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.     

Effects of three-body interaction on dynamic and static structure factors of an optically-trapped Bose gas

We investigate how three-body interactions affect the elementary excitations and dynamic structure factor of a Bose- Einstein condensate trapped in a one-dimensional optical lattice. To this end, we numerically solve the Gross-Pitaevskii equation and then the corresponding Bogoliubov equations. Our results show that three-body interactions can change both the Bogoliubov band structure and the dynamical structure factor dramatically, especially in the case of the two-body interaction being relatively small. Furthermore, when the optical lattice is strong enough, the analytical results, combined with the sum-rule approach, help us to understand that： the effects of three-body interactions on the static structure Ihctor can be significantly amplified by an optical lattice. Our predictions should be observable within the current Bragg spectroscopy experiment.     

Band structures of a slowly rotating dipolar Bose-Einstein condensate with a quantized vortex along a one-dimensional optical lattice

We derive the effective Gross-Pitaevskii equation for a slowly rotating dipolar Bose-Einstein condensate (BEC) with a quantized vortex along a one-dimensional optical lattice and calculate its band structures. The band structure of a slowly rotating BEC in a lattice becomes interesting when dipole-dipole interaction (DDI) is involved. Under rotation, a dipolar rotating term emerges from the DDI potential. The dipolar rotating term makes a BEC with an attractive DDI more stable than one with a repulsive DDI. The dipolar rotating term changes and generalizes the definition for the type of BEC, which cannot be simply determined by an s-wave scattering length or an effective contact interaction term. The dipolar rotating term also makes the band structure fascinating and tunable. A so-called swallowtail band structure, i.e., a multi-valued solution due to nonlinear interaction, can either elongate or shrink as the band index increases, in contrast to a non-rotating dipolar BEC system with a monotonic dependence. With the dipolar rotating term, various band structures as well as an attractive BEC without collapse can be easily achieved. We demonstrate that a rotating dipolar BEC system subject to an optical lattice combines features of a crystal and a superfluid and promises wide applications.     

Wave Trains Generation in a Delayed Nonlinear Response of Bose-Einstein Condensates with Three-Body Interactions

We investigate the modulational instability of matter-wave condensates in a modified Gross-Pitaevskii equation which takes into account effects of the three-body interaction. This three-body interaction consists of a quintic term and an additional one representing the delayed nonlinear response of condensates which are trapped both in an attractive and a repulsive harmonic potentials. Our theoretical study uses a modified lens-type transformation and we obtain a modulational instability criterion, and an explicit growth rate. We show that the presence of the three-body interaction destabilizes the condensate, and enhances the appearance of instability in the condensate. Numerical experiments agree well with analytical predictions. Furthermore, our numerical simulations show that the three-body interaction modifies the symmetry of the trail of soliton chains created. The expulsive potential enhances the instability, while the attractive potential appears to soften the instability.     

Modulational instability and complex dynamics of confined matter-wave solitons

We study the formation of bright solitons in a Bose-Einstein condensate of 7Li atoms induced by a sudden change in the sign of the scattering length from positive to negative, as reported in a recent experiment [Nature (London) 417, 150 (2002)]]. The numerical simulations are performed by using the Gross-Pitaevskii equation with a dissipative three-body term. We show that a number of bright solitons is produced and this can be interpreted in terms of the modulational instability of the time-dependent macroscopic wave function of the Bose condensate. In particular, we derive a simple formula for the number of solitons that is in good agreement with the numerical results. We find that during the motion of the soliton train in an axial harmonic potential the number of solitonic peaks changes in time and the density of individual peaks shows an intermittent behavior.     

偶极相互作用对自旋轨道耦合自旋-1凝聚体中磁畴分布的影响

研究准一维简谐势阱中存在自旋轨道耦合（SOC）的自旋-1偶极玻色-爱因斯坦凝聚体,数值求解旋量Gross-Pitaevskii方程,给出磁畴的分布。计算结果表明：磁畴结构与偶极-偶极相互作用（DDIs）密切相关,随着自旋轨道耦合强度和磁化强度的增强,原来的空间对称分布被破坏,随之出现新的分布模式。     

Integrability of a general Gross-Pitaevskii equation and exact solitonic solutions of a Bose-Einstein condensate in a periodic potential

