  In this work, we combine a systematic experimental investigation of the
power- and temperaturedependent evolution of the spatial coherence function,
g(1) (r), in a one-dimensional excitonpolariton channel with a modern
microscopic numerical theory based on a stochastic master equation approach.
The spatial coherence function g(1) (r) is extracted via high-precision
Michelson interferometry, which allows us to demonstrate that in the regime of
non-resonant excitation, the dependence g(1) (r) reaches a saturation value
with a plateau, determined by the intensity of pump and effective temperature
of the crystal lattice. The theory, which was extended to allow for treating
incoherent excitation in a stochastic frame, matches the experimental data with
good qualitative and quantitative agreement. This allows us to verify the
prediction that the decay of the off-diagonal long range order can be almost
fully suppressed in one-dimensional condensate systems.
