Motion of a condensate in a shaken and vibrating harmonic trap

The dynamics of a Bose-Einstein condensate (BEC) in a time-dependent harmonic trapping potential is determined for arbitrary variations of the position of the center of the trap and its frequencies. The dynamics of the BEC wavepacket is soliton-like. The motion of the center of the wavepacket, and the spatially and temporally dependent phase (which affects the coherence properties of the BEC) multiplying the soliton-like part of the wavepacket, are analytically determined.Comment: Accepted for publication in J. Phys. B: At Mol Opt Phy

Expansion of an interacting Fermi gas

We study the expansion of a dilute ultracold sample of fermions initially trapped in a anisotropic harmonic trap. The expansion of the cloud provides valuable information about the state of the system and the role of interactions. In particular the time evolution of the deformation of the expanding cloud behaves quite differently depending on whether the system is in the normal or in the superfluid phase. For the superfluid phase, we predict an inversion of the deformation of the sample, similarly to what happens with Bose-Einstein condensates. Viceversa, in the normal phase, the inversion of the aspect ratio is never achieved, if the mean field interaction is attractive and collisions are negligible.Comment: 4 pages, 3 figures, final versio

Critical Dynamics of a Two-dimensional Superfluid near a Non-Thermal Fixed Point

Critical dynamics of an ultracold Bose gas far from equilibrium is studied in two spatial dimensions. Superfluid turbulence is created by quenching the equilibrium state close to zero temperature. Instead of immediately re-thermalizing, the system approaches a meta-stable transient state, characterized as a non-thermal fixed point. A focus is set on the vortex density and vortex-antivortex correlations which characterize the evolution towards the non-thermal fixed point and the departure to final (quasi-)condensation. Two distinct power-law regimes in the vortex-density decay are found and discussed in terms of a vortex binding-unbinding transition and a kinetic description of vortex scattering. A possible relation to decaying turbulence in classical fluids is pointed out. By comparing the results to equilibrium studies of a two-dimensional Bose gas, an intuitive understanding of the location of the non-thermal fixed point in a reduced phase space is developed.Comment: 11 pages, 13 figures; PRA versio

Superconductivity from repulsive interactions in the two dimensional electron gas

We present a well-controlled perturbative renormalization group (RG) treatment of superconductivity from short-ranged repulsive interactions in a variety of model two dimensional electronic systems. Our analysis applies in the limit where the repulsive interactions between the electrons are small compared to their kinetic energy.Comment: 10 pages 3 figure

Bound states of three and four resonantly interacting particles

We present an exact diagrammatic approach for the problem of dimer-dimer scattering in 3D for dimers being a resonant bound state of two fermions in a spin-singlet state, with corresponding scattering length $a_F$. Applying this approach to the calculation of the dimer-dimer scattering length $a_B$, we recover exactly the already known result $a_B=0.60 a_F$. We use the developed approach to obtain new results in 2D for fermions as well as for bosons. Namely, we calculate bound state energies for three $bbb$ and four $bbbb$ resonantly interacting bosons in 2D. For the case of resonant interaction between fermions and bosons we calculate exactly bound state energies of the following complexes: two bosons plus one fermion $bbf$, two bosons plus two fermions $bf_{\uparrow}bf_{\downarrow}$, and three bosons plus one fermion $bbbf$.Comment: 10 pages, 9 figure