General Hubbard model for strongly interacting fermions in an optical lattice and its phase detection

Based on consideration of the system symmetry and its Hilbert space, we show that strongly interacting fermions in an optical lattice or superlattice can be generically described by a lattice resonance Hamiltonian. The latter can be mapped to a general Hubbard model with particle assisted tunneling rates. We investigate the model under population imbalance and show the attractive and the repulsive models have the same complexity in phase diagram under the particle-hole mapping. Using this mapping, we propose an experimental method to detect possible exotic superfluid/magnetic phases for this system.Comment: 5 pages, 4 figure

Trapped ion quantum computation with transverse phonon modes

We propose a scheme to implement quantum gates on any pair of trapped ions immersed in a large linear crystal, using interaction mediated by the transverse phonon modes. Compared with the conventional approaches based on the longitudinal phonon modes, this scheme is much less sensitive to ion heating and thermal motion outside of the Lamb-Dicke limit thanks to the stronger confinement in the transverse direction. The cost for such a gain is only a moderate increase of the laser power to achieve the same gate speed. We also show how to realize arbitrary-speed quantum gates with transverse phonon modes based on simple shaping of the laser pulses.Comment: 5 page

States of fermionic atoms in an optical superlattice across a Feshbach resonance

We investigate states of fermionic atoms across a broad Feshbach resonance in an optical superlattice which allows interaction only among a small number of lattice sites. The states are in general described by superpositions of atomic resonating valence bonds and dressed molecules. As one scans the magnetic field, level crossing is found between states with different symmetry properties, which may correspond to a quantum phase transition in the many-body case.Comment: 10 pages, 11 figure

Test of Particle-Assisted Tunneling for Strongly Interacting Fermions in an Optical Superlattice

Fermions in an optical lattice near a wide Feshbach resonance are expected to be described by an effective Hamiltonian of the general Hubbard model with particle-assisted tunneling rates resulting from the strong atomic interaction [Phys. Rev. Lett. 95, 243202 (2005)]. Here, we propose a scheme to unambiguously test the predictions of this effective Hamiltonian through manipulation of ultracold atoms in an inhomogeneous optical superlattice. The structure of the low-energy Hilbert space as well as the particle assisted tunneling rates can be inferred from measurements of the time-of-flight images.Comment: 4 pages, 4 figure