Vector Solitons and Soliton Collisions in Two-Component Bose-Einstein Condensates

With realistic parameters, both analytical and computational studies demonstrate the feasibility of forming bright-bright vector solitons in a self-repulsive two-component Bose-Einstein condensate with attractive intercomponent interaction. Moreover, the stability of such solitons is confirmed by direct numerical simulations, by a Bogoliubov spectrum analysis, and by examining the collisions between two vector solitons. Our results are of considerable experimental interest.     

Dynamics of Bright Solitons in Bose-Einstein Condensates with Complicated Potential

We present analytical solutions of the one-dimensional nonlinear Schrodinger equations of Bose-Einstein condensates in an expulsive parabolic background with a complex potential and gravitational field, by performing the Darboux transformation from a trivial seed solution. It is shown that under a safe range of parameter, the shape of bright soliton can be controlled well by adjusting the experimental parameter of the ratio of axial oscillation to radial oscillation and feeding condensates from a thermal cloud. The gravitational field can change the contrail of the bright soliton trains without changing their peak and width.     

Quantum Effects of Many Atoms in Spinor Bose-Einstein Condensates

We have studied the evolutions of the population transfer, tunnelling current and antibunching effects between spin-（＋1） and spin-（-1） in the case of the strong laser pulses. It is found that the population transfer and tunnelling current exhibit periodical oscillation. For the same Rabi frequency, the larger the atom number, the longer the oscillation period is. For the spin-（-1） component, when the atomic numbers are N=4 and 10, the antibunching effect can appear. For different atomic numbers, the appearing regions are very different. For spin component ＋1, the antibunching effect can always appear for different atomic numbers.     

Small Amplitude Solitons in Bose--Einstein Condensates with External Perturbation

By developing a small amplitude soliton approximation method, we study analytically weak nonlinear excitations in cigar-shaped condensates with repulsive interatomic interaction under consideration of external perturbation potential. It is shown that matter wave solitons may exist and travel over a long distance without attenuation and change in shape by properly adjusting the strength of interatomic interaction to compensate for the effect of external perturbation potential.     

Collapse of triaxial bright solitons in atomic Bose-Einstein condensates

We study triaxial bright solitons made of attractive Bose-condensed atoms characterized by the absence of confinement in the longitudinal axial direction but trapped by an anisotropic harmonic potential in the transverse plane. By numerically solving the three-dimensional Gross-Pitaevskii equation we investigate the effect of the transverse trap anisotropy on the critical interaction strength above which there is the collapse of the condensate. The comparison with previous predictions [A. Gammal, L. Tomio, T. Frederico, Phys. Rev. A 66 (2002) 043619] shows significant differences for large anisotropies.     

Bright solitary waves of trapped atomic Bose-Einstein condensates

Motivated by recent experimental observations, we study theoretically multiple bright solitary waves of trapped Bose-Einstein condensates. Through variational and numerical analyses, we determine the threshold for collapse of these states. Under π-phase differences between adjacent waves, we show that the experimental states lie consistently at the threshold for collapse, where the corresponding in-phase states are highly unstable. Following the observation of two long-lived solitary waves in a trap, we perform detailed three-dimensional simulations which confirm that in-phase waves undergo collapse while a π-phase difference preserves the long-lived dynamics and gives excellent quantitative agreement with experiment. Furthermore, intermediate phase differences lead to the growth of population asymmetries between the waves, which ultimately triggers collapse.     

Generation of generalized coherent states with two coupled Bose-Einstein condensates

We present a scheme to prepare generalized coherent states in a system with two species of Bose-Einstein condensates. First, within the two-mode approximation, we demonstrate that a Schrödinger cat-like state can be dynamically generated and, by controlling the Josephson-like coupling strength, the number of coherent states in the superposition can be varied. Later, we analyze numerically the dynamics of the whole system when interspecies collisions are inhibited. Variables such as fractional population, Mandel parameter and variances of annihilation and number operators are used to show that the evolved state is entangled and exhibits sub-Poisson statistics.     

