The rotational properties of an attractively interacting Bose gas are studied using analytical and numerical methods. We study perturbatively the ground-state phase space for weak interactions, and find that in an anharmonic trap the rotational ground states are vortex or center-of-mass rotational states; the crossover line separating these two phases is calculated. We further show that the Gross-Pitaevskii equation is a valid description of such a gas in the rotating frame and calculate numerically the phase-space structure using this equation. It is found that the transition between vortex and center-of-mass rotation is gradual; furthermore, the perturbative approach is valid only in an exceedingly small portion of phase space. We also present an intuitive picture of the physics involved in terms of correlated successive measurements for the center-of-mass state.

We examine the phase diagram of an effectively repulsive Bose-Einstein condensate of atoms that rotates in a quadratic-plus-quartic potential. With use of a variational method we identify the three possible phases of the system as a function of the rotational frequency of the trap and of the coupling constant. The derived phase diagram is shown to be universal and partly exact in the limit of weak interactions and small anharmonicity. The variational results are found to be consistent with numerical solutions of the Gross-Pitaevskii equation.

We examine the static and dynamic stability of the solutions of the Gross-Pitaevskii equation and demonstrate the intimate connection between them. All salient features related to dynamic stability are reflected systematically in static properties. We find, for example, the obvious result that static stability always implies dynamic stability and present a simple explanation of the fact that dynamic stability can exist even in the presence of static instability.

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.

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. The 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.

The dynamics of a kicked quantum mechanical wave packet 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.

A rotated and harmonically trapped Bose gas with attractive interactions is expected to either remain stationary or escape from the trap. Here we report that, on the contrary, in an anharmonic trapping potential the Bose gas with attractive interactions responds to external rotation very differently, namely, through center-of-mass motion or by formation of vortices.

We report Monte Carlo wave function simulation results on cold collisions between magnesium atoms in a strong red-detuned laser field. This is the normal situation, e.g., in magneto-optical traps (MOT). The Doppler limit heating rate due to radiative collisions is calculated for Mg-24 atoms in an MOT based on the S-1(0)-P-1(1) atomic laser cooling transition. We find that radiative heating does not seem to affect the Doppler limit in this case. We also describe a channeling mechanism due to the missing Q branch in the excitation scheme, which could lead to a suppression of inelastic collisions, and find that this mechanism is not present in our simulation results due to the multistate character of the excitation process.