  We demonstrate condensate formation in a dark state in an ultracold quantum
gas coupled to a high-finesse cavity and pumped by a shaken optical lattice. We
show experimentally and theoretically that the atoms in the dark state display
a strong suppression of the coupling to the cavity. On the theory side, this is
supported by solving the dynamics of a minimal three-level model and of the
full atom-cavity system. The symmetry of the condensate wave function is
anti-symmetric with respect to the potential minima of the pump lattice, and
displays a staggered sign along the cavity direction. This symmetry decouples
the dark state from the cavity, and is preserved when the pump intensity is
switched off.
