Dynamics of gap solitons in a dipolar Bose-Einstein condensate on a three-dimensional optical lattice

We suggest and study the stable disk- and cigar-shaped gap solitons of a dipolar Bose-Einstein condensate of $^{52}$Cr atoms localized in the lowest band gap by three optical-lattice (OL) potentials along orthogonal directions. The one-dimensional version of these solitons of experimental interest confined by an OL along the dipole moment direction and harmonic traps in transverse directions is also considered. Important dynamics of (i) breathing oscillation of a gap soliton upon perturbation and (ii) dragging of a gap soliton by a moving lattice along axial $z$ direction demonstrates the stability of gap solitons. A movie clip of dragging of three-dimensional gap soliton is included.Comment: To see the dragging movie clip please download sourc

Dissipation-managed soliton in a quasi-one-dimensional Bose-Einstein condensate

We use the time-dependent mean-field Gross-Pitaevskii equation to study the formation of a dynamically-stabilized dissipation-managed bright soliton in a quasi-one-dimensional Bose-Einstein condensate (BEC). Because of three-body recombination of bosonic atoms to molecules, atoms are lost (dissipated) from a BEC. Such dissipation leads to the decay of a BEC soliton. We demonstrate by a perturbation procedure that an alimentation of atoms from an external source to the BEC may compensate for the dissipation loss and lead to a dynamically-stabilized soliton. The result of the analytical perturbation method is in excellent agreement with mean-field numerics. It seems possible to obtain such a dynamically-stabilized BEC soliton without dissipation in laboratory.Comment: 5 pages, 3 figure

Dynamics of quasi-one-dimensional bright and vortex solitons of a dipolar Bose-Einstein condensate with repulsive atomic interaction

By numerical and variational analysis of the three-dimensional Gross-Pitaevskii equation we study the formation and dynamics of bright and vortex-bright solitons in a cigar-shaped dipolar Bose-Einstein condensate for large repulsive atomic interactions. Phase diagram showing the region of stability of the solitons is obtained. We also study the dynamics of breathing oscillation of the solitons as well as the collision dynamics of two solitons at large velocities. Two solitons placed side-by-side at rest coalesce to form a stable bound soliton molecule due to dipolar attraction.Comment: To obtain the included video clips S1, S2, S3 and S4, please download sourc

Stabilization of bright solitons and vortex solitons in a trapless three-dimensional Bose-Einstein condensate by temporal modulation of the scattering length

Using variational and numerical solutions of the mean-field Gross-Pitaevskii equation we show that a bright soliton can be stabilized in a trapless three-dimensional attractive Bose-Einstein condensate (BEC) by a rapid periodic temporal modulation of scattering length alone by using a Feshbach resonance. This scheme also stabilizes a rotating vortex soliton in two dimensions. Apart from possible experimental application in BEC, the present study suggests that the spatiotemporal solitons of nonlinear optics in three dimensions can also be stabilized in a layered Kerr medium with sign-changing nonlinearity along the propagation direction.Comment: 6 pages, 7 PS figure

Free expansion of fermionic dark solitons in a boson-fermion mixture

We use a time-dependent dynamical mean-field-hydrodynamic model to study the formation of fermionic dark solitons in a trapped degenerate fermi gas mixed with a Bose-Einstein condensate in a harmonic as well as a periodic optical-lattice potential. The dark soliton with a "notch" in the probability density with a zero at the minimum is simulated numerically as a nonlinear continuation of the first vibrational excitation of the linear mean-field-hydrodynamic equations, as suggested recently for pure bosons. We study the free expansion of these dark solitons as well as the consequent increase in the size of their central notch and discuss the possibility of experimental observation of the notch after free expansion.Comment: 14 pages, 6 figure

Quantum scattering in one dimension

A self-contained discussion of nonrelativistic quantum scattering is presented in the case of central potentials in one space dimension, which will facilitate the understanding of the more complex scattering theory in two and three dimensions. The present discussion illustrates in a simple way the concept of partial-wave decomposition, phase shift, optical theorem and effective-range expansion.Comment: 8 page

Convergent variational calculation of positronium-hydrogen-atom scattering lengths

We present a convergent variational basis-set calculational scheme for elastic scattering of positronium atom by hydrogen atom in S wave. Highly correlated trial functions with appropriate symmetry are needed for achieving convergence. We report convergent results for scattering lengths in atomic units for both singlet ($=3.49\pm 0.20$) and triplet ($=2.46\pm 0.10$) states.Comment: 11 pages, 1 postscript figure, Accepted in J. Phys. B (Letter

Self-trapping of a binary Bose-Einstein condensate induced by interspecies interaction

The problem of self-trapping of a Bose-Einstein condensate (BEC) and a binary BEC in an optical lattice (OL) and double well (DW) is studied using the mean-field Gross-Pitaevskii equation. For both DW and OL, permanent self-trapping occurs in a window of the repulsive nonlinearity $g$ of the GP equation: $g_{c1}<g<g_{c2}$. In case of OL, the critical nonlinearities $g_{c1}$ and $g_{c2}$ correspond to a window of chemical potentials $\mu_{c1}<\mu<\mu_{c2}$ defining the band gap(s) of the periodic OL. The permanent self-trapped BEC in an OL usually represents a breathing oscillation of a stable stationary gap soliton. The permanent self-trapped BEC in a DW, on the other hand, is a dynamically stabilized state without any stationary counterpart. For a binary BEC with intraspecies nonlinearities outside this window of nonlinearity, a permanent self trapping can be induced by tuning the interspecies interaction such that the effective nonlinearities of the components fall in the above window

Localization of a dipolar Bose-Einstein condensate in a bichromatic optical lattice

By numerical simulation and variational analysis of the Gross-Pitaevskii equation we study the localization, with an exponential tail, of a dipolar Bose-Einstein condensate (DBEC) of $^{52}$Cr atoms in a three-dimensional bichromatic optical-lattice (OL) generated by two monochromatic OL of incommensurate wavelengths along three orthogonal directions. For a fixed dipole-dipole interaction, a localized state of a small number of atoms ($\sim 1000$) could be obtained when the short-range interaction is not too attractive or not too repulsive. A phase diagram showing the region of stability of a DBEC with short-range interaction and dipole-dipole interaction is given