  We report on the experimental realization of a flat, superconducting
microwave resonator, a microwave billiard, with partially violated
time-reversal (T ) invariance, induced by inserting a ferrite into the cavity
and magnetizing it with an external magnetic field perpendicular to the
resonator plane. In order to prevent its expulsion caused by the
Meissner-Ochsenfeld effect we used a cavity of which the top and bottom plate
were made from niobium, a superconductor of type II, and cooled it down to
liquid-helium temperature T LHe ' 4 K. The Cavity had the shape of a chaotic
Afrivca billiard. Superconductivity rendered possible the accurate
determination of complete sequences of the resonance frequencies and of the
widths and strengths of the resonances, an indispensable prerequisite for the
unambiguous detection of T invariance violation, especially when it is only
partially violated. This allows for the first time the precise specification of
the size of T invariance violation from the fluctuation properties of the
resonance frequencies and from the strength distribution, which actually
depends sensitively on it and thus provides a most suitable measure. For this
purpose we derived an analytical expression for the latter which is valid for
isolated resonances in the range from no T invariance violation to complete
violation.
