  We propose an approach to cool a mechanical resonator (MR) via quantum
interference in a triple quantum dot (TQD) capacitively coupled to the MR. The
TQD connected to three electrodes is an electronic analog of a three-level atom
in $\Lambda$ configuration. The electrons can tunnel from the left electrode
into one of the two dots with lower-energy states, but can only tunnel out from
the higher-energy state at the third dot to the right electrode. When the two
lower-energy states are tuned to be degenerate, an electron in the TQD can be
trapped in a superposition of the degenerate states called the dark state. This
effect is caused by the destructive quantum interference between tunneling from
the two lower-energy states to the higher-energy state. Under this condition,
an electron in the dark state readily absorbs an energy quantum from the MR.
Repeating this process, the MR can be cooled to its ground state. Moreover, we
propose a scheme for verifying the cooling result by measuring the current
spectrum of a charge detector adjacent to a double quantum dot coupled to the
MR.
