Stationary Classical Chaos of Trapped Two-Component Bose-Einstein Condensates in 1-D Optical Lattice Potentials

We study the nonlinear dynamics of two-component Bose-Einstein condensates in one-dimensional pe-riodic optical lattice potentials.The stationary state perturbation solutions of the coupled two-component nonlinearSchr?dinger/Gross-Pitaevskii equations are constructed by using the direct perturbation method.Theoretical analysisrevels that the perturbation solution is the chaotic one,which indicates the existence of chaos and chaotic region inparameter space.The corresponding numerical calculation results agree well with the analytical results.By applying thechaotic perturbation solution,we demonstrate the atomic spatial population and the energy distribution of the systemare chaotic generally.

Tunneling dynamics of Bose-Einstein condensates with higher-order interactions in optical lattice

The nonlinear Landau Zener tunneling and nonlinear Rabi oscillations of Bose-Einstein condensate （BEC） with higher-order atomic interaction between the Bloch bands in an accelerating optical lattice are discussed. Within the two-level model, the tunneling probability of BEC with higher-order atomic interaction between Bloch bands is obtained. We finds that the tunneling rate is closely related to the higher-order atomic interaction. Furthermore, the nonlinear Rabi oscillations of BEC with higher-order atomic interaction between the bands are discussed by imposing a periodic modulation on the level bias. Analytical expressions of the critical higher-order atomic interaction for suppressing/enhancing the Rabi oscillations are obtained. It is shown that the critical value strongly depends on the modulation parameters （i.e., the modulation amplitude and frequency） and the strength of periodic potential.

Energy Spectrum of Two-Component Bose-Einstein Condensates in Optical Lattices

With the method of Green's function, we investigate the energy spectra of two-component ultracold bosonic atoms in optical lattices. We End that there are two energy bands for each component. The critical condition of the superfluid-Mott insulator phase transition is determined by the energy band structure. We also find that the nearest neighboring and on-site interactions fail to change the structure of energy bands, but shift the energy bands only. According to the conditions of the phase transitions, three stable superfluid and Mott insulating phases can be found by adjusting the experiment parameters. We also discuss the possibility of observing these new phases and their transitions in further experiments.

Effect of interaction strength on gap solitons of Bose-Einstein condensates in optical lattices

We have developed a systematic analytical approach to the study on the dynamic properties of the linear and the nonlinear excitations for quasi-one-dimensional Bose-Einstein condensate trapped in optical lattices. A novel linear dispersion relation and an algebraic soliton solution of the condensate are derived analytically under consideration of Bose-Einstein condensate with a periodic potential. By analysing the soliton solution, we find that the interatomic interaction strength has an important effect on soliton dynamic properties of Bose-Einstein condensate.

Stability of Two-Component Bose-Einstein Condensates in Bessel Optical Lattices

The stability of the ground state of two-component Bose-Einstein condensates （BEGs） loaded into the central well of an axially symmetric Bessel lattices （BLs） potential with attractive or repulsive atoms interactions is studied using the time-dependent Gross-Pitaevskii equation （GPE）. By using the variational method, we find that stable ground state of two-component BEGs can exist in BLs. The BLs＇s depth and the intra-species atom interaction play an important role in the stability of ground state. The collapse of two-component BEGs in BLs is also studied and a collapse condition for trapped two-component BEGs is obtained. It is shown that the two-component BEGs exhibit rich collapse dynamics. That is, the two-component BEGs can collapse in the system with both intra- and inter-attractive, or with intra-attractive and inter-repulsive, or with intra-repulsive and inter-attractive atom interactions. Furthermore, the control of the collapse of the two-component BEGs in BLs is discussed in detail. The stability diagram of the ground state in parameter space is obtained. The results show that the collapse of two-component BEGs can be controlled by temporal modulation of the atom interaction.

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.

Stability of trapped Bose-Einstein condensates in one-dimensional tilted optical lattice potential

Using the direct perturbation technique, this paper obtains a general perturbed solution of the Bose-Einstein condensates trapped in one-dimensional tilted optical lattice potential. We also gave out two necessary and sufficient conditions for boundedness of the perturbed solution. Theoretical analytical results and the corresponding numerical results show that the perturbed solution of the Bose-Einstein condensate system is unbounded in general and indicate that the Bose-Einstein condensates are Lyapunov-unstable. However, when the conditions for boundedness of the perturbed solution are satisfied, then the Bose-Einstein condensates are Lyapunov-stable.

