Deviation from one-dimensionality in stationary properties and collisional dynamics of matter-wave solitons

By means of analytical and numerical methods, we study how the residual three-dimensionality affects dynamics of solitons in an attractive Bose-Einstein condensate loaded into a cigar-shaped trap. Based on an effective 1D Gross-Pitaevskii equation that includes an additional quintic self-focusing term, generated by the tight transverse confinement, we find a family of exact one-soliton solutions and demonstrate stability of the entire family, despite the possibility of collapse in the 1D equation with the quintic self-focusing nonlinearity. Simulating collisions between two solitons in the same setting, we find a critical velocity, $V_{c}$, below which merger of identical in-phase solitons is observed. Dependence of $V_{c}$ on the strength of the transverse confinement and number of atoms in the solitons is predicted by means of the perturbation theory and investigated in direct simulations. Symmetry breaking in collisions of identical solitons with a nonzero phase difference is also shown in simulations and qualitatively explained by means of an analytical approximation.Comment: 10 pages, 7 figure

Non-adiabatic molecular association in thermal gases driven by radio-frequency pulses

The molecular association process in a thermal gas of $^{85}$Rb is investigated where the effects of the envelope of the radio-frequency field are taken into account. For experimentally relevant parameters our analysis shows that with increasing pulse length the corresponding molecular conversion efficiency exhibits low-frequency interference fringes which are robust under thermal averaging over a wide range of temperatures. This dynamical interference phenomenon is attributed to St\"uckelberg phase accumulation between the low-energy continuum states and the dressed molecular state which exhibits a shift proportional to the envelope of the radio-frequency pulse intensity.Comment: 5 pages, 3 figure

Two-dimensional discrete solitons in rotating lattices

We introduce a two-dimensional (2D) discrete nonlinear Schr\"{o}dinger (DNLS) equation with self-attractive cubic nonlinearity in a rotating reference frame. The model applies to a Bose-Einstein condensate stirred by a rotating strong optical lattice, or light propagation in a twisted bundle of nonlinear fibers. Two species of localized states are constructed: off-axis fundamental solitons (FSs), placed at distance $R$ from the rotation pivot, and on-axis (R=0) vortex solitons (VSs), with vorticities $$ and 2. At a fixed value of rotation frequency $\Omega$, a stability interval for the FSs is found in terms of the lattice coupling constant $C$, , with monotonically decreasing $C_{\mathrm{cr}}(R)$. VSs with S=1 have a stability interval, \tilde{C}_{\mathrm{cr}%}^{(S=1)}(\Omega), which exists for $$ below a certain critical value, $\Omega_{\mathrm{cr}}^{(S=1)}$. This implies that the VSs with S=1 are \emph{destabilized} in the weak-coupling limit by the rotation. On the contrary, VSs with S=2, that are known to be unstable in the standard DNLS equation, with $\Omega =0$, are \emph{stabilized} by the rotation in region $0<C<C_{\mathrm{cr}}^{(S=2)}$%, with $C_{\mathrm{cr}}^{(S=2)}$ growing as a function of $\Omega$. Quadrupole and octupole on-axis solitons are considered too, their stability regions being weakly affected by $\Omega \neq 0$.Comment: To be published in Physical Review

A quasi-pure Bose-Einstein condensate immersed in a Fermi sea

We report the observation of co-existing Bose-Einstein condensate and Fermi gas in a magnetic trap. With a very small fraction of thermal atoms, the 7Li condensate is quasi-pure and in thermal contact with a 6Li Fermi gas. The lowest common temperature is 0.28 muK = 0.2(1) T_C = 0.2(1) T_F where T_C is the BEC critical temperature and T_F the Fermi temperature. Behaving as an ideal gas in the radial trap dimension, the condensate is one-dimensional.Comment: 4 pages, 5 figure

Matter-wave vortices in cigar-shaped and toroidal waveguides

We study vortical states in a Bose-Einstein condensate (BEC) filling a cigar-shaped trap. An effective one-dimensional (1D) nonpolynomial Schroedinger equation (NPSE) is derived in this setting, for the models with both repulsive and attractive inter-atomic interactions. Analytical formulas for the density profiles are obtained from the NPSE in the case of self-repulsion within the Thomas-Fermi approximation, and in the case of the self-attraction as exact solutions (bright solitons). A crucially important ingredient of the analysis is the comparison of these predictions with direct numerical solutions for the vortex states in the underlying 3D Gross-Pitaevskii equation (GPE). The comparison demonstrates that the NPSE provides for a very accurate approximation, in all the cases, including the prediction of the stability of the bright solitons and collapse threshold for them. In addition to the straight cigar-shaped trap, we also consider a torus-shaped configuration. In that case, we find a threshold for the transition from the axially uniform state, with the transverse intrinsic vorticity, to a symmetry-breaking pattern, due to the instability in the self-attractive BEC filling the circular trap.Comment: 6 pages, Physical Review A, in pres

Symbiotic gap and semi-gap solitons in Bose-Einstein condensates

Using the variational approximation and numerical simulations, we study one-dimensional gap solitons in a binary Bose-Einstein condensate trapped in an optical-lattice potential. We consider the case of inter-species repulsion, while the intra-species interaction may be either repulsive or attractive. Several types of gap solitons are found: symmetric or asymmetric; unsplit or split, if centers of the components coincide or separate; intra-gap (with both chemical potentials falling into a single bandgap) or inter-gap, otherwise. In the case of the intra-species attraction, a smooth transition takes place between solitons in the semi-infinite gap, the ones in the first finite bandgap, and semi-gap solitons (with one component in a bandgap and the other in the semi-infinite gap).Comment: 5 pages, 9 figure

Formation of a Matter-Wave Bright Soliton

We report the production of matter-wave solitons in an ultracold lithium 7 gas. The effective interaction between atoms in a Bose-Einstein condensate is tuned with a Feshbach resonance from repulsive to attractive before release in a one-dimensional optical waveguide. Propagation of the soliton without dispersion over a macroscopic distance of 1.1 mm is observed. A simple theoretical model explains the stability region of the soliton. These matter-wave solitons open fascinating possibilities for future applications in coherent atom optics, atom interferometry and atom transport.Comment: 11 pages, 5 figure

Scattering and Trapping of Nonlinear Schroedinger Solitons in External Potentials

Soliton motion in some external potentials is studied using the nonlinear Schr\"odinger equation. Solitons are scattered by a potential wall. Solitons propagate almost freely or are trapped in a periodic potential. The critical kinetic energy for reflection and trapping is evaluated approximately with a variational method.Comment: 9 pages, 7 figure