Effects of three-body interaction on collective excitation and stability of Bose--Einstein condensate

This paper investigates the collective excitation and stability of low-dimensional Bose--Einstein condensates with two- and three-body interactions by the variational analysis of the time-dependent Gross--Pitaevskii--Ginzburg equation. The spectrum of the low-energy excitation and the effective potential for the width of the condensate are obtained. The results show that: (i) the repulsive two-body interaction among atoms makes the frequency red-shifted for the internal excitation and the repulsive or attractive three-body interaction always makes it blue-shifted; (ii) the region for the existence of the stable bound states is obtained by identifying the critical value of the two- and three-body interactions.     

Feshbach resonance management of vector solitons in two-component Bose—Einstein condensates

We consider two coupled Gross-Pitaevskii equations describing a two-component Bose-Einstein condensate with time-dependent atomic interactions loaded in an external harmonic potential,and investigate the dynamics of vector solitons.By using a direct method,we construct a novel family of vector soliton solutions,which are the linear combination between dark and bright solitons in each component.Our results show that due to the superposition between dark and bright solitons,such vector solitons possess many novel and interesting properties.The dynamics of vector solitons can be controlled by the Feshbach resonance technique,and the vector solitons can keep the dynamic stability against the variation of the scattering length.     

Moving bright solitons in a pseudo-spin polarization Bose-Einstein condensate

We study the moving bright solitons in the weak attractive Bose–Einstein condensate with a spin–orbit interaction. By solving the coupled nonlinear Schr ?dinger equation with the variational method and the imaginary time evolution method,two kinds of solitons(plane wave soliton and stripe solitons) are found in different parameter regions. It is shown that the soliton speed dominates its structure. The detuning between the Raman beam and energy states of the atoms decides the spin polarization strength of the system. The soliton dynamics is also studied for various moving speed and we find that the shape of individual components can be kept when the speed of soliton is low.     

Dynamics of vector solitons in two-component Bose--Einstein condensates with time-dependent interactions and harmonic potential

We present two kinds of exact vector-soliton solutions for coupled nonlinear Schr?dinger equations with time-varying interactions and time-varying harmonic potential. Using the variational approach, we investigate the dynamics of the vector solitons. It is found that the two bright solitons oscillate about slightly and pass through each other around the equilibration state which means that they are stable under our model. At the same time, we obtain the opposite situation for dark--dark solitons.     

Solitonic Diffusion of Wavepackets in One-Dimensional Bose–Einstein Condensates

Solitonic characteristics are revealed in the diffusion process of a hump or a notch wave packet in a one-dimensional Bose–Einstein condensate. By numerically solving the time-dependent Gross–Pitaevskii equation, we find completely different spreading behavior for attractive or repulsive condensates. For the attractive condensate, a series of bright solitons are continuously generated one after another at the wave front and they nearly stay at the positions where they are generated in the whole diffusion process. In contrast, for the repulsive condensate,the initial wave packet splits at the beginning into a series of grey solitons that travel at different velocities. The moving velocity of the grey soliton depends on nonlinear interaction strength, as well as the shape of a particular grey soliton.     

Quantum Squeezing of Matter-Wave Solitons in Bose–Einstein Condensates

We investigate the quantum squeezing of matter-wave solitons in atomic Bose–Einstein condensates. By calculating quantum fluctuations of the solitons via solving the Bogoliubov–de Gennes equations, we show that significant quantum squeezing can be realized for both bright and dark solitons. We also show that the squeezing efficiency of the solitons can be enhanced and manipulated by atom–atom interaction and soliton blackness. The results reported here are beneficial not only for understanding q...     

Fission and Fusion of Two Bright Solitons in a Growing Bose--Einstein Condensate

We analytically study the interaction characteristics of two bright solitons in a one-dimensional growing Bose- Einstein condensate with time-dependent periodic atomic scattering length. It is shown that the interaction between two bright solitons can generate fission and fusion in the presence of both time-dependent periodic atomic scattering length and the growing case. Furthermore, we propose experimental protocols to realize these interaction phenomena by varying the scattering length via the Feshbach resonance in the future experiment.     

