Quantum signatures of the topological phase in bosonic quadratic systems

Quantum entanglement and classical topology are two distinct phenomena that are difficult to be connected together. Here we discover that an open bosonic quadratic chain exhibits topology-induced entanglement effect. When the system is in the topological phase, the edge modes can be entangled in the steady state, while no entanglement appears in the trivial phase. This finding is verified through the covariance approach based on the quantum master equations, which provide exact numerical results without truncation process. We also obtain concise approximate analytical results through the quantum Langevin equations, which perfectly agree with the exact numerical results. We show the stationary entanglement originates from the matching between the near-zero eigenenergies of the topological edge states and the system-environment coupling (denoted by the dissipation rate). Our work reveals that the stationary entanglement can be a quantum signature of the topological phase in bosonic systems and, inversely, the topological quadratic systems can be powerful platforms to generate robust entanglement.