  We apply the quantum Langevin equations approach to study nonlinear light
propagation through one-dimensional interacting open quantum lattice models. We
write a large set of quantum Langevin equations of lattice operators obtained
after integrating out the light fields and use them to derive nonequilibrium
features of the lattice models. We first consider a Heisenberg like interacting
spin-1/2 chain with nearest-neighbor coupling. The transient and steady-state
transport properties of an incoming monochromatic laser light are calculated
for this model. We find how the local features of the spin chain and the chain
length dependence of light transport coefficient evolve with an increasing
power of the incident light. The steady-state light transmission coefficient at
a higher power depends non-monotonically on the interaction in a finite chain.
While the nonlinear light transmission in our studied model seems to be
ballistic in the absence of interaction and for a high interaction, it shows an
apparent system-size dependence at intermediate interactions. Later, we extend
this method to the long-range interaction between spins of the
driven-dissipative lattice model and to incorporate various losses typical in
many atomic and solid-state systems.
