  We report on the present progress in development of the dark matter axion
search experiment with Rydberg-atom-cavity detectors in Kyoto, CARRACK I and
CARRACK II. The axion search has been performed with CARRACK I in the 8 % mass
range around $ 10 \mu {\rm eV} $, and CARRACK II is now ready for the search in
the wide range $ 2 \mu {\rm eV} - 50 \mu {\rm eV} $. We have also developed
quantum theoretical calculations on the axion-photon-atom system in the
resonant cavity in order to estimate precisely the detection sensitivity for
the axion signal. Some essential features on the axion-photon-atom interaction
are clarified, which provide the optimum experimental setup for the axion
search.
