Correlated hopping of bosonic atoms induced by optical lattices

In this work we analyze a particular setup with ultracold atoms trapped in state-dependent lattices. We show that any asymmetry in the contact interaction translates into one of two classes of correlated hopping. After deriving the effective lattice Hamiltonian for the atoms, we obtain analytically and numerically the different phases and quantum phase transitions. We find for weak correlated hopping both Mott insulators and charge density waves, while for stronger correlated hopping the system transitions into a pair superfluid. We demonstrate that this phase exists for a wide range of interaction asymmetries and has interesting correlation properties that differentiate it from an ordinary atomic Bose-Einstein condensate.Comment: 24 pages with 9 figures, to appear in New Journal of Physic

Quantum computation with unknown parameters

We show how it is possible to realize quantum computations on a system in which most of the parameters are practically unknown. We illustrate our results with a novel implementation of a quantum computer by means of bosonic atoms in an optical lattice. In particular we show how a universal set of gates can be carried out even if the number of atoms per site is uncertain.Comment: 3 figure

On the shape of vortices for a rotating Bose Einstein condensate

For a Bose-Einstein condensate placed in a rotating trap, we study the simplified energy of a vortex line derived in Aftalion-Riviere Phys. Rev. A 64, 043611 (2001) in order to determine the shape of the vortex line according to the rotational velocity and the elongation of the condensate. The energy reflects the competition between the length of the vortex which needs to be minimized taking into account the anisotropy of the trap and the rotation term which pushes the vortex along the z axis. We prove that if the condensate has the shape of a pancake, the vortex stays straight along the z axis while in the case of a cigar, the vortex is bent

Split vortices in optically coupled Bose-Einstein condensates

We study a rotating two-component Bose-Einstein condensate in which an optically induced Josephson coupling allows for population transfer between the two species. In a regime where separation of species is favored, the ground state of the rotating system displays domain walls with velocity fields normal to them. Such a configuration looks like a vortex split into two halves, with atoms circulating around the vortex and changing their internal state in a continuous way.Comment: 4 EPS pictures, 4 pages; Some errata have been corrected and thep resentation has been slightly revise

Three-dimensional vortex configurations in a rotating Bose Einstein condensate

We consider a rotating Bose-Einstein condensate in a harmonic trap and investigate numerically the behavior of the wave function which solves the Gross Pitaevskii equation. Following recent experiments [Rosenbuch et al, Phys. Rev. Lett., 89, 200403 (2002)], we study in detail the line of a single quantized vortex, which has a U or S shape. We find that a single vortex can lie only in the x-z or y-z plane. S type vortices exist for all values of the angular velocity Omega while U vortices exist for Omega sufficiently large. We compute the energy of the various configurations with several vortices and study the three-dimensional structure of vortices

Structural instability of vortices in Bose-Einstein condensates

In this paper we study a gaseous Bose-Einstein condensate (BEC) and show that: (i) A minimum value of the interaction is needed for the existence of stable persistent currents. (ii) Vorticity is not a fundamental invariant of the system, as there exists a conservative mechanism which can destroy a vortex and change its sign. (iii) This mechanism is suppressed by strong interactions.Comment: 4 pages with 3 figures. Submitted to Phys. Rev. Let

Construction of exact solutions by spatial traslations in inhomogeneous Nonlinear Schrodinger equations. Applications to Bose-Einstein condensation

In this paper we study a general nonlinear Schr\"odinger equation with a time dependent harmonic potential. Despite the lack of traslational invariance we find a symmetry trasformation which, up from any solution, produces infinitely many others which are centered on classical trajectories. The results presented here imply that, not only the center of mass of the wave-packet satisfies the Ehrenfest theorem and is decoupled from the dynamics of the wave-packet, but also the shape of the solution is independent of the behaviour of the center of the wave. Our findings have implications on the dynamics of Bose-Einstein condensates in magnetic trapsComment: Submitted to Phys. Re

Split Instability of a Vortex in an Attractive Bose-Einstein Condensate

An attractive Bose-Einstein condensate with a vortex splits into two pieces via the quadrupole dynamical instability, which arises at a weaker strength of interaction than the monopole and the dipole instabilities. The split pieces subsequently unite to restore the original vortex or collapse.Comment: 4 pages, 4 figures, added figures and references, revised tex

Anomalous rotational properties of Bose-Einstein condensates in asymmetric traps

We study the rotational properties of a Bose-Einstein condensate confined in a rotating harmonic trap for different trap anisotropies. Using simple arguments, we derive expressions for the velocity field of the quantum fluid for condensates with or without vortices. While the condensed gas describes open spiraling trajectories, on the frame of reference of the rotating trap the motion of the fluid is against the trap rotation. We also find explicit formulae for the angular momentum and a linear and Thomas-Fermi solutions for the state without vortices. In these two limits we also find an analytic relation between the shape of the cloud and the rotation speed. The predictions are supported by numerical simulations of the mean field Gross-Pitaevskii model.Comment: 4 RevTeX pages, 2 EPS figures; typos fixed, reference adde