  Quantum entanglement not only plays an important role in the study of the
fundamentals of quantum theory, but also is considered as a crucial resource in
quantum information science. The generation of macroscopic entanglement
involving multiple optical and mechanical modes is a desired task in cavity
optomechanics. However, the dark-mode effect is a critical obstacle against the
generation of quantum entanglement in multimode optomechanical systems
consisting of multiple degenerate or near-degenerate mechanical modes coupled
to a common cavity mode. Here we propose an auxiliary-cavity-mode method to
enhance optomechanical entanglement in a multimode optomechanical system by
breaking the dark-mode effect. We find that the introduction of the auxiliary
cavity mode not only assists the entanglement creation between the cavity mode
and the mechanical modes, but also improves the immunity of the optomechanical
entanglement to the thermal excitations by about three orders of magnitude. We
also study the optomechanical entanglement in the network-coupled
optomechanical system consisting of two mechanical modes and two cavity modes.
By analyzing the correspondence between the optomechanical entanglement and the
dark-mode effect, we find that optomechanical entanglement can be largely
enhanced once the dark mode is broken. In addition, we study the mechanical
entanglement and find that it is negligibly small. We also present some
discussions on the experimental implementation with a microwave optomechanical
setup, on the relationship between the dark-mode-breaking mechanism and the
center-of-mass and relative coordinates, and on the explanation of the
important role of the dark-mode breaking in the enhancement of optomechanical
entanglement. Our results pave the way towards the preparation of entangled
optomechanical networks and noise-resistant quantum resources.
