Coherence of nonlinear Bloch dynamics of Bose-Einstein condensates in deep optical lattices

Atomic interaction leads to dephasing and damping of Bloch oscillations(BOs)in optical lattices,which limits observation and applications of BOs.How to obtain persistent BOs is particularly important.Here,the nonlinear Bloch dynamics of the Bose-Einstein condensate with two-body and three-body interactions in deep optical lattices is studied.The damping rate induced by interactions is obtained.The damping induced by two-body interaction plays a dominant role,while the damping induced by three-body interaction is weak.However,when the two-body and three-body interactions satisfy a threshold,long-lived coherent BOs are observed.Furthermore,the Bloch dynamics with periodical modulation of linear force is studied.The frequencies of linear force corresponding to resonance and pseudoresonance are obtained,and rich dynamical phenomena,i.e.,stable and strong BOs,drifting and dispersion of wave packet,are predicted.The controllable Bloch dynamics is provided with the periodic modulation of the linear force.

The stability of Bose-Einstein condensates in a two-dimensional shallow trap

The stability of Bose Einstein condensates （BECs） loaded into a two-dimensional shallow harmonic potential well is studied. By using the variational method, the ground state properties for interacting BECs in the shallow trap are discussed. It is shown that the possible stable bound state can exist. The depth of the shallow well plays an important role in stabilizing the BECs, The stability of BECs in the shallow trap with the periodic modulating of atom interaction by using the Feshbach resonance is also discussed. The results show that the collapse and diffusion of BECs in a shallow trap can be controlled by the temporal modulation of the scattering length.

Spatial Chaos of Bose-Einstein Condensates in a Cigar-Shaped Trap

The spatial chaos of Bose-Einstein condensates in a cigar-shaped trap is studied.For a system with asteady current,we construct the general solution of the 1st-order equation.From the boundedness condition of thegeneral solution, we obtain the Melnikov function predicting the onset of chaos.The unpredictability of the system's dis-tribution of atom density is also theoretically analyzed.For a ^(23)Na system meeting the perturbation oondition,numericalsimulations show the existence of chaos,which is in accordance with our analytical results.Numerical simulations of a^(87)Rb system dissatisfying the perturbation condition also demonstrate that there exists chaos in the system.The casewithout a current is also investigated.

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.

Adjustable half-skyrmion chains induced by SU(3)spin-orbit coupling in rotating Bose-Einstein condensates

The ground state properties of the rotating Bose–Einstein condensates(BECs) with SU(3) spin–orbit coupling(SOC)in a two-dimensional harmonic trap are studied. The results show that the ferromagnetic and antiferromagnetic systems present three half-skyrmion chains at an angle of 120°to each other along the coupling directions. With the enhancement of isotropic SU(3) SOC strength, the position of the three chains remains unchanged, in which the number of half-skyrmions increases gradually. With the increase of rotation frequency and atomic density–density interaction, the number of halfskyrmions on the three chains and in the regions between two chains increases gradually. The relationships of the total number of half-skyrmions on the three chains with the increase of SU(3) SOC strength, rotation frequency and atomic density–density interaction are also given. In addition, changing the anisotropic SU(3) SOC strength can regulate the number and morphology of the half-skyrmion chains.

Dynamic stability and manipulation of bright matter-wave solitons by optical lattices in Bose-Einstein condensates

An extended variation approach to describing the dynamic evolution of self-attractive Bose-Einstein condensates is developed. We consider bright matter-wave solitons in the presence of a parabolic magnetic potential and a timespace periodic optical lattice. The dynamics of condensates is shown to be well approximated by four coupled nonlinear differential equations. A noteworthy feature is that the extended variation approach gives a critical strength ratio to support multiple stable lattice sites for the condensate. We further examine the existence of the solitons and their stabilities at the multiple stable lattice sites. In this case, the analytical predictions of Bose-Einstein condensates variational dynamics are found to be in good agreement with numerical simulations. We then find a stable region for successful manipulating matter-wave solitons without collapse, which are dragged from an initial stationary to a prescribed position by a moving periodic optical lattice.

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.

Effective Two-State Model and NOON States for Double-Well Bose-Einstein Condensates in Strong-Interaction Regime

The model of double-well Bose-Einstein condensates in the strong-interaction regime is shown to reduce adiabatically to an effective two-state model describing the Rabi oscillations between the two atomic Fock states ｜N, 0〉 and [0, N〉, and the NOON states of arbitrary ultracold atoms can therefore be generated periodically from the initial state of either one of the Foek states.

Symmetry Breaking Ground States of Bose-Einstein Condensates in 1D Double Square Well and Optical Lattice Well

We investigate the phenomena of symmetry breaking and phase transition in theground state of Bose-Einstein condensates (BECs) trapped in a double square well and in an opticallattice well, respectively. By using standing-wave expansion method, we present symmetric andasymmetric ground state solutions of nonlinear Schroedinger equation (NLSE) with a symmetric doublesquare well potential for attractive nonlinearity. In particular, we study the ground state wavefunction's properties by changing the depth of potential and atomic interactions (here we restrictourselves to the attractive regime). By using the Fourier grid Hamiltonian method, we also reveal aphase transition of BECs trapped in one-dimensional optical lattice potential.

