It is well known that some nonlinear phenomena such as strong photon blockade are difficult to observe in optomechanical systems with current experimental technology. Here we present a coherent feedback control strategy in which a linear cavity is coherently controlled by an optomechanical controller in a feedback manner. The coherent feedback loop transfers quantum nonlinearity from the controller to the controlled cavity causing destructive quantum interference to occur, and making it possible to observe strong nonlinear effects. With the help of the coherent feedback loop, large and tunable bistability and strong photon blockade of the cavity modes can be achieved even in the optomechanical weak coupling regime. Additionally, the coherent feedback loop leads to two-photon and multiphoton tunnelings for the controlled linear cavity, which are also typical quantum nonlinear phenomena. We hope that our work can give new perspectives on engineering nonlinear interactions in quantum systems.

Quantum coherent feedback has been proven to be an efficient way to tune the dynamics of quantum optical systems and, recently, those of solid-state quantum circuits. Here, inspired by the recent progress of quantum feedback experiments, especially those in mesoscopic circuits, we prove that superconducting circuit QED systems, shunted with a coherent feedback loop, can change the dynamics of a superconducting transmission line resonator, i.e., a linear quantum cavity, and lead to strong on-chip nonlinear optical phenomena. We find that bistability can occur under the semiclassical approximation and photon antibunching can be shown in the quantum regime. Our study presents alternate perspectives for engineering nonlinear quantum dynamics on a chip.

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