Artificial electromagnetism for neutral atoms: Escher staircase and Laughlin liquids

We present a method for creating fields that couple to neutral atoms in the same way that electromagnetic fields couple to charged particles. We show that this technique opens the door for a range of neutral atom experiments, including probing the interplay between periodic potentials and quantum Hall effects. Furthermore, we propose, and analyze, seemingly paradoxical geometries which can be engineered through these techniques. For example, we show how to create a ring of sites where an atom continuously reduces its potential energy by moving in a clockwise direction.