Bose-Einstein Condensates in Optical Lattices with Higher-Order Interactions

The higher-order interactions of Bose-Einstein condensate in multi-dimensional optical lattices are discussed both analytically and numerically.It is demonstrated that the effects of the higher-order atomic interactions on the sound speed and the stabilities of Bloch waves strongly depend on the lattice strength.In the presence of higher-order effects,tighter and high-dimensional lattices are confirmed to be two positive factors for maintaining the system's energetic stability,and the dynamical instability of Bloch waves can take place simultaneously with the energetic instability.In addition,we find that the higher-order interactions exhibit a long-range behavior and the long-lived coherent Bloch oscillations in a tilted optical lattice exist.Our results provide an effective way to probe the higher-order interactions in optical lattices.

Dynamics of Bose-Einstein condensates in a one-dimensional optical lattice with double-well potential

We study dynamical behaviors of the weakly interacting Bose-Einstein condensate in the one- dimensional optical lattice with an overall double-well potential by solving the time-dependent Gross-Pitaevskii equation. It is observed that the double-well potential dominates the dynamics of such a system even if the lattice depth is several times larger than the height of the double-well potential. This result suggests that the condensate flows without resistance in the periodic lattice just like the case of a single particle moving in periodic potentials. Nevertheless, the effective mass of atoms is increased, which can be experimentally verified since it is connected to the Josephson oscillation frequency. Moreover, the periodic lattice enhances the nonlinearity of the double-well condensate, making the condensate more ＂self-trapped＂ in the ^-mode self-trapping regime.

Tunable ground-state solitons in spin–orbit coupling Bose–Einstein condensates in the presence of optical lattices

Properties of the ground-state solitons, which exist in the spin-orbit coupling （SOC） Bose-Einstein condensates （BEC） in the presence of optical lattices, are presented. Results show that several system parameters, such as SOC strength, lattice depth, and lattice frequency, have important influences on properties of ground state solitons in SOC BEC. By controlling these parameters, structure and spin polarization of the ground-state solitons can be effectively tuned, so ma- nipulation of atoms may be realized.

Nonlinear dynamical stability of gap solitons in Bose-Einstein condensate loaded in a deformed honeycomb optical lattice

We investigate the existence and dynamical stability of multipole gap solitons in Bose-Einstein condensate loaded in a deformed honeycomb optical lattice.Honeycomb lattices possess a unique band structure,the first and second bands intersect at a set of so-called Dirac points.Deformation can result in the merging and disappearance of the Dirac points,and support the gap solitons.We find that the two-dimensional honeycomb optical lattices admit multipole gap solitons.These multipoles can have their bright solitary structures being in-phase or out-of-phase.We also investigate the linear stabilities and nonlinear stabilities of these gap solitons.These results have applications of the localized structures in nonlinear optics,and may helpful for exploiting topological properties of a deformed lattice.

Effects of periodic optical lattice potential on dark solitons in a Bose Einstein condensate

This paper investigates the dynamics of dark solitons in a Bose-Einstein condensate with a magnetic trap and an optical lattice （OL） trap, and analyses the effects of the periodic OL potential on the dynamics by applying the variational approach based on the renormalized integrals of motion. The results show that the dark soliton becomes only a standing-wave and free propagation of the dark soliton is not possible when the periodic length of the OL potential is approximately equal to the effective width of the dark soliton. When the periodic length is very small or very large, the effects of the OL potential on the dark soliton will be sharply reduced. Finally, the numerical results confirm these theoretical findings.

Dynamical properties of ultracold Bose atomic gases in one-dimensional optical lattices created by two schemes

An optical lattice could be produced either by splitting an input light(splitting scheme) or by reflecting the input light by a mirror(retro-reflected scheme).We study quantum dynamical properties of an atomic Bose-Einstein condensate(BEC) in the two schemes.Adopting a mean field theory and neglecting collision interactions between atoms, we find that the momentum and spatial distributions of BEC are always symmetric in the splitting scheme which, however, are asymmetric in the retro-reflected scheme.The reason for this difference is due to the local field effect.Furthermore, we propose an effective method to avoid asymmetric diffraction.

