  We propose a domino-cooling method to realize simultaneous ground-state
cooling of a coupled mechanical-resonator chain through an optomechanical
cavity working in the unresolved-sideband regime. This domino-effect cooling is
realized by combining the cold-damping feedback on the first mechanical
resonator with nearest-neighbor couplings between other neighboring mechanical
resonators. We obtain analytical results for the effective susceptibilities,
noise spectra, final mean phonon numbers, and cooling rates of these mechanical
resonators, and find the optimal-cooling condition for these resonators.
Particularly, we analyze a two-mechanical-resonator case and find that by
appropriately engineering either the laser power or the feedback, a flexible
switch between symmetric and asymmetric ground-state cooling can be achieved.
This could be used for preparing symmetric quantum states in mechanical
systems. We also simulate the cooling performance of a coupled
$N$-mechanical-resonator chain and confirm that these resonators can be
simultaneously cooled to their quantum ground states in the unresolved-sideband
regime. Under proper parameter conditions, the cooling of the
mechanical-resonator chain shows a temperature gradient along the chain. This
study opens a route to quantum manipulation of multiple mechanical resonators
in the bad-cavity regime.
