  We demonstrate a scheme for the Fourier synthesis of periodic optical
potentials with asymmetric unit cells for atoms. In a proof of principle
experiment, an atomic Bose-Einstein condensate is exposed to either symmetric
or sawtooth-like asymmetric potentials by superimposing a conventional standing
wave potential of $\lambda/2$ spatial periodicity with a fourth-order lattice
potential of $\lambda/4$ periodicity. The high periodicity lattice is realized
using dispersive properties of multiphoton Raman transitions. Future
applications of the demonstrated scheme could range from the search for novel
quantum phases in unconventionally shaped lattice potentials up to
dissipationless atomic quantum ratchets.
