Bosons at very low temperatures are known to undergo
Bose-Einstein condensation and gather in the ground state, often with
intriguing consequences like superfluidity. The many-body wave function
thus formed is positive real under most general circumstances and hence
topologically trivial as has been early pointed out by Feynman. However,
under certain conditions, condensation can also occur in metastable
excited states, which can lead to highly non-trivial superfluid order
with unusual properties. I will introduce the experimental arena of
optical lattices, where atomic gases crystallized in a web of light are
used to simulate ultracold condensed matter, and discuss our recent
observations of unconventional forms of superfluidity in metastable
higher bands.