Dynamical stability of dipolar condensate in a parametrically modulated one-dimensional optical lattice

We study the stabilization properties of dipolar Bose–Einstein condensate in a deep one-dimensional optical lattice with an additional external parametrically modulated harmonic trap potential. Through both analytical and numerical methods, we solve a dimensionless nonlocal nonlinear discrete Gross–Pitaevskii equation with both the short-range contact interaction and the long-range dipole–dipole interaction. It is shown that, the stability of dipolar condensate in modulated deep optical lattice can be controled by coupled effects of the contact interaction, the dipolar interaction and the external modulation. The system can be stabilized when the dipolar interaction, the contact interaction, the average strength of potential and the ratio of amplitude to frequency of the modulation satisfy a critical condition. In addition, the breather state, the diffused state and the attractive-interaction-induced-trapped state are predicted. The dipolar interaction and the external modulation of the lattice play important roles in stabilizing the condensate.     

Stability of Bright Solitons in Bose-Einstein Condensates

We investigate the stability of bright solitons in Bose-Einstein condensates by including a feeding term and a loss one in the Oross-Pitaevskii equation. Based on the direct approach of perturbation theory for the nonlinear Schroedinger equation, we give the explicit dependence of the height and other related quantities of bright solitons on the feeding and loss term. It is found that the three-body recombination loss plays a crucial role in stabilizing bright solitons.     

Effects of parameters on the stationary state and self-trapping of three coupled Bose-Einstein condensate solitons

The stability of three coupled Bose-Einstein condensate (BEC) solitons is investigated by the variational approach in two conventional time-independent trapping potentials. The effects of parameters of the potentials and the initial conditions of the BEC soliton system on the stationary state and self-trapping are discussed. It is found that the trapping potentials play an important role in the stability of the system and change the characteristics of the system, and there are different critical potential amplitude values corresponding to different trapping potentials and initial conditions of the BEC soliton system.     

Quench Dynamics of Bose–Einstein Condensates in Boxlike Traps

By quenching the interatomic interactions, we investigate the nonequilibrium dynamics of two-dimensional Bose–Einstein condensates in boxlike traps with power-law potential boundaries. We show that ring dark solitons can be excited during the quench dynamics for both concave and convex potentials. The quench’s modulation strength and the steepness of the boundary are two major factors influencing the system’s evolution. In terms of the number of ring dark solitons excited in the condensate, five...     

Critical rotation of an anharmonically trapped Bose--Einstein condensate

We consider rotational motion of an interacting atomic Bose-Einstein condensate (BEC) with both two- and three-body interactions in a quadratic-plus-quartic and harmonic-plus-Gaussian trap. By using the variational method, the influence of the three-body interaction and the anharmonicity of the trap on the lowest energy surface mode excitation and the spontaneous shape deformation (responsible for the vortex formation) in a rotating BEC is discussed in detail. It is found that the repulsive three-body interaction helps the formation of the vortex and reduces the lowest energy surface mode frequency and the critical rotational frequency of the system. Moreover, the critical rotational frequency for the vortex formation in the harmonic-plus-Gaussian potential is lower than that in the quadratic-plus-quartic potential.     

Soliton and rogue wave solutions of two-component nonlinear Schr?dinger equation coupled to the Boussinesq equation

The nonlinear Schr?dinger(NLS) equation and Boussinesq equation are two very important integrable equations.They have widely physical applications. In this paper, we investigate a nonlinear system, which is the two-component NLS equation coupled to the Boussinesq equation. We obtain the bright–bright, bright–dark, and dark–dark soliton solutions to the nonlinear system. We discuss the collision between two solitons. We observe that the collision of bright–bright soliton is inelastic and two solitons oscillating periodically can happen in the two parallel-traveling bright–bright or bright–dark soliton solution. The general breather and rogue wave solutions are also given. Our results show again that there are more abundant dynamical properties for multi-component nonlinear systems.     

