Kármán vortex street in a spin–orbit-coupled Bose–Einstein condensate with PT symmetry

The dynamics of spin–orbit-coupled Bose–Einstein condensate with parity-time symmetry through a moving obstacle potential is simulated numerically. In the miscible two-component condensate, the formation of the Kármán vortex street is observed in one component, while ‘the half-quantum vortex street' is observed in the other component. Other patterns of vortex shedding, such as oblique vortex dipoles, V-shaped vortex pairs, irregular turbulence, and combined modes of various wakes, can also be found. The ratio of inter-vortex spacing in one row to the distance between vortex rows is approximately0.18, which is less than the stability condition 0.28 of classical fluid. The drag force acting on the obstacle potential is simulated. The parametric regions of Kármán vortex street and other vortex patterns are calculated. The range of Kármán vortex street is surrounded by the region of combined modes. In addition, spin–orbit coupling disrupts the symmetry of the system and the gain-loss affects the local particle distribution of the system, which leads to the local symmetry breaking of the system, and finally influences the stability of the Kármán vortex street. Finally, we propose an experimental protocol to realize the Kármán vortex street in a system.

Mode dynamics of Bose–Einstein condensates in a single-well potential

We investigate dynamics of Bose–Einstein condensates(BECs) in a single-well potential using the mode-coupling method. Symmetry is shown to play a key role in the coupling between modes. A proper mode-coupling theory of the dynamics of BECs in a single-well potential should include at least four modes. In this context, the ideal BEC system can be decomposed into two independent subsystems when the coupling is caused by external potential perturbation and is linear. The mode dynamics of non-ideal BECs with interaction shows rich behavior. The combination of nonlinear coupling and initial condition leads to the different regimes of mode dynamics, from regularity to non-regularity, which also indicates a change of the dependence of coupling on the symmetry of modes.

Probability of Obtaining the Planck Constant, in a Universe Modeled as a Giant Black Hole by Bose Einstein Condensates of Gravitons Using Hawking Argument and Scaling

We use the methodology of A. D. Linde to model the probability of obtaining a cosmological constant which is in turn affected by scaling arguments for a Bose Einstein gravitational condensate as given by Chavanis, in 2015. The net result, is that the scaling argument so provided allows for a gravitational constant commensurate with the size of the Universe, using arguments which appear to be simple but which give, if one has the conditions for modeling the Universe as a “black hole” virtually 100 % chance for the cosmological constant arising.

Modified White Hole Enthalpy Coupled to Quantum Bose-Einstein Condensate at Extremely Low Entropy

We model the universe as a white hole, and in the process we perform detailed analysis of the enthalpy equation of the modified white hole, and we get a much detailed picture of when and how did;quantum gravity (cosmology) phase, inflationary phase, and the acceleration phase of the universe happened. We determine the field equations of the modified white hole and evolve the scale factor and compare the evolution to the thermodynamic properties of the universe. We also illustrate that the strong energy condition is violated, but both the null energy condition and the strong cosmic censorship are not violated. Lastly, we couple the enthalpy to the Bose-Einstein condensate at extremely low entropy at the quantum gravity (cosmology) regime. Thereafter, we determine the unstable condition of the Bose-Einstein quantum equation which we interpret as the moment when the big bang occurred.

Bose-Einstein凝聚态基态解的加权数值方法及稳定性分析

构造加权法离散归一化梯度流,求解玻色-爱因斯坦凝聚态(Bose-Einstein condensate, BEC)的基态解,整合和扩充了离散归一化梯度流的经典有限差分法。同时,结合冯·诺伊曼(von Neumann)条件和冻结系数法证明了不同加权因子下数值格式的稳定性条件。从局部截断误差大小来看,加权法的最优加权因子为1/2。数值实验验证了加权法的稳定性条件,表明加权法可有效求解基态,且在求解过程中能量随时间演化呈递减趋势。另外,当加权因子取值为1/3时,数值结果展示对应数值格式在空间方向具有二阶收敛性。

Exact periodic wave and soliton solutions in two-component Bose-Einstein condensates

We present several families of exact solutions to a system of coupled nonlinear Schrodinger equations. The model describes a binary mixture of two Bose-Einstein condensates in a magnetic trap potential. Using a mapping deformation method, we find exact periodic wave and soliton solutions, including bright and dark soliton pairs.

