Multimode optomechanical cooling via general dark-mode control

The dark-mode e ff ect 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 e ff ect, 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 network-coupled 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 e ff ect and to realize the simultaneous ground-state cooling in a multiple-mechanical-mode optomechanical system. We also demonstrate the physical mechanism behind the dark-mode breaking by studying the breaking of dark-state e ff ect in the N -type four-level atomic system. Our results not only provide a general method to control various dark-mode and dark-state e ff ects in physics, but also present an opportunity to the study of macroscopic quantum phenomena and applications in multiple-mechanical-resonator