Critical temperature and condensed fraction of Bose-Einstein condensation in optical lattices

Critical temperature and condensate fraction of Bose-Einstein condensation in the optical lattice are studied. The results show that the critical temperature in optical lattices can be characterized with an equivalent critical temperature in a single lattice, which provide a fast evaluation of critical temperature and condensate fraction of Bose-Einstein condensation confined with pure optical trap. Critical temperature can be estimated with an equivalent critical temperature. It is predicted that critical temperature is proportional to q ?3/2 in q number lattices for superfluid state and should be equal to that in a single lattic for Mott insulate state. Required potential depth or Rabi frequency and maximum atom number in the lattices both for superfluid state and Mott state are presented based on views of thermal mechanical statistics.

Quantum phases of Bose gases on a lattice with pair-tunneling

We investigate the strongly interacting lattice Bose gases on a lattice with two-body interaction of nearest neighbors characterized by pair tunneling. The excitation spectrum and the depletion of the condensate of lattice Bose gases are investigated using the Bogoliubov transformation method and the results show that there is a pair condensate as well as a single particle condensate. The various possible quantum phases, such as the Mott-insulator phase （MI）, the superfluid phase （SF） of an individual atom, the charge density wave phase （CDW）, the supersolid phase （SS）, the pair-superfluid （PSF） phase, and the pair-supersolid phase （PSS） are discussed in different parametric regions within our extended Bose-Hubbard model using perturbation theory.

Properties of spin-orbit-coupled Bose-Einstein condensates

The experimental and theoretical research of spin-orbit-coupled ultracold atomic gases has advanced and expanded rapidly in recent years. Here, we review some of the progress that either was pioneered by our own work, has helped to lay the foundation, or has developed new and relevant techniques. Af- ter examining the experimental accessibility of all relevant spin-orbit coupling parameters, we discuss the fundamental properties and general applications of spin-orbit-coupled Bose-Einstein condensates （BECs） over a wide range of physical situations. For the harmonically trapped case, we show that the ground state phase transition is a Dicke-type process and that spin-orbit-coupled BECs provide a unique platform to simulate and study the Dicke model and Dicke phase transitions. For a homo- geneous BEC, we discuss the collective excitations, which have been observed experimentally using Bragg spectroscopy. They feature a roton-like minimum, the softening of which provides a potential mechanism to understand the ~round state phase transition. On the other hand, if the collective dy- namics are excited by a sudden quenching of the spin-orbit coupling parameters, we show that the resulting collective dynamics can be related to the famous Zitterbewegung in the relativistic realm. Finally, we discuss the case of a BEC loaded into a periodic optical potential. Here, the spin-orbit coupling generates isolated fiat bands within the lowest Bloch bands whereas the nonlinearity of the system leads to dynamical instabilities of these Bloch waves. The experimental verification of this instability illustrates the lack of Galilean invariance in the system.

Dynamic Structure Factor of an Optically Trapped Dipolar Bose–Einstein Condensate

Motivated by the recent experimental achievements in using the Bragg spectroscopy to measure the excitation spectrum of an ultra-cold atomic system with long-range interactions, we investigate the dynamic structure factor of a cigar-shaped dipolar Bose condensate trapped in a one-dimensional optical lattices. Our results show that the Bogoliubov bands of the system, particularly the lowest one, can be significantly influenced when one tunes the dipole orientation. Consequently, the calculated static structure factor of an optically trapped dipolar Bose gas shows marked difference from the non-dipolar one. Moreover, we show that the effects of dipole-dipole interaction on the dynamic structure factor is also strongly affected by the strength of the optical confinement.

斜光格子中玻色-爱因斯坦凝聚的Melnikov混沌控制(英文)

研究了斜光格子中玻色-爱因斯坦凝聚的混沌特征,利用直接微扰法获得了Gross-Pitaevskii方程的微扰解。理论解析表明:这个微扰解是混沌解,因为它满足Melnikov混沌判据,此结果意味该系统存在混沌行为,而相应的数值模拟结果印证了其理论结果。然而,系统的混沌可以通过调节系统参数或改变初始条件加以控制,由此表明,系统参数或初始条件在控制混沌中扮演了非常重要的角色。

运动光格中玻色-爱因斯坦凝聚系统的混沌时空动力学

本文研究了运动光格中原子间呈排斥作用的玻色-爱因斯坦凝聚系统的混沌时空动力学.通过理论分析,我们得到了具有简单零点的Melnikov函数,这表明系统存在Smale马蹄混沌.数值模拟显示,在一定的参数条件下,光格势强度的增大或s波散射长度的减小,都将迫使系统由规则状态进入混沌状态.