  Quantum manipulation of coupled mechanical resonators has become an important
research topic in optomechanics because these systems can be used to study the
quantum coherence effects involving multiple mechanical modes. A prerequisite
for observing macroscopic mechanical coherence is to cool the mechanical
resonators to their ground state. Here we propose a theoretical scheme to cool
two coupled mechanical resonators by introducing an optomechanical interface.
The final mean phonon numbers in the two mechanical resonators are calculated
exactly and the results show that the ground-state cooling is achievable in the
resolved-sideband regime and under the optimal driving. By adiabatically
eliminating the cavity field in the large-decay regime, we obtain analytical
results of the cooling limits, which show the smallest achievable phonon
numbers and the parameter conditions under which the optimal cooling is
achieved. Finally, the scheme is extended to the cooling of a chain of coupled
mechanical resonators.
