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.

Dynamical nonlinear excitations induced by interaction quench in a two-dimensional box-trapped Bose-Einstein condensate

Manipulating nonlinear excitations,including solitons and vortices,is an essential topic in quantum many-body physics.A new progress in this direction is a protocol proposed in[Phys.Rev.Res.2043256(2020)]to produce dark solitons in a one-dimensional atomic Bose–Einstein condensate(BEC)by quenching inter-atomic interaction.Motivated by this work,we generalize the protocol to a two-dimensional BEC and investigate the generic scenario of its post-quench dynamics.For an isotropic disk trap with a hard-wall boundary,we find that successive inward-moving ring dark solitons(RDSs)can be induced from the edge,and the number of RDSs can be controlled by tuning the ratio of the after-and before-quench interaction strength across different critical values.The role of the quench played on the profiles of the density,phase,and sound velocity is also investigated.Due to the snake instability,the RDSs then become vortex–antivortex pairs with peculiar dynamics managed by the initial density and the after-quench interaction.By tuning the geometry of the box traps,demonstrated as polygonal ones,more subtle dynamics of solitons and vortices are enabled.Our proposed protocol and the discovered rich dynamical effects on nonlinear excitations can be realized in near future cold-atom experiments.

Effects of drive imbalance on the particle emission from a Bose-Einstein condensate in a one-dimensional lattice

Time-periodic driving has been an effective tool in the field of nonequilibrium quantum dynamics,which enables precise control of the particle interactions.We investigate the collective emission of particles from a Bose-Einstein condensate in a one-dimensional lattice with periodic drives that are separate in modulation amplitudes and relative phases.In addition to the enhancement of particle emission,we find that amplitude imbalances lead to energy shift and band broadening,while typical relative phases may give rise to similar gaps.These results offer insights into the specific manipulations of nonequilibrium quantum systems with tone-varying drives.

Interference-induced suppression of particle emission from a Bose-Einstein condensate in lattice with time-periodic modulations

Emission of matter-wave jets from a parametrically driven condensate has attracted significant experimental and theoretical attention due to the appealing visual effects and potential metrological applications.In this work,we investigate the collective particle emission from a Bose-Einstein condensate confined in a one-dimensional lattice with periodically modulated interparticle interactions.We give the regimes for discrete modes,and find that the emission can be distinctly suppressed.The configuration induces a broad band,but few particles are ejected due to the interference of the matter waves.We further qualitatively model the emission process and demonstrate the short-time behaviors.This engineering provides a way to manipulate the propagation of particles and the corresponding dynamics of condensates in lattices,and may find application in the dynamical excitation control of other nonequilibrium problems with time-periodic driving.

Nonlinear modes coupling of trapped spin-orbit coupled spin-1 Bose-Einstein condensates

We study analytically and numerically the nonlinear collective dynamics of quasi-one-dimensional spin-orbit coupled spin-1 Bose-Einstein condensates trapped in harmonic potential.The ground state of the system is determined by minimizing the Lagrange density,and the coupled equations of motions for the center-of-mass coordinate of the condensate and its width are derived.Then,two low energy excitation modes in breathing dynamics and dipole dynamics are obtained analytically,and the mechanism of exciting the anharmonic collective dynamics is revealed explicitly.The coupling among spin-orbit coupling,Raman coupling and spin-dependent interaction results in multiple external collective modes,which leads to the anharmonic collective dynamics.The cooperative effect of spin momentum locking and spin-dependent interaction results in coupling of dipolar and breathing dynamics,which strongly depends on spin-dependent interaction and behaves distinct characters in different phases.Interestingly,in the absence of spin-dependent interaction,the breathing dynamics is decoupled from spin dynamics and the breathing dynamics is harmonic.Our results provide theoretical evidence for deep understanding of the ground sate phase transition and the nonlinear collective dynamics of the system.

Modulational Instability of Trapped Two-Component Bose-Einstein Condensates

The modulational instability of two-component Bose-Einstein condensates(BECs)under an external parabolic potential is discussed.Based on the trapped two-component Gross-Pitaevskill equations,a time-dependent dispersion relation is obtained analytically by means of the modified lens-type transformation and linear stability analysis.It is shown that a modulational unstable time scale exists for trapped two-component BECs.The modulational properties-which are determined by the wave number,external trapping parameter,intraand inter-species atomic interactions-are modified significantly.The analytical results are confirmed by direct numerical simulation.Our results provide a criterion for judging the occurrence of instability of the trapped two-component BECs in experiment.

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.

Special breathing structures induced by bright solitons collision in a binary dipolar Bose–Einstein condensates

We numerically investigate the breathing dynamics induced by collision between bright solitons in a binary dipolar Bose–Einstein condensates, whose dipole–dipole interaction and contact interaction are attractive. We identify three special breathing structures, such as snakelike special breathing structure, mixed breathing structure, and divide breathing structure.The characteristics of these breathing structures can be described by breathing frequency ?, maximum breathing amplitude A and lifetime τ, which can be manipulated by atomic number Ni and interspecies scattering length a12. Meanwhile, the above breathing structures can realize the process of quasi-transition with a reasonable Ni and a12. Additionally, the collision of two special breathing structures also can bring more abundant breathing dynamics. Our results provide a reference for the study of soliton interactions and deepen the understanding of soliton properties in a binary dipolar Bose–Einstein condensates.

Nonlinear transport of Bose-Einstein condensates in a double barrier potential

The stable nonlinear transport of the Bose-Einstein condensates through a double barrier potential in a waveguide is studied. By using the direct perturbation method we have obtained a perturbed solution of Cross-Pitaevskii equation. Theoretical analysis reveals that this perturbed solution is a stable periodic solution, which shows that the transport of Bose-Einstein condensed atoms in this system is a stable nonlinear transport. The corresponding numerical results are in good agreement with the theoretical analytical results.

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.

Influence of Decoherence on Interference Between Two Bose-Einstein Condensates

The influence of decoherence on interference between two trapped Bose-Einstein condensates with arbitraryinitial states is studied. Analytic expressions of the intensity and visibility of the interference pattern are found. It isshown that the decoherence weakens the interference intensity and decreases the visibility of the interference pattern.

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.

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.

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.

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.

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.

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.

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.