  It appears feasible with nanostructures to perform calorimetry at the level
of individual thermal phonons. Here I outline an approach employing
monocrystalline mesoscopic insulators, which can now be patterned from
semiconductor heterostructures into complex geometries with full, three-
dimensional relief. Successive application of these techniques also enables
definition of integrated nanoscale thermal transducers; coupling these to a dc
SQUID readout yields the requisite energy sensitivity and temporal resolution
with minimal back action. The prospect of phonon counting opens intriguing
experimental possibilities with analogies in quantum optics. These include
fluctuation-based phonon spectroscopy, phonon shot noise in the energy
relaxation of nanoscale systems, and quantum statistical phenomena such as
phonon bunching and anticorrelated electron-phonon exchange.