Solitons in nonlinear systems and eigen-states in quantum wells

We study the relations between solitons of nonlinear Schro¨dinger equation and eigen-states of linear Schro¨dinger equation with some quantum wells. Many different non-degenerated solitons are re-derived from the eigen-states in the quantum wells. We show that the vector solitons for the coupled system with attractive interactions correspond to the identical eigen-states with the ones of the coupled systems with repulsive interactions. Although their energy eigenvalues seem to be different, they can be reduced to identical ones in the same quantum wells. The non-degenerated solitons for multi-component systems can be used to construct much abundant degenerated solitons in more components coupled cases.Meanwhile, we demonstrate that soliton solutions in nonlinear systems can also be used to solve the eigen-problems of quantum wells. As an example, we present the eigenvalue and eigen-state in a complicated quantum well for which the Hamiltonian belongs to the non-Hermitian Hamiltonian having parity–time symmetry. We further present the ground state and the first exited state in an asymmetric quantum double-well from asymmetric solitons. Based on these results, we expect that many nonlinear physical systems can be used to observe the quantum states evolution of quantum wells, such as a water wave tank, nonlinear fiber, Bose–Einstein condensate, and even plasma, although some of them are classical physical systems. These relations provide another way to understand the stability of solitons in nonlinear Schro¨dinger equation described systems, in contrast to the balance between dispersion and nonlinearity.     

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.     

Interactions between bright solitons in different species of Bose—Einstein condensates

The dynamics of a bright-bright vector soliton in a cigar-shaped Bose-Einstein condensate trapping in a harmonic potential is studied.The interaction between bright solitons in different species with small separation is derived.Unlike the interaction between solitons of the same species,it is independent of the phase difference between solitons.It may be of attraction or repulsion.In the former case,each soliton will oscillate about and pass through each other around the mass-center of the system,which will also oscillate harmonically due to the harmonic trapping potential.     

Three-dimensional Bose–Einstein condensate vortex soliton sunder optical lattice and harmonic confinements

We predict three-dimensional vortex solitons in a Bose-Einstein condensate under a complex potential which is the combination of a two-dimensional parabolic trap along the transverse radial direction and a one-dimensional optical-lattice potential along the z axis direction. The vortex solitons are built in the form of layer-chain structure made up of several fundamental vortices along the optical-lattice direction, which were not reported before in the three-dimensional Bose-Einstein condensate. By using the combination of the energy density functional method with the direct numerical simulation, we find three-dimensional vortex solitons with topological charge χ=1, χ=2, and χ=3. Moreover, the macroscopic quantum tunneling and the chirp phenomena of the vortex solitons are shown in the evolution. Thereinto, the occurrence of the macroscopic quantum tunneling provides a possibility for the realization of the quantum tunneling in experiment. Specifically, we manipulate the vortex solitons along the optical lattice direction successfully. The stability limits for dragging the vortex solitons from an initial fixed position to a prescribed location are further pursued.     

Nonautonomous bright solitons and soliton collisions in a nonlinear medium with an external potential

We present exact bright multi-soliton solutions of a generalized nonautonomous nonlinear Schrdinger equation with time-and space-dependent distributed coefficients and an external potential which describes a pulse propagating in nonlinear media when its transverse and longitudinal directions are nonuniformly distributed.Such solutions exist in certain constraint conditions on the coefficients depicting dispersion,nonlinearity,and gain(loss).Various shapes of bright solitons and interesting interactions between two solitons are observed.Physical applications of interest to the field and stability of the solitons are discussed.     

Collision induced splitting of bright soliton in Bose--Einstein condensate

This paper studies the collision dynamics of bright soliton in Bose--Einstein condensate with trapezoid potential. It is found that besides the total reflection and total transmission, one bright soliton can be divided into two bright solitons with different amplitudes in a controllable manner.     

Nonlinear Wave in a Disc-Shaped Bose-Einstein Condensate

We discuss the possible nonlinear waves of atomic matter wave in a Bose-Einstein condensate. One and two of two-dimensional （2D） dark solitons in the Bose-Einstein condensed system are investigated. A rich dynamics is studied for the interactions between two solitons. The interaction profiles of two solitons are greatly different if the angle between them are different. If the angle is small enough, the maximum amplitude during the interaction between two solitons is even less than that of a single soliton. However, if the angle is large enough, the maximum amplitude of two solitons can gradually attend to the sum of two soliton amplitudes.