Nonreciprocal entanglement by dynamically encircling a nexus.

Nonreciprocal entanglement, characterized by inherently robust operation, is a cornerstone for quantum information processing and communications. However, it remains challenging to achieve nonreciprocal entanglement characterized by stability and robustness against environmental fluctuations. Here, we propose a universal nonlinear mechanism to engineer magnetic-free nonreciprocity in dissipative optomechanics by utilizing bistability, a phenomenon ubiquitous across nonlinear physical systems. By dynamically encircling the nexus of bistability, a cusp converged by the bistable surfaces, we obtain nonreciprocal displacement and then utilize it to achieve robust nonreciprocal entanglement. Owing to the unique landscape of bistability, our nonreciprocal displacement and entanglement exhibit stability and robustness through closed-loop operations. Our work presents a foundational framework for leveraging nonlinearity to achieve nonreciprocal quantum information processing. It paves new avenues for exploring nonreciprocal quantum information processing and designing backaction-immune quantum metrology with nonlinearity.