Quantum phases of electric dipole ensembles in atom chips

We present how a phase factor is generated when an electric dipole moves along a closed trajectory inside a magnetic field gradient. The similarity of this situation with charged particles in a magnetic field can be employed to simulate condensed matter models, such as the quantum Hall effect and chiral spin Hamiltonians, with ultra cold atoms integrated on atom chips. To illustrate this we consider a triangular configuration of a two dimensional optical lattice, where the chiral spin Hamiltonian $\vec{\sigma}_i \cdot \vec{\sigma}_j \times \vec{\sigma}_k$ can be generated between any three neighbours on a lattice yielding an experimentally implementable chiral ground state.