  The dark-mode effect is a stubborn obstacle for ground-state cooling of
multiple degenerate mechanical modes optomechanically coupled to a common
cavity-field mode. Here we propose an auxiliary-cavity-mode method for
simultaneous ground-state cooling of two degenerate or near-degenerate
mechanical modes by breaking the dark mode. We find that the introduction of
the auxiliary cavity mode not only breaks the dark-mode effect, but also
provides a new cooling channel to extract the thermal excitations stored in the
dark mode. Moreover, we study the general physical-coupling configurations for
breaking the dark mode in a generalized networkcoupled four-mode optomechanical
system consisting of two cavity modes and two mechanical modes. We find the
analytical dark-mode-breaking condition in this system. This method is general
and it can be generalized to break the dark-mode effect and to realize the
simultaneous ground-state cooling in a multiple-mechanicalmode optomechanical
system. We also demonstrate the physical mechanism behind the dark-mode
breaking by studying the breaking of dark-state effect in the N-type four-level
atomic system. Our results not only provide a general method to control various
dark-mode and dark-state effects in physics, but also present an opportunity to
the study of macroscopic quantum phenomena and applications in
multiple-mechanical-resonator systems.
