Directed transport and Floquet analysis for a periodically kicked wavepacket at a quantum resonance

The dynamics of a kicked quantum mechanical wavepacket at a quantum resonance is studied in the framework of Floquet analysis. It is seen how a directed current can be created out of a homogeneous initial state at certain resonances in an asymmetric potential. The almost periodic parameter dependence of the current is found to be connected with level crossings in the Floquet spectrum.Comment: 8 pages, 4 figures, submitted to Phys. Rev.

Calculation of collective modes for the Bose-Hubbard model with confinement

The collective excitations in the Bose-Hubbard model in a trap are studied by means of numerical diagonalization in one dimension. The strength function is calculated for monopole and dipole perturbations, and moments of the strength function are utilized in order to obtain information about the collective behavior under external forces. In the superfluid regime, the spectrum is found to be exhausted by one single frequency, while in systems that contain a Mott insulating plateau several frequencies are excited. An explanation of recent experimental findings in terms of a Mott plateau is suggested.Comment: 4 pages, 5 figures; submitted to PRA. One figure change

Ratchet effect for cold atoms in an optical lattice

The realization of a directed current for a quantum particle in a flashing asymmetric potential is studied. It is found that a positive current, i.e. in the direction expected for a conventional diffusive ratchet, can be attained at short times in the limit where the potential is weak and quantum diffusion dominates, while current reversal is obtained for stronger potentials. A single parameter, the ratio between the kicking frequency and the optical lattice potential strength, determines both the degree to which quantum effects dominate, and the possibility of obtaining a ratchet current. The effect should be readily observable in experiments.Comment: 4 pages, 3 figure

Dipole and monopole modes in the Bose-Hubbard model in a trap

The lowest-lying collective modes of a trapped Bose gas in an optical lattice are studied in the Bose-Hubbard model. An exact diagonalization of the Hamiltonian is performed in a one-dimensional five-particle system in order to find the lowest few eigenstates. Dipole and breathing character of the eigenstates is confirmed in the limit where the tunneling dominates the dynamics, but under Mott-like conditions the excitations do not correspond to oscillatory modes.Comment: 19 pages, 11 figures; submitted to Phys. Rev.

Transition from a two-dimensional superfluid to a one-dimensional Mott insulator

A two-dimensional system of atoms in an anisotropic optical lattice is studied theoretically. If the system is finite in one direction, it is shown to exhibit a transition between a two-dimensional superfluid and a one-dimensional Mott insulating chain of superfluid tubes. Monte Carlo simulations are consistent with the expectation that the phase transition is of Kosterlitz-Thouless type. The effect of the transition on experimental time-of-flight images is discussed.Comment: 4 pages, 4 figures. Slightly revised according to referee request