Photo-induced dynamics of Bose-Einstein condensates in optical superlattice

The photo-induced dynamics of cold atoms in a one-dimensional optical superlattice is observed. Steady state distribution of the probability amplitudes and the site population in a one-dimensional optical superlattice is found. It is shown that this solution of the equations, which describes the temporal behavior of a Bose-Einstein condensate in a superlattice, is unstable at the sufficiently high level of boson density. The expression for the increment of modulational instability is obtained on the basis of the linear stability analysis. The numerical examples of non-stationary solutions for boson density in a superlattice for the general model are discussed as applied to both the attraction and repulsion potentials of boson interaction.     

Ratchet-induced matter-wave transport and soliton collisions in Bose-Einstein condensates

We study the dynamics of bright matter-wave solitons in a Bose-Einstein condensate with negative scattering length under the influence of a time-periodic ratchet potential. The potential is formed by a one-dimensional bichromatic optical lattice which flashes on and off so that the time average of its amplitude vanishes. Due to the broken space and time-reversal symmetries of the potential, the soliton is transported with a nonzero average velocity. By employing the non-dissipative mean-field model for the matter waves, we study the dependence of the transport velocity on the initial state of the soliton and show how the properties of the individual localized states affect the outcome of their collisions. A useful insight into the transport properties is provided by Hamiltonian theory for the mean field, which treats the extended matter-wave excitation as an effective classical particle.     

Analytical studies of two-component Bose-Einstein condensates in two-dimensional optical lattices

The two-component Bose-Einstein condensates (BECs) trapped in 2D optical lattice potential is studied analytically. A new family of stationary exact solutions of the coupled Gross-Pitaevskii (GP) equations with 2D periodic potential are obtained. In particular, the phase diagram of the system in the trigonometric limit is determined analytically according to the nontrivial phase macroscopic wave functions of the condensates.     

Dynamical stabilization of self-trapping of two weakly coupled Bose-Einstein condensates

We investigate the effect of an external periodic driving field on the self-trapping of two weakly coupled Bose-Einstein condensates with dissipation. It is shown that the macroscopic self-trapping can be stabilized against dissipation by a high frequency periodic driving field. The parameter ranges for stabilizing self-trapping are found analytically and confirmed numerically.     

Stability Diagrams of a Bose-Einstein Condensate in a Periodic Array of Quantum Wells

With the help of a set of exact closed-form solutions to the stationary Gross Pitaevskii equation, we compre-hensively investigate Landau and dynamical instabilities of a Bose-Einstein condensate in a periodic array of quantum wells. In the tight-binding limit, the anaiyticai expressions for both Landau and dynamical instabilities are obtained in terms of the compressibility and effective mass of the BEC system. Then the stability phase diagrams are shown to be similar to the one in the case of the sinusoidal optical lattice.     

Modulating the amplitude of dark soliton by scattering-length management in Bose-Einstein condensates

We present a family of soliton solutions of the quasi-one-dimensional Bose-Einstein condensates with time-dependent scattering length, by developing multiple-scale method combined with truncated Painlevé expansion. Then, by numerical calculating the solutions, it is shown that there exhibit two types of dark solitons—black soliton (the zero minimum amplitude at its center) and gray soliton (the minimum density does not drop to zero) in a repulsive condensate. Furthermore, we propose experimental protocols to realize the exchange between black and gray solitons by varying the scattering length via the Feshbach resonance in currently experimental conditions.     

Switching and Self-trapping Dynamics of Dark Solitons in a Two-Component Bose-Einstein Condensate

Two coupled dark solitons are considered in a two-component Bose-Einstein condensate, and their dynamics are investigated by the variational approach based the renormalized integrals of motion. The stationary states as physical solutions to the describing equations are obtained, and the dynamic mechanism is demonstrated by performing a coordinate of a classical particle moving in an effective potential field. The switching and selftrapping dynamics of the coupled dark vector solitons are discussed by the evolution of the atom population transferring ratio.     

