoff process

A quantum theoretical treatment of the interactions of cosmic axions with Rydberg atoms in resonant cavities via the Primakoff process is developed, by taking into account the finite temperature and the dissipation due to the finite damping time of the cavities. The time evolution of the number of the excited Rydberg atoms, evaluated numerically based on the theoretical formulations, enables us to obtain the detection efficiency of the axion-converted photons with a good signal-to-noise ratio. The optimum experimental setup to search for dark matter axions with Rydberg atoms is presented.