  We describe a method to create fractional quantum Hall states of atoms
confined in optical lattices. We show that the dynamics of the atoms in the
lattice is analogous to the motion of a charged particle in a magnetic field if
an oscillating quadrupole potential is applied together with a periodic
modulation of the tunneling between lattice sites. We demonstrate that in a
suitable parameter regime the ground state in the lattice is of the fractional
quantum Hall type and we show how these states can be reached by melting a Mott
insulator state in a super lattice potential. Finally we discuss techniques to
observe these strongly correlated states.
