  It is generally difficult to study the dynamical properties of a quantum
system with both inherent quantum noises and non-perturbative nonlinearity. Due
to the possibly drastic intensity increase of an input coherent light in the
gain-loss waveguide couplers with parity-time (PT) symmetry, the Kerr effect
from a nonlinearity added into the systems can be greatly enhanced, and is
expected to create the macroscopic entangled states of the output light fields
with huge photon numbers. Meanwhile, the quantum noises also coexist with the
amplification and dissipation of the light fields. Under the interplay between
the quantum noises and nonlinearity, the quantum dynamical behaviors of the
systems become rather complicated. However, the important quantum noise effects
have been mostly neglected in the previous studies about nonlinear PT-symmetric
systems. Here we present a solution to this non-perturbative quantum nonlinear
problem, showing the real-time evolution of the system observables. The
enhanced Kerr nonlinearity is found to give rise to a previously unknown
decoherence effect that is irrelevant to the quantum noises, and imposes a
limit on the emergence of macroscopic nonclassicality. In contrast to what
happen in the linear systems, the quantum noises exert significant impact on
the system dynamics, and can create the nonclassical light field states in
conjunction with the enhanced Kerr nonlinearity. This first study on the noise
involved quantum nonlinear dynamics of the coupled gain-loss waveguides can
help to better understand the quantum noise effects in the broad nonlinear
systems.