Periodically modulated interaction effect on transport of Bose–Einstein condensates in lattice with local defects

We theoretically investigate the periodically modulated interaction effect on the propagation properties of a traveling plane wave in a Bose–Einstein condensate(BEC) trapped in a deep annular lattice with local defects both analytically and numerically. By using the two-mode ansatz and the tight-binding approximation, a critical condition for the system preserving the superfluidity is obtained analytically and confirmed numerically. We find that the coupled effects of periodic modulated atomic interactions, the quasi-momentum of the plane wave, and the defect can control the superfluidity of the system. Particularly, when we consider the periodic modulation in the system with single defect, the critical condition for the system entering the superfluid regime depends on both the defect and the momentum of the plane wave. This is different from the case for the system without the periodic modulation, where the critical condition is only determined by the defect. The modulation and quasi-momentum of the plane wave can enhance the system entering the superfluid regime. Interestingly, when the modulated amplitude/frequency, the defect strength, and the quasi-momentum of the plane wave satisfy a certain condition, the system will always be in the superfluid region. This engineering provides a possible means for studying the periodic modulation effect on propagation properties and the corresponding dynamics of BECs in disordered optical lattices.

Landau damping of collective modes in a harmonically trapped Bose-Einstein condensate

This paper proposes a method for calculating the Landau damping of a low-energy collective mode in a harmonically trapped Bose-Einstein condensate. Based on the divergence-free analytical solutions for ground-state wavefunction of the condensate and eigenvalues and eigenfunctions for thermally excited quasiparticles, obtained beyond Thomas-Fermi approximation, this paper calculates the coupling matrix elements describing the interaction between the collective mode and the quasiparticles. With these analytical results this paper evaluates the Landau damping rate of a monopole mode in a spherical trap and discusses its dependence on temperature, particle number and trapping frequency of the system.

Landau damping of collective mode in a quasi-two-dimensional repulsive Bose-Einstein condensate

We investigate the Landau damping of the collective mode in a quasi-two-dimension repulsive Bose-Einstein condensate by using the self-consistent time-dependent Hatree-Fock-Bogoliubov approximation and a complete and orthogonal eigenfunction set for the elementary excitation of the system. We calculate the three-mode coupling matrix element between the collective mode and the thermal excited quasi-particles and the Landau damping rate of the collective mode. We discuss the dependence of the Landau damping on temperature, on atom number in the condensate, on transverse trapping frequency and on the length of the condensate. The energy width of the collective mode is taken into account in our calculation. With little approximation, our theoretic calculation results agree well with the experimental ones and are helpful for deducing the damping mechanics and the inter-particle interaction.

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.

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.

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.

Landau damping and frequency-shift of a quadrupole mode in a disc-shaped rubidium Bose–Einstein condensate

The damping and frequency-shift in Landau mechanism of a quadrupole mode in a disc-shaped rubidium Bose-Einstein condensate are investigated by using the Hartree-Fock-Bogoliubov approximation. The practical relaxations of the elementary excitations and the orthometric relation among them are taken into account to obtain advisable calculation formula for damping as well as frequency-shift. The first approximation of Gaussian distribution function is employed for the ground-state wavefunction to suitably eliminate the divergence of the analytic three-mode coupling matrix elements. According to these methods, both Landau damping rate and frequency-shift of the quadrupole mode are analytically calculated. In addition, all the theoretical results agree with the experimental ones.

Elliptic Function Waves of Spinor Bose-Einstein Condensates in an Optical Lattice

与不同的一个改进非线性的 Schrödinger 方程平常在一个光格子的旋量鲍斯·爱因斯坦冷凝物(BEC ) 之一被小心地为旋转的概率振幅在运动的方程考虑一个非线性的术语获得。例如，模型的椭圆形的功能波浪答案在特定的边界状况下面被发现原子链的二结束被修理。在限制的情况中，椭圆形的函数波浪解决方案被简化为 spin-wave-like 或 solitons。

Generation and control of chaos in a Bose-Einstein condensate

For a Bose-Einstein condensate （BEC） confined in a double lattice consisting of two weak laser standing waves we find the Melnikov chaotic solution and chaotic region of parameter space by using the direct perturbation method. In the chaotic region, spatial evolutions of the chaotic solution and the corresponding distribution of particle number density are bounded but unpredictable between their superior and inferior limits. It is illustrated that when the relation k1≈ k2 between the two laser wave vectors is kept, the adjustment from k2 〈 k1 to k2 ≥ k1 can transform the chaotic region into regular one or the other way round. This suggests a feasible scheme for generating and controlling chaos, which could lead to an experimental observation in the near future.

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.

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-Ginsburg equation. The spectrum of the low-energy excitation and the effective potential for the width of the condensate axe 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.

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 dynamic regimes have been identified. The condensate undergoes damped radius oscillation in the absence of ring dark soliton excitations. When it comes to the appearance of ring dark solitons, their decay produces interesting structures. The excitation patterns for the concave potential show a nested structure of vortex-antivortex pairs. The dynamic excitation patterns for the convex potential, on the other hand, show richer structures with multiple transport behaviors.

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.