Edge states of a three dimensional kicked rotor

Edge localization is a fascinating quantum phenomenon. In this paper, the underlying mechanism generating it is presented analytically and verified numerically for a weakly kicked three-dimensional rotor. Analogy to tight binding model in solid state physics is used. The edge states result of the edge at zero angular momentum of the three-dimensional kicked rotor.Comment: 16 pages, 3 figure

A simple model for interactions and corrections to the Gross-Pitaevskii Equation

One of the assumptions leading to the Gross-Pitaevskii Equation (GPE) is that the interaction between atom pairs can be written effectively as a \delta -function so that the interaction range of the particles is assumed to vanish. A simple model that takes into account the extension of the inter-particle potential is introduced. The correction to the GPE predictions for the energy of a condensate confined by a harmonic trap in the Thomas-Fermi (TF) regime is estimated. Although it is found to be small, we believe that in some situations it can be measured using its dependance on the frequency of the confining trap. Due to the simplicity of the model, it may have a wide range of applications.Comment: 22 pages, 2 figure

Double humped states in the nonlinear Schroedinger equation with a random potential

The role of double humped states in spreading of wave packets for the nonlinear Schroedinger equation (NLSE) with a random potential is explored and the spreading mechanism is unraveled. Comparison with an NLSE with a double-well potential is made. There are two independent affects of the nonlinearity on the double humped states for the NLSE: coupling to other states and destruction. The interplay between these effects is discussed.Comment: 10 pages, 3 figure

Direct observation of number squeezing in an optical lattice

We present an in-situ study of an optical lattice with tunneling and single lattice site resolution. This system provides an important step for realizing a quantum computer. The real-space images show the fluctuations of the atom number in each site. The sub-Poissonian distribution results from the approach to the Mott insulator state, combined with the dynamics of density-dependent losses, which result from the high densities of optical lattice experiments. These losses are clear from the shape of the lattice profile. Furthermore, we find that the lattice is not in the ground state despite the momentum distribution which shows the reciprocal lattice. These effects may well be relevant for other optical lattice experiments, past and future. The lattice beams are derived from a microlens array, resulting in lattice beams which are perfectly stable relative to one another