Creating effective vector potentials with light*

Ultra cold atoms are remarkable systems with a truly unprecedented level of experimental control and one application of this control is engineering the systems hamiltonian. To date this has focused mostly on the real-space potential that the atoms experience for example, multiple-well traps or optical lattice potentials. Here we present our experimental work which tailors the energy-momentum dispersion of the cold atoms. We couple different internal states of rubidium 87 via a momentum-selective Raman transition and load our system into the resulting adiabatic eigenstates. Using this technique we show the controlled modification of the energy-momentum dispersion leads to an effective vector potential. This work was performed in collaboration with Y.-J. Lin, R.~L.~Compton, A.~R.~Perry, W.~D.~Phillips and J.~V.~Porto.