  Cavity exciton-polaritons (polaritons) are bosonic quasi-particles offering a
unique solid-state system to investigate interacting condensates. Up to now,
disorder induced localization and short lifetimes have prevented the
establishment of long range off diagonal order needed for any quantum
manipulation of the condensate wavefunction. In this work, using a wire
microcavity with polariton lifetimes ten times longer than in all previously
existing samples, we show that polariton condensates can propagate over
macroscopic distances outside the excitation area, while preserving their
spontaneous spatial coherence. An extended condensate wave-function builds-up
with a degree of spatial coherence larger than 50% over distances 50 times the
polariton De Broglie wavelength. The expansion of the condensate is shown to be
governed by the repulsive potential induced by photo-generated excitons within
the excitation area. The control of this local potential offers a new and
versatile method to manipulate extended polariton condensates. As an
illustration, we demonstrate synchronization of extended condensates via
controlled tunnel coupling and localization of condensates in a trap with
optically controlled dimensions.
