Dark-mode theory for quadratic bosonic networks
Abstract
Abstract Determining dark modes in quadratic bosonic networks is both fundamental and imperative, since the dark modes are critical to coherent network manipulation and quantum resource transfer, and such networks are applicable to wide parameter regimes and various physical areas. Here, we develop a symplectic singular value decomposition (SSVD) method for identifying the number and form of the dark modes in quadratic bosonic networks. This method maps the emergence of dark modes onto a computationally tractable symplectic null-space problem, enabling their systematic identification in large-scale quadratic bosonic networks.We adopt the SSVD method to study both the collective cooling of multiple mechanical modes and optomechanical entanglement generation in linearized optomechanical networks. We find that the appearance of the dark modes suppresses the cooling performance and entanglement generation. Our work paves the way for engineering dark modes in quadratic bosonic networks, and the SSVD method has wide applicability in quantum physics, quantum information science, and many-body physics.
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