  Propagation of light pulses through negative group velocity media is known to
give rise to a number of paradoxical situations that seem to violate causality.
The solution of these paradoxes has triggered the investigation of a number of
interesting and unexpected features of light propagation. Here we report a
combined theoretical and experimental study of the ring-down oscillations in
optical cavities filled with a medium with such a strongly negative frequency
dispersion to give a negative round-trip group delay time. We theoretically
anticipate that causality imposes the existence of additional resonance peaks
in the cavity transmission, resulting in a non-exponential decay of the cavity
field and in a breakdown of the cavity decay rate concept. Our predictions are
validated by simulations and by an experiment using a room-temperature gas of
metastable helium atoms in the detuned electromagnetically induced transparency
regime as the cavity medium.
