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 anti-bunching can be shown in the quantum regime. Our study presents new
perspectives for engineering nonlinear quantum dynamics on a chip.Comment: 10 pages, 9 figure