Matter-Wave Solitons in Two-Component Bose-Einstein Condensates with Tunable Interactions and Time Varying Potential

We present three families of exact matter-wave soliton solutions for an effective one-dimension two-component Bose-Einstein condensates (BECs) with tunable interactions, harmonic potential and gain or loss term.We investigate the dynamics of bright-bright solitons, bright-dark solitons
and dark-dark solitons for the time-dependent expulsive harmonic trap potential,periodically modulated harmonic trap potential, and kinklike modulated harmonic trap potential.Through the Feshbach resonance, these dynamics can be realized in experiments by suitable control of time-dependent trap parameters, atomic interactions, and interaction with thermal cloud.     

Sound Wave of Spin-Orbit Coupled Bose-Einstein Condensates in Optical Lattice

We study the phonon mode excitation of spin-orbit(SO) coupled Bose-Einstein condensates trapped in a one-dimensional optical lattice. The sound speed of the system is obtained analytically. Softening of the phonon mode,i.e., the vanishing of sound speed, in the optical lattice is revealed. When the lattice is absent, the softening of phonon mode occurs only at the phase transition point, which is not influenced by the atomic interaction and Raman coupling when the SO coupling is strong. However, when the lattice is present, the softening of phonon modes can take place in a regime near the phase transition point. Particularly, the regime is widened as lattice strength and SO coupling increase or atomic interaction decreases. The suppression of sound speed by the lattice strongly depends on atomic interaction, Raman coupling, and SO coupling. Furthermore, we find that the sound speed in plane wave phase regime and zero-momentum phase regime behaves with very different characteristics as Raman coupling and SO coupling change. In zero-momentum phase regime, sound speed monotonically increases/decreases with Raman coupling/SO coupling, while in plane wave phase regime, sound speed can either increase or decrease with Raman coupling and SO coupling, which depends on atomic interaction.     

Matter-Wave Solitons in Two-Dimensional Bose-Einstein Condensates with Time-Dependent Scattering Length in a Harmonic Trap

We present three families of one-soliton solutions for (2+1)-dimensional Gross-Pitaevskii equation with both time-dependent scattering length and gain or loss in a harmonic trap. Then we investigate the dynamics of these solitons in Bose-Einstein condensates (BECs) by some selected control functions. Our results show that the intensities of these solitons first increase rapidly to the condensation peak, then decay very slowly to the background; thus the lifetime of a bright soliton, a train of bright solitons and a dark soliton in BECs can be all greatly extended. Our results offer a useful method for observing matter-wave solitons in BECs in future experiments.     

Ground State Phases of Spin-Orbit Coupled Spin-1 Dipolar Bose-Einstein Condensates

International Journal of Theoretical Physics - The ground state phases of spin-1 Bose-Einstein condensates with Rashba spin-orbit coupled (SOC) and dipole-dipole interaction (DDI) are studied....     

Rabi-coupled Binary Bose-Einstein Condensates with Spatially Modulated Nonlinear Spin-Orbit Coupling

International Journal of Theoretical Physics - We study the ground-state phases of Rabi-coupled two-component Bose-Einstein condensates with rotation and spatially modulated nonlinear spin-orbit...     

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.     

Quantum Entanglement in a Spin-Orbit Coupled Bose-Einstein Condensate

We study the spin-field and the spin-spin entanglement in the ground state of a spin-orbit coupled Bose- Einstein condensate. It is found that the spin-field and the spin-spin entanglement can be induced by the spin-orbit coupling. By mapping the system to the Dicke-like model, the system exhibits a quantum phase transition from a normal (spin balanced) phase to superradiant (spin polarized) phase. The Dicke-like phase transition can be captured by the spin-field and the spin-spin entanglement arising from the spin-orbit coupling. The spin-field and the spin-spin entanglement increase as the Raman coupling increases in the superradiant phase, while they decrease with the Raman coupling increasing in the normal phase. We also consider the effect of a finite detuning on these entanglement show that the presence of the detuning suppresses the spin-field and the spin-spin entanglement.     

An Exotic Type of Fulde-Ferrel-Larkin-Ovchinnikov States in Spin-Orbit Coupled Condensates

We find for the first time that a model Hamiltonian or s-wave superconductors in tne presence or spm-orbit interactions and a Zeeman field is exactly solvable. Most intriguingly, based on the exact solutions, a novel type of Fulde Ferrel-Larkin-Ovchinnikov ground state is rigorously revealed, in which the center-of-mass momentum of the fermion pair is proportional to the Zeeman field. We also generalize our exact analysis to the spin-orbit- coupled Bose-Einstein condensate.     

