Kinetic energy functional for Fermi vapors in spherical harmonic confinement

Two equations are constructed which reflect, for fermions moving independently in a spherical harmonic potential, a differential virial theorem and a relation between the turning points of kinetic energy and particle densities. These equations are used to derive a differential equation for the particle density and a non-local kinetic energy functional.Comment: 8 pages, 2 figure

Vortex macroscopic superpositions in ultracold bosons in a double-well potential

We study macroscopic superpositions in the orbital rather than the spatial degrees of freedom, in a three-dimensional double-well system. We show that the ensuing dynamics of $N$ interacting excited ultracold bosons, which in general requires at least eight single-particle modes and ${N+7 \choose N}$ Fock vectors, is described by a surprisingly small set of many-body states. An initial state with half the atoms in each well, and purposely excited in one of them, gives rise to the tunneling of axisymmetric and transverse vortex structures. We show that transverse vortices tunnel orders of magnitude faster than axisymmetric ones and are therefore more experimentally accessible. The tunneling process generates macroscopic superpositions only distinguishable by their orbital properties and within experimentally realistic times.Comment: 9 pages, 6 figure

Collective excitation frequencies of Bosons in a parabolic potential with interparticle harmonic interactions

The fact that the ground-state first-order density matrix for Bosons in a parabolic potential with interparticle harmonic interactions is known in exact form is here exploited to study collective excitations in the weak-coupling regime. Oscillations about the ground-state density are treated analytically by a linearized equation of motion which includes a kinetic energy contribution. We show that the dipole mode has the frequency of the bare trap, in accord with the Kohn theorem, and derive explicit expressions for the frequencies of the higher-multipole modes in terms of a frequency renormalized by the interactions.Comment: 6 pages, no figures, accepted for publication on Physics Letters

Particle density and non-local kinetic energy density functional for two-dimensional harmonically confined Fermi vapors

We evaluate analytically some ground state properties of two-dimensional harmonically confined Fermi vapors with isotropy and for an arbitrary number of closed shells. We first derive a differential form of the virial theorem and an expression for the kinetic energy density in terms of the fermion particle density and its low-order derivatives. These results allow an explicit differential equation to be obtained for the particle density. The equation is third-order, linear and homogeneous. We also obtain a relation between the turning points of kinetic energy and particle densities, and an expression of the non-local kinetic energy density functional.Comment: 7 pages, 2 figure

Symmetry breaking and singularity structure in Bose-Einstein condensates

We determine the trajectories of vortex singularities that arise after a single vortex is broken by a discretely symmetric impulse in the context of Bose-Einstein condensates in a harmonic trap. The dynamics of these singularities are analyzed to determine the form of the imprinted motion. We find that the symmetry-breaking process introduces two effective forces: a repulsive harmonic force that causes the daughter trajectories to be ejected from the parent singularity, and a Magnus force that introduces a torque about the axis of symmetry. For the analytical non-interacting case we find that the parent singularity is reconstructed from the daughter singularities after one period of the trapping frequency. The interactions between singularities in the weakly interacting system do not allow the parent vortex to be reconstructed. Analytic trajectories were compared to the actual minima of the wavefunction, showing less 0.5% error for impulse strength of (v=0.00005). We show that these solutions are valid within the impulse regime for various impulse strengths using numerical integration of the Gross-Pitaevskii equation. We also show that the actual duration of the symmetry breaking potential does not significantly change the dynamics of the system as long as the strength is below (v=0.0005).Comment: 14 pages, 10 figure

Tunneling, self-trapping and manipulation of higher modes of a BEC in a double well

We consider an atomic Bose-Einstein condensate trapped in a symmetric one-dimensional double well potential in the four-mode approximation and show that the semiclassical dynamics of the two ground state modes can be strongly influenced by a macroscopic occupation of the two excited modes. In particular, the addition of the two excited modes already unveils features related to the effect of dissipation on the condensate. In general, we find a rich dynamics that includes Rabi oscillations, a mixed Josephson-Rabi regime, self-trapping, chaotic behavior, and the existence of fixed points. We investigate how the dynamics of the atoms in the excited modes can be manipulated by controlling the atomic populations of the ground states.Comment: 12 pages, 5 figure

Macroscopic Superposition of Ultracold Atoms with Orbital Degrees of Freedom

We introduce higher dimensions into the problem of Bose-Einstein condensates in a double-well potential, taking into account orbital angular momentum. We completely characterize the eigenstates of this system, delineating new regimes via both analytical high-order perturbation theory and numerical exact diagonalization. Among these regimes are mixed Josephson- and Fock-like behavior, crossings in both excited and ground states, and shadows of macroscopic superposition states.Comment: 21 pages, 9 figure