Generating Kerr nonlinearity with an engineered non-Markovian environment

Kerr nonlinearity is an important resource for creating squeezing and entanglement in quantum technology. Here we propose a scheme for generating Kerr nonlinearity originated from an engineered non-Markovian environment, which is different from the previous efforts using nonlinear media or quantum systems with special energy structures. In the present work, the generation of Kerr nonlinearity depends on the system-environment interaction time, the energy spectrum of the environment, and the system-environment coupling strength, regardless of the environmental initial state. The scheme can be realized in systems originally containing no Kerr interaction, such as superconducting circuit systems, optomechanical systems, and cavity arrays connected by transmission lines.