  We show how lasers may create fields which couple to neutral atoms in the
same way that the electromagnetic fields couple to charged particles. These
fields are needed for using neutral atoms as an analog quantum computer for
simulating the properties of many-body systems of charged particles. They allow
for seemingly paradoxical geometries, such as a ring where atoms continuously
reduce their potential energy while moving in a closed path. We propose neutral
atom experiments which probe quantum Hall effects and the interplay between
magnetic fields and periodic potentials.