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.     

Interactions between Components of Various Vector Solitons in Bose-Einstein Condensates

We investigate the interactions between components of various vector solitons in Bos-Einstein condensates by means of the least action principle, and derive the effective potentials for different vector solitons, which indicate that the interactions are of short range, and may be repulsive or attractive decided by the different intra- and inter-species interactions in such a system. In the case of attraction, the two solitons will oscillate about and pass through each other around the equilibrium state. The comparison of analytical results with mumertical simulation is presented.     

Dynamics of Analytical Matter-Wave Solutions in Three-Dimensional Bose–Einstein Condensates with Two- and Three-Body Interactions

Using the F-expansion method we present analytical matter-wave solutions to Bose-Einstein condensates with two- and three-body interactions through the generalized three-dimensional Gross-Pitaevskii equation with time- dependent coefficients, for the periodically time-varying interactions and quadratic potential strength. Such solutions exist under certain conditions, and impose constraints on the functions describing potential strength, nonlinearities, and gain （loss）. Various shapes of analytical matter-wave solutions which have important applications of physical interest are s~udied in details.     

异核两组分玻色-爱因斯坦凝聚体中暗孤子的形成及其性质

数值模拟准一维异核两组分玻色-爱因斯坦凝聚体在谐振子势阱中的运动,研究调制不稳定性条件(MI条件)下暗孤子的形成及其性质.在调制不稳定性条件下,凝聚体基态形成后,瞬间使组分间的相互排斥力变为相互吸引力,实时演化可以形成暗孤子.对各组分自身相互作用系数分析发现,它们之间满足一定关系时暗孤子在不同的组分内形成,而且形成的暗孤子在谐振子势阱中呈现周期性的往返对穿运动.讨论了形成暗孤子数目与两种粒子的质量比率和粒子数比率存在的关系.     

Solitons in Bose-Einstein Condensates with Time-Dependent Atomic Scattering Length in a Harmonic Trap

We obtain the integrable relation for the one-dimensional nonlinear Schrodinger equations which describes the dynamics of a Bos-Einstein Condensates with time-dependent scattering length in a harmonic potential. The exact one- and two-soliton solutions are constructed analytically by using the Hirota method. Then we further discuss the dynamics of the one soliton and the interactions between two solitons in currently experimental conditions.     

Solitons in Bose-Einstein Condensates with Time-Dependent Atomic Scattering Length in a Harmonic Trap

We obtain the integrable relation for the one-dimensional nonlinear Schrödinger equations which describes the dynamics of a Bose-Einstein Condensates with time-dependent scattering length in a harmonic potential. The exact one- and two-soliton solutions are constructed analytically by using the Hirota method. Then we further discuss the dynamics of the one soliton and the interactions between two solitons in currently experimental conditions.     

Competition Among Three Coupled Bose-Einstein Condensates due to Potential Deviation

Three coupled Bose-Einstein condensates are investigated by the variational approach in finite potentials with potential deviation, and the effects of the potential deviation on dynamics of the three Bose-Einstein condensates are studied. The potential deviation leads to the shift of the stationary state, resets the stability condition, causes the population imbalance competition, and changes the switching and self-trapping effects on the Bose-Einstein condensates. The effect mechanism is demonstrated by performing a coordinate of classical particles moving in an effective potential field. The critical behaviors are analyzed, and are confirmed by evolution of the atom population imbalance ratio. PACS: 03.75.Fi, 32.80.Pj     

Effect of Time-Dependent Atomic Scattering Length on Solitons in Bose-Einstein Condensates with a Complex Potential

We consider the one-dimensional nonlinear Schrǒdinger equations that describe the dynamics of a Bose-Einstein Condensates with time-dependent scattering length in a complex potential. Our results show that as long as the integrable relation is satisfied, exact solutions of the one-dimensional nonlinear Schrǒdinger equation can be found in a general closed form, and interactions between two solitons are modulated in a complex potential We find that the changes of the scattering length and trapping potential can be effectively used to control the interaction between two bright soliton.     

Stability and Chaos of Two Coupled Bose-Einstein Condensates with Three-Body Interaction

We study the dynamics of two Bose-Einstein condensates （BECs） tunnel-coupled by a double-well potential. A real three-body interaction term is considered and a two-mode approximation is used to derive two coupled equations, which describe the relative population and relative phase. By solving the equations and analyzing the stability of the system, we find the stable stationary solutions for a constant atomic scattering length. When a periodically time- varying scattering length is applied, Melnikov analysis and numerical calculation demonstrate the existence of chaotic behavior and the dependence of chaos on the three-body interaction parameters.