  We propose phonon spectroscopy by electric measurements of the
low-temperature conductance of coupled-quantum dots, specifically employing
dephasing of the quantum electronic transport by the phonons. The setup we
consider consists of a T-shaped double-quantum-dot (DQD) system in which only
one of the dots (dot 1) is connected to external leads and the other (dot 2) is
coupled solely to the first one. For noninteracting electrons, the differential
conductance of such a system vanishes at a voltage located in-between the
energies of the bonding and the anti-bonding states, due to destructive
interference. When electron-phonon (e-ph) on the DQD is invoked, we find that,
at low temperatures, phonon emission taking place on dot 1 does not affect the
interference, while phonon emission from dot 2 suppresses it. The amount of
this suppression, as a function of the bias voltage, follows the effective e-ph
coupling reflecting the phonon density of states and can be used for phonon
spectroscopy.