Hyperbolic Bending of Vortex Lines with Finite Number and Length in Rotating Trapped Bose-Einstein Condensates

The minimal energy configurations of hyperbolic bending vortex lines in the rotating trapped Bose-Einstein condensates are investigated by using a variational ansatz and numerical simulation. The theoretical calculation of the energy of the vortex lines as a function of the rotation frequency gives self-consistently vortex number, curvature and configuration. The numerical results show that bending is more stable than straight vortex line along the z-axis, and the vortex configuration in the xy-plane has a little expansion by increasing z.     

Periodic spin domains of spinor Bose-Einstein condensates in an optical lattice

The periodic spin domains of spinor Bose-Einstein condensates confined in a one-dimensional optical lattice are studied in terms of the equation of motion of the spinor which is reduced to the nonlinear Schrödinger equation with the help of Holstein-Primakoff transformation. It is shown that the spin domains obtained analytically can be easily controlled by adjusting the light-induced dipole-dipole interaction, which is realizable in optical lattice created by red-detuned laser beams with modulating intensity. The dynamical stability of the spin domains is also demonstrated.     

Controlled Manipulation with a Bose--Einstein Condensates N-Soliton Train under the Influence of Harmonic and Tilted Periodic Potentials

A model of the perturbed complex Toda chain （PCTC） to describe the dynamics of a Bose-Einstein condensate （BEC） N-soliton train trapped in an applied combined external potential consisting of both a weak harmonic and tilted periodic component is first developed. Using the developed theory, the BEC N-soliton train dynamics is shown to be well approximated by 4N coupled nonlinear differential equations, which describe the fundamental interactions in the system arising from the interplay of amplitude, velocity, centre-of-mass position, and phase. The simplified analytic theory allows for an efficient and convenient method for characterizing the BEC N-soliton train behaviour. It further gives the critical values of the strength of the potential for which one or more localized states can be extracted from a soliton train and demonstrates that the BEC N-soliton train can move selectively from one lattice site to another by simply manipulating the strength of the potential.     

Matter-wave interference in Bose-Einstein condensates: A dispersive hydrodynamic perspective

The interference pattern generated by the merging interaction of two Bose-Einstein condensates reveals the coherent, quantum wave nature of matter. An asymptotic analysis of the nonlinear Schrödinger equation in the small dispersion (semiclassical) limit, experimental results, and three-dimensional numerical simulations show that this interference pattern can be interpreted as a modulated soliton train generated by the interaction of two rarefaction waves propagating through the vacuum. The soliton train is shown to emerge from a linear, trigonometric interference pattern and is found by use of the Whitham modulation theory for nonlinear waves. This dispersive hydrodynamic perspective offers a new viewpoint on the mechanism driving matter-wave interference.     

Bose-Einstein Condensates in a One-Dimensional Optical Lattice: from Superfluidity to Number-Squeezed States

We study the phase coherence property of Bose-Einstein condensates confined in a one-dimensional optical lattice formed by a standing-wave laser field. The lattice depth is determined using a method of Kapitza-Dirac scattering between a condensate and a short pulse lattice potential. Condensates are then adiabatically loaded into the optical lattice. The phase coherence property of the confined condensates is reflected by the interference patterns of the expanded atomic cloud released from the optical lattice. For weak lattice, nearly all of the atoms stay in a superfluid state. However, as the lattice depth is increased, the phase coherence of the whole condensate sample is gradually lost, which confirms that the sub-condensates in each lattice well have evolved into number-squeezed states.     

Exact transmission state of a Bose-Einstein condensate in a near-harmonic trap

We introduce a new confining potential which simulates preferably the realistic near-harmonic trap for a quasi-one-dimensional (1D) Bose-Einstein condensate (BEC). An exact transmission state of the BEC system is found and the corresponding spatial configurations, metastability, superfluidity and the transport properties are analyzed. Resonant transmission through the potential is predicted from the exact solution.