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Cosmic gravitons are expected in the MHz-GHz regions that are currently
unreachable by the operating wide-band interferometers and where various
classes of electromechanical detectors have been proposed through the years.
The minimal chirp amplitude detectable by these instruments is often set on the
basis of the sensitivities reachable by the detectors currently operating in
the audio band. By combining the observations of the pulsar timing arrays, the
limits from wide-band detectors and the other phenomenological bounds we show
that this requirement is far too generous and even misleading since the actual
detection of relic gravitons well above the kHz would demand chirp and spectral
amplitudes that are ten or even fifteen orders of magnitude smaller than the
ones currently achievable in the audio band, for the same classes of stochastic
sources. We then examine more closely the potential high-frequency signals and
show that the sensitivity in the chirp and spectral amplitudes must be even
smaller than the ones suggested by the direct and indirect constraints on the
cosmic gravitons. We finally analyze the high-frequency detectors in the
framework of Hanbury-Brown Twiss interferometry and argue that they are
actually more essential than the ones operating in the audio band (i.e. between
few Hz and few kHz) if we want to investigate the quantumness of the relic
gravitons and their associated second-order correlation effects. We suggest, in
particular, how the statistical properties of thermal and non-thermal gravitons
can be distinguished by studying the corresponding second-order interference
effects.