Josephson oscillation and induced collapse in an attractive Bose-Einstein condensate

Using the axially-symmetric time-dependent Gross-Pitaevskii equation we study the Josephson oscillation of an attractive Bose-Einstein condensate (BEC) in a one-dimensional periodic optical-lattice potential. We find that the Josephson frequency is virtually independent of the number of atoms in the BEC and of the inter-atomic interaction (attractive or repulsive). We study the dependence of Josephson frequency on the laser wave length and the strength of the optical-lattice potential. For a fixed laser wave length (795 nm), the Josephson frequency decreases with increasing strength as found in the experiment of Cataliotti {\it et al.} [Science {\bf 293}, 843 (2001)]. For a fixed strength, the Josephson frequency remains essentially unchanged for a reasonable variation of laser wave length around 800 nm. However, for a fixed strength, the Josephson oscillation is disrupted with the increase of laser wave length beyond 2000 nm leading to a collapse of a sufficiently attractive BEC. These features of Josephson oscillation can be tested experimentally with present set ups.Comment: 7 pages, 12 ps and eps figures, Physical Review

Finite-well potential in the 3D nonlinear Schroedinger equation: Application to Bose-Einstein condensation

Using variational and numerical solutions we show that stationary negative-energy localized (normalizable) bound states can appear in the three-dimensional nonlinear Schr\"odinger equation with a finite square-well potential for a range of nonlinearity parameters. Below a critical attractive nonlinearity, the system becomes unstable and experiences collapse. Above a limiting repulsive nonlinearity, the system becomes highly repulsive and cannot be bound. The system also allows nonnormalizable states of infinite norm at positive energies in the continuum. The normalizable negative-energy bound states could be created in BECs and studied in the laboratory with present knowhow.Comment: 8 pages, 12 figure

Stability and collapse of fermions in a binary dipolar boson-fermion 164Dy-161Dy mixture

We suggest a time-dependent mean-field hydrodynamic model for a binary dipolar boson-fermion mixture to study the stability and collapse of fermions in the $^{164}$Dy-$^{161}$Dy mixture. The condition of stability of the dipolar mixture is illustrated in terms of phase diagrams. A collapse is induced in a disk-shaped stable binary mixture by jumping the interspecies contact interaction from repulsive to attractive by the Feshbach resonance technique. The subsequent dynamics is studied by solving the time-dependent mean-field model including three-body loss due to molecule formation in boson-fermion and boson-boson channels. Collapse and fragmentation in the fermions after subsequent explosions are illustrated. The anisotropic dipolar interaction leads to anisotropic fermionic density distribution during collapse. The present study is carried out in three-dimensional space using realistic values of dipolar and contact interactions

Stable and mobile two-dimensional dipolar ring-dark-in-bright Bose-Einstein condensate soliton

We demonstrate robust, stable, mobile two-dimensional (2D) dipolar ring-dark-in-bright (RDB) Bose-Einstein condensate (BEC) solitons for repulsive contact interaction, subject to a harmonic trap along the $y$ direction perpendicular to the polarization direction $z$. Such a RDB soliton has a ring-shaped notch (zero in density) imprinted on a 2D bright soliton free to move in the $x-z$ plane. At medium velocity the head-on collision of two such solitons is found to be quasi elastic with practically no deformation. The possibility of creating the RDB soliton by phase imprinting is demonstrated. The findings are illustrated using numerical simulation employing realistic interaction parameters in a dipolar $^{164}$Dy BEC.Comment: arXiv admin note: text overlap with arXiv:1409.514

Demixing and symmetry breaking in binary dipolar Bose-Einstein condensate solitons

We demonstrate fully demixed (separated) robust and stable bright binary dipolar Bose-Einstein condensate soliton in a quasi-one-dimensional setting formed due to dipolar interactions for repulsive contact interactions. For large repulsive interspecies contact interaction the first species may spatially separate from the second species thus forming a demixed configuration, which can be spatially-symmetric or symmetry-broken. In the spatially-symmetric case, one of the the species occupies the central region, whereas the other species separates into two equal parts and stay predominantly out of this central region. In the symmetry-broken case, the two species stay side by side. Stability phase diagrams for the binary solitons are obtained. The results are illustrated with realistic values of parameters in the binary 164Dy-168Er and 164Dy-162Dy mixtures. The demixed solitons are really soliton molecules formed of two types of atoms. A proposal for creating dipolar solitons in experiments is also presented