We consider a general form of the Gross-Pitaevskii equation with time- and space-dependent effective mass, external potential and strength of interatomic interaction. Using the inverse-scattering method, we derive the integrability condition of this equation within a general scheme that can be used to find exact solutions of a wide range of linear and nonlinear partial differential equations. We use this condition to derive exact solitonic solutions of the one-dimensional time-dependent Gross-Pitaevskii equation corresponding to a Bose-Einstein condensate trapped by a periodic potential. Both attractive and repulsive interatomic interactions are considered. The values of the parameters of the potential can be chosen such that the periodic potential becomes almost identical to that of an optical lattice.     

光晶格中双组分偶极玻色-爱因斯坦凝聚体的调制不稳定性

利用线性稳定性分析的方法,对光晶格中双组分偶极玻色-爱因斯坦凝聚体(Bose-Einstein condensates,简称BECs)的调制不稳定性进行了研究.得到了光晶格中双组分偶极BECs原子系统调制不稳定性区域的分布与在位相互作用和由偶极-偶极相互作用所导致的格点间BECs相互作用之间的关系.结果显示,格点间BECs的相互作用对光晶格中双组分偶极BECs的调制不稳定性有较大的影响,这可为实际应用中如何操控双组分偶极BECs提供有用的信息. 关键词： 光晶格 双组分玻色-爱因斯坦凝聚体 调制不稳定性 偶极-偶极相互作用     

Effective field theory for spinor dipolar Bose Einstein condensates

We show that the effective theory of long wavelength low energy behavior of a dipolar Bose-Einstein condensate(BEC) with large dipole moments (treated as a classical spin) can be modeled using an extended non-linear sigma model (NLSM) like energy functional with an additional non-local term that represents long ranged anisotropic dipole-dipole interaction. Minimizing this effective energy functional we calculate the density and spin-profile of the dipolar Bose-Einstein condensate in the mean-field regime for various trapping geometries. The resulting configurations show strong intertwining between the spin and mass density of the condensate, transfer between spin and orbital angular momentum in the form of Einstein-de Hass effect, and novel topological properties. We have also described the theoretical framework in which the collective excitations around these mean field solutions can be studied and discuss some examples qualitatively.     

共心双环外势中两分量偶极玻色-爱因斯坦凝聚体的基态结构研究

利用虚时演化方法研究了共心双环外势中具有偶极-偶极相互作用的两分量玻色-爱因斯坦凝聚体的基态结构, 探索了接触相互作用和长程各向异性的偶极-偶极相互作用对系统基态的影响. 研究发现, 偶极-偶极相互作用作为系统的又一调控参数, 可用于得到系统的不同的基态相, 并用于控制不同基态相间的转化.     

Observation of dipole-dipole interaction in a degenerate quantum gas

We have investigated the expansion of a Bose-Einstein condensate of strongly magnetic chromium atoms. The long-range and anisotropic magnetic dipole-dipole interaction leads to an anisotropic deformation of the expanding chromium condensate which depends on the orientation of the atomic dipole moments. Our measurements are consistent with the theory of dipolar quantum gases and show that a chromium condensate is an excellent model system to study dipolar interactions in such gases.     

Bose-Einstein condensation at finite momentum and magnon condensation in thin film ferromagnets

We use the Gross-Pitaevskii equation to determine the spatial structure of the condensate density of interacting bosons whose energy dispersion ϵ _k has two degenerate minima at finite wave-vectors ± q. We show that in general the Fourier transform of the condensate density has finite amplitudes for all integer multiples of q. If the interaction is such that many Fourier components contribute, the Bose condensate is localized at the sites of a one-dimensional lattice with spacing 2 π/|q|; in this case Bose-Einstein condensation resembles the transition from a liquid to a crystalline solid. We use our results to investigate the spatial structure of the Bose condensate formed by magnons in thin films of ferromagnets with dipole-dipole interactions.     

