  In the control of classical mechanical systems, the feedback has been
successfully applied to the production of the desired nonlinear dynamics.
However, how much this can be done is still an open problem in quantum
mechanical systems. This paper proposes a scheme of generating strong nonlinear
quantum effects via the recently developed coherent feedback techniques, which
can be shown to outperform the measurement-based quantum feedback scheme that
can only generate pseudo-nonlinear quantum effects. Such advancement is
demonstrated by two application examples in quantum optics on chip. In the
first example, we show that the nonlinear Kerr effect can be generated and
amplified to be comparable with the linear effect in a transmission line
resonator (TLR). In the second example, we show that by tuning the gains of the
quantum amplifiers in a TLR coherent feedback network, non-Gaussian "light"
(microwave field) can be generated and manipulated via the nonlinear effects
which exhibits fully quantum sub-Poisson photoncount statistics and photon
antibunching phenomenon. The scheme opens promising applications in
demonstrating strong nonlinear quantum optics on chip, which is extremely weak
and inflexible in traditional quantum optical devices.