Self trapping of a dipolar Bose-Einstein condensate in a double well

We study the Josephson oscillation and self trapping dynamics of a cigar-shaped dipolar Bose-Einstein condensate of $^{52}$Cr atoms polarized along the symmetry axis of an axially-symmetric double-well potential using the numerical solution of a mean-field model, for dominating repulsive contact interaction (large positive scattering length a) over an anisotropic dipolar interaction. Josephson-type oscillation emerges for small and very large number of atoms, whereas self trapping is noted for an intermediate number of atoms. The dipolar interaction pushes the system away from self trapping towards Josephson oscillation. We consider a simple two-mode description for a qualitative understanding of the dynamics

Stable, mobile, dark-in-bright, dipolar Bose-Einstein condensate soliton

We demonstrate robust, stable, mobile, quasi-one-dimensional, dark-in-bright dipolar Bose-Einstein condensate (BEC) soliton with a notch in the central plane formed due to dipolar interaction for repulsive contact interaction. At medium velocity the head on collision of two such solitons is found to be quasi elastic with practically no deformation. A proposal for creating dipolar dark-in-bright solitons in laboratories by phase imprinting is also discussed. A rich variety of such solitons can be formed in dipolar binary BEC, where one can have a dark-in-bright soliton coupled to a bright soliton or two coupled dark-in-bright solitons. The findings are illustrated using numerical simulation in three spatial dimensions employing realistic interaction parameters for a dipolar 164Dy BEC and a binary 164Dy-162Dy BEC.Comment: arXiv admin note: text overlap with arXiv:1401.318

Dipolar Bose-Einstein condensate in a ring or in a shell

We study properties of a trapped dipolar Bose-Einstein condensate (BEC) in a circular ring or a spherical shell using the mean-field Gross-Pitaevskii equation. In the case of the ring-shaped trap we consider different orientations of the ring with respect to the polarization direction of the dipoles. In the presence of long-range anisotropic dipolar and short-range contact interactions, the anisotropic density distribution of the dipolar BEC in both traps is discussed in detail. The stability condition of the dipolar BEC in both traps is illustrated in phase plot of dipolar and contact interactions. We also study and discuss the properties of a vortex dipolar BEC in these traps

Two-dimensional bright and dark-in-bright dipolar Bose-Einstein condensate solitons on a one-dimensional optical lattice

We study the statics and dynamics of anisotropic, stable, bright and dark-in-bright dipolar quasi-two-dimensional Bose-Einstein condensate (BEC) solitons on a one-dimensional (1D) optical-lattice (OL) potential. These solitons mobile in a plane perpendicular to the 1D OL trap can have both repulsive and attractive contact interactions. The dark-in-bright solitons are the excited states of the bright solitons. The solitons, when subject to a small perturbation, exhibit sustained breathing oscillation. The dark-in-bright solitons can be created by phase imprinting a bright soliton. At medium velocities the collision between two solitons is found to be quasi elastic.The results are demonstrated by a numerical simulation of the three-dimensional mean-field Gross-Pitaevskii equation in three spatial dimensions employing realistic interaction parameters for a dipolar $^{164}$Dy BEC

Vortex lattice in a uniform Bose-Einstein condensate in a box trap

We study numerically the vortex-lattice formation in a rapidly rotating uniform quasi-two-dimensional Bose-Einstein condensate (BEC) in a box trap. We consider two types of boxes: square and circle. In a square-shaped 2D box trap, when the number of generated vortices is the square of an integer, the vortices are found to be arranged in a perfect square lattice, although deviations near the center are found when the number of generated vortices is arbitrary. In case of a circular box trap, the generated vortices in the rapidly rotating BEC lie on concentric closed orbits. Near the center, these orbits have the shape of polygons, whereas near the periphery the orbits are circles. The circular box trap is equivalent to the rotating cylindrical bucket used in early experiment(s) with liquid He II. The number of generated vortices in both cases is in qualitative agreement with Feynman's universal estimate. The numerical simulation for this study is performed by a solution of the underlying mean-field Gross-Pitaevskii (GP) equation in the rotating frame, where the wave function for the generated vortex lattice is a stationary state. Consequently, the imaginary-time propagation method can be used for a solution of the GP equation, known to lead to an accurate numerical solution. We also demonstrated the dynamical stability of the vortex lattices in real-time propagation upon a small change of the angular frequency of rotation, using the converged imaginary-time wave function as the initial state