Comparing contact and dipolar interactions in a Bose-Einstein condensate

We have measured the relative strength epsilon dd of the magnetic dipole-dipole interaction compared with the contact interaction in a dipolar chromium Bose-Einstein condensate. We analyze the asymptotic velocities of expansion of the condensate with different orientations of the atomic magnetic moments. By comparing the experimental results with numerical solutions of the hydrodynamic equations for dipolar condensates, we obtain epsilon dd = 0.159+/-0.034. We use this result to determine the s-wave scattering length a = (5.08+/-1.06 x 10(-9)) m = (96+/-20) a0 of 52Cr. This is fully consistent with our previous measurements on the basis of Feshbach resonances and therefore confirms the validity of the theoretical approach used to describe the dipolar Bose-Einstein condensate.     

Dissipation-Managed Bright Soliton in a 1D Bose-Einstein Condensate in an Optical-Lattice Potential

We study the formation of a dynamically-stabilized dissipation-managed bright soliton in a quasi-one-dimensional Bose-Einstein condensate by including an imaginary three-body recombination loss term and an imaginary linear feeding one in the Gross-Pitaevskii equation, trapped in a shallow optical-latticepotential. Based on the direct approach of perturbation theory for the nonlinear Schrödinger equation, we demonstrate that the height (as well as width) of bright soliton may have little change through selecting experimental parameters.     

Spontaneous circulation in ground-state spinor dipolar Bose-Einstein condensates

We report on a study of the spin-1 ferromagnetic Bose-Einstein condensate with magnetic dipole-dipole interactions. By solving the nonlocal Gross-Pitaevskii equations for this system, we find three ground-state phases. Moreover, we show that a substantial orbital angular momentum accompanied by chiral symmetry breaking emerges spontaneously in a certain parameter regime. We predict that all these phases can be observed in the spin-1 87Rb condensate by changing the number of atoms or the trap frequency.     

Stability Diagrams of a Bose-Einstein Condensate in Excited Bloch Bands

Landau and dynamical instabilities o/a Bose-Einstein condensate （BEC） in the excited bands of a one-dimensional optical lattice are investigated by the Gross Pitaevskii theory. Our results show that there always exists Landau instability for a BEC in the whole region of excited bands. We also map out the dangerous zones of the dynamical instability. The experimental implications of the stability diagram are discussed.     

Observation of dynamical instability for a Bose-Einstein condensate in a moving 1D optical lattice

We have experimentally studied the unstable dynamics of a harmonically trapped Bose-Einstein condensate loaded into a 1D moving optical lattice. The lifetime of the condensate in such a potential exhibits a dramatic dependence on the quasimomentum state. This is unambiguously attributed to the onset of dynamical instability, after a comparison with the predictions of the Gross-Pitaevskii theory. Deeply in the unstable region we observe the rapid appearance of complex structures in the atomic density profile, as a consequence of the condensate phase uniformity breakdown.     

d-wave collapse and explosion of a dipolar bose-einstein condensate

We investigate the collapse dynamics of a dipolar condensate of 52Cr atoms when the s-wave scattering length characterizing the contact interaction is reduced below a critical value. A complex dynamics, involving an anisotropic, d-wave symmetric explosion of the condensate, is observed. The atom number decreases abruptly during the collapse. We find good agreement between our experimental results and those of a numerical simulation of the three-dimensional Gross-Pitaevskii equation, including contact and dipolar interactions as well as three-body losses. The simulation indicates that the collapse induces the formation of two vortex rings with opposite circulations.     

Spin waves in a Bose-Einstein--condensed atomic spin chain

The spin dynamics of atomic Bose-Einstein condensates confined in a one-dimensional optical lattice is studied. The condensates at each lattice site behave like spin magnets that can interact with each other through both the light-induced dipole-dipole interaction and the static magnetic dipole-dipole interaction. We show how these site-to-site dipolar interactions can distort the ground-state spin orientations and lead to the excitation of spin waves. The dispersion relation of the spin waves is studied and possible detection schemes are proposed.     

Effective interactions between two impurities in quasi-two-dimensional dipolar Bose–Einstein condensates

We investigate the effective interaction between two heavy impurities immersed in a quasi-twodimensional dipolar Bose-Einstein condensate via a variation approach. We show that the mediated interaction is highly tunable via the contact and the dipole-dipole interactions between the background gas atoms. Interestingly, the mediated interaction potential may become an oscillating function of inter-impurity distance when roton excitation emerges under sufficiently strong dipolar interaction. Our system therefore provides an efficient way for tuning the mediated interaction between impurities.