Efficient optomechanical refrigeration of two vibrations via an auxiliary feedback loop: Giant enhancement in mechanical susceptibilities and net cooling rates

We propose a method to realize the simultaneous ground-state refrigeration of two vibrational modes beyond the resolved-sideband regime via an auxiliary feedback loop (AFL). This is realized by introducing the AFL to break the dark mode, which is formed by two vibrational modes coupled to a common cavity-field mode. We obtain analytical results of the effective mechanical susceptibilities and net-refrigeration rates, and find that in the presence of the AFL a giant enhancement can be achieved for these susceptibilities and refrigeration rates. Remarkably, the net-cooling rates under the AFL mechanism can be up to four orders of magnitude larger than those in cases without the AFL. Moreover, we show that the simultaneous ground-state refrigeration arises from the AFL mechanism, without which it vanishes. This is because in the absence of the AFL, the dark mode prevents energy extraction through the cooling channels. However, by introducing the AFL, dark-mode breaking rebuilds the refrigeration channels, and, as a result, leads to the simultaneous cooling of these vibrations. Our approach has remarkable flexibility and scalability and can be extended to the simultaneous refrigeration of a large number of vibrations beyond the resolved-sideband regime.