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 Matter-Wave Solitons in Spin-Orbit Coupled Bose-Einstein Condensates

We investigate the moving matter-wave solitons in spin-orbit coupled Bose Einstein condensates （BECs） by a perturbation method. Starting with the one-dimensional Gross Pitaevskii equations, we derive a new KdV-like equation to which an approximate solution is obtained by assuming weak Raman coupling and strong spin orbit coupling. The derivation of the KdV-like equation may be useful to understand the properties of solitons excitation in spin-orbit coupled BECs. We find different types of moving solitons： dark-bright, bright bright and dark dark solitons. Interestingly, moving dark-dark soliton for attractive intra- and inter-species interactions is found, which depends on the Raman coupling. The amplitude and velocity of the moving solitons strongly depend on the Raman coupling and spin orbit coupling.

Self-Trapping of Two Weakly Coupled Bose-Einstein Condensates with Oscillating Atomic Scattering Length

We investigate the self-tapping phenomena for two weakly coupled Bose-Einstein condensates with a rapid periodic modulation of the atomic scattering length. By using an averaging method, the equations of motion of the slow dynamics are derived to analyze the self-trapping behavior. It is shown numerically that under certain conditions, an alternative self-trapping in either well appears.

Atomic population oscillations between two coupled Bose-Einstein condensates with time-dependent nonlinear interaction

The atomic population oscillations between two Bose-Einstein condensates with time-dependent nonlinear interaction in a double-well potential are studied. We first analyse the stabilities of the system＇s steady-state solutions. And then in the perturbative regime, the Melnikov chaotic oscillation of atomic population imbalance is investigated and the Melnikov chaotic criterion is obtained. When the system is out of the perturbative regime, numerical calculations reveal that regulating the nonlinear parameter can lead the system to step into chaos via period doubling bifurcations. It is also numerically found that adjusting the nonlinear parameter and asymmetric trap potential can result in the running-phase macroscopic quantum self-trapping （MQST）. In the presence of a weak asymmetric trap potential, there exists the parametric resonance in the system.

Parallel numerical simulations for quantized vortices in Bose-Einstein condensates

We employ the parallel computing technology to study numerically the three-dimensional structure of quantized vortices of Bose-Einstein condensates, For anisotropic cases, the bending process of vortices is described in detail by the decrease of Gross-Pitaevskii energy. A completely straight vortex and the steady and symmetrical multiple-vortex configurations are obtained. We analyse the effect of initial conditions and angular velocity on the number and shape of vortices.

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.

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.

Manipulating vortices in F=2 Bose-Einstein condensates through magnetic field and spin-orbit coupling

We investigate the vortex structures excited by Ioffe-Pritchard magnetic field and Dresselhaus-type spin-orbit coupling in F=2 ferromagnetic Bose-Einstein condensates.In the weakly interatomic interacting regime,an external magnetic field can generate a polar-core vortex in which the canonical particle current is zero.With the combined effect of spin-orbit coupling and magnetic field,the ground state experiences a transition from polar-core vortex to Mermin-Ho vortex,in which the canonical particle current is anticlockwise.For fixed spin-orbit coupling strengths,the evolution of phase winding,magnetization,and degree of phase separation with magnetic field are studied.Additionally,with further increasing spin-orbit coupling strength,the condensate exhibits symmetrical density domains separated by radial vortex arrays.Our work paves the way to explore exotic topological excitations in high-spin systems.

The dynamics of triple-well trapped Bose-Einstein condensates with atoms feeding and loss effects

In this paper, we consider the macroscopic quantum tunnelling and self-trapping phenomena of Bose-Einstein condensates （BECs） with three-body recombination losses and atoms feeding from thermal cloud in triple-well potential. Using the three-mode approximation, three coupled Gross-Pitaevskii equations （GPEs）, which describe the dynamics of the system, are obtained. The corresponding numerical results reveal some interesting characteristics of BECs for different scattering lengths. The self-trapping and quantum tunnelling both are found in zero-phase and ：r-phase modes. Furthermore, we observe the quantum beating phenomenon and the resonance character during the self-trapping and quantum tunnelling. It is also shown that the initial phase has a significant effect on the dynamics of the system.

Measuring gravitational effect of superintense laser by spin-squeezed Bose-Einstein condensates interferometer

We consider an extremely intense laser,enclosed by an atom interferometer.The gravitational potential generated from the high-intensity laser is solved from the Einstein field equation under the Newtonian limit.We compute the strength of the gravitational force and study the feasibility of measuring the force by the atom interferometer.The intense laser field from the laser pulse can induce a phase change in the interferometer with Bose-Einstein condensates.We push up the sensitivity limit of the interferometer with Bose-Einstein condensates by spin-squeezing effect and determine the sensitivity gap for measuring the gravitational effect from intense laser by atom interferometer.