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.

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。

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.

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.

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.

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

An improved nonlinear Schrodinger equation different from usual one of spinor Bose-Einstein condensates （BECs） in an optical lattice are obtained by taking into account a nonlinear term in the equation of motion for probability amplitude of spins carefully. The elliptic function wave solutions of the model are found under specific boundary condition, for example, the two ends of the atomic chain are fixed. In the case of limit the elliptic function wave solutions are reduced into spin-wave-like or solitons.

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.

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.

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.

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 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.

Phase diffusion of a two-component Bose-Einstein condensates:exact and short-time solutions for arbitrary coherent spin state

We investigate phase diffusion of a two-component Bose--Einstein condensates prepared initially in arbitrary coherent spin state ｜θ0,φ0｜. Analytical expression of the phase-diffusion time is presented for θ0～π/2 case. In comparison with the symmetrical case （i.e., θ0=π/2）, we find that the diffusion process becomes slow due to the reduced atom number variance.

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.

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 a localized impurity on soliton dynamics in the Bose-Einstein condensates

By using a multiple-scale method, we analytically study the effect of a localized impurity on the soliton dynamics in the Bose-Einstein condensates. It is shown that a dark soliton can be transmitted through a repulsive （or attractive） impurity, while at the position of the localized impurity the soliton can be quasitrapped by the impurity. Additionally, we find that the strength of the localized impurity has an important effect on the dark soliton dynamics. With increasing strength of the localized impurity, the amplitude of the dark soliton becomes bigger, while its width is narrower, and the soliton propagates slower.

The dynamics of nonstationary solutions in one-dimensional two-component Bose-Einstein condensates

This paper investigates the dynamical properties of nonstationary solutions in one-dimensional two-component Bose-Einstein condensates. It gives three kinds of stationary solutions to this model and develops a general method of constructing nonstationary solutions. It obtains the unique features about general evolution and soliton evolution of nonstationary solutions in this model.

Dynamics of vector solitons in two-component Bose-Einstein condensates with time-dependent interactions and harmonic potential

We present two kinds of exact vector-soliton solutions for coupled nonlinear Schrodinger equations with time- varying interactions and time-varying harmonic potential. Using the variational approach, we investigate the dynamics of the vector solitons. It is found that the two bright sol/tons oscillate about slightly and pass through each other around the equilibration state which means that they are stable under our modeh At the same time, we obtain the opposite situation for dark-dark solitons.