  The nonequilibrium steady state of the one-dimensional (1D)
Kardar-Parisi-Zhang (KPZ) universality class is studied in-depth by exact
solutions, yet no direct experimental evidence of its characteristic
statistical properties has been reported so far. This is arguably because, for
an infinitely large system, infinitely long time is needed to reach such a
stationary state and also to converge to the predicted universal behavior. Here
we circumvent this problem in the experimental system of growing liquid-crystal
turbulence, by generating an initial condition that possesses a long-range
property expected for the KPZ stationary state. The resulting interface
fluctuations clearly show characteristic properties of the 1D stationary KPZ
interfaces, including the convergence to the Baik-Rains distribution. We also
identify finite-time corrections to the KPZ scaling laws, which turn out to
play a major role in the direct test of the stationary KPZ interfaces. This
paves the way to explore unsolved properties of the stationary KPZ interfaces
experimentally, making possible connections to nonlinear fluctuating
hydrodynamics and quantum spin chains as recent studies unveiled relation to
the stationary KPZ.
