  The design and test of a detector of small harmonic displacements is
presented. The detector is based on the principle of the parametric conversion
of power between the resonant modes of two superconducting coupled microwave
cavities. The work is based on the original ideas of Bernard, Pegoraro, Picasso
and Radicati, who, in 1978, suggested that superconducting coupled cavities
could be used as sensitive detectors of gravitational waves, and on the work of
Reece, Reiner and Melissinos, who, {in 1984}, built a detector of this kind.
They showed that an harmonic modulation of the cavity length l produced an
energy transfer between two modes of the cavity, provided that the frequency of
the modulation was equal to the frequency difference of the two modes. They
achieved a sensitivity to fractional deformations of dl/l~10^{-17} Hz^{-1/2}.
We repeated the Reece, Reiner and Melissinos experiment, and with an improved
experimental configuration and better cavity quality, increased the sensitivity
to dl/l~10^{-20} Hz^{-1/2}. In this paper the basic principles of the device
are discussed and the experimental technique is explained in detail. Possible
future developments, aiming at gravitational waves detection, are also
outlined.
