We propose a scheme to generate an arbitrary Abelian vector potential for atoms trapped in a two-dimensional optical lattice. By making the optical lattice potential dependent on the atomic state, we transform the problem into that of a two-dimensional imaging. It is shown that an arbitrarily fine pattern of the gauge field in the lattice can be realized without need of diffraction-limited imaging.

• Received 8 January 2011

DOI:https://doi.org/10.1103/PhysRevLett.107.260402