Solid-state gravitational-wave detectors at GHz frequencies: the search for the primordial stochastic GW background and light primordial black hole binaries

Reheating after inflation is one of the strongest sources of gravitational waves (GW), producing a stochastic background (SGWB) with a non-thermal spectrum peaked at frequencies of order a few GHz. Detecting it is difficult: experiments based on the inverse Gertsenshtein effect in intense magnetic fields reach the MHz but not the GHz band, where the typical strain is around 10-30. The same window contains the coalescence of light primordial black hole (PBH) binaries, whose merger frequency f 4.4 kHz,(M/M) falls in the MHz--GHz range for planetary to sub-planetary masses; since such objects are necessarily sub-solar, their detection would be strong evidence for PBHs as a component of the dark matter. We propose a solid-state detector at GHz frequencies that could integrate over months to years the GW continuously arriving from the Big Bang and search for light PBH binary coalescence. As a concrete realization we consider a modular array of about10 cubed ultra-pure sapphire (10 cm) cubed monocrystals forming a cubic-metre detector read out by cryogenic single-phonon sensors, whose segmentation provides thermal isolation, favourable counting statistics and coincidence-based background rejection. We also compare candidate materials, finding diamond superior per unit volume but limited by the unavailability of large single crystals. Finally, we contrast the two targets. The stationary background is a shot-noise-limited counting problem, best served by a narrow, resonance-enhanced, long-integration search; the loud transient chirp of a nearby merger is better caught by a fast, broad-band search with coincidence tagging. Because the phonon spectrum is continuous, a modular solid-state array can serve both, by staggering resonant cells across the band while running a broad-band subset for chirp tracking.