Vortex Dynamics in Spin-1 Spin-orbit-coupled Rotating Bose-Einstein Condensates

International Journal of Theoretical Physics - We study the vortex dynamics of spin-orbit-coupled (SOC) spin-1 Bose-Einstein condensates by numerical simulations of the Gross-Pitaevskii equation....     

Vortex Dynamics of Rotating Dipolar Bose-Einstein Condensates in Synthetic Magnetic Field

In the framework of time-dependent two-dimensional Gross-Pitaevskii equation, we investigate the dynamics of vortex formation in rotating dipolar Bose-Einstein condensates in synthetic magnetic field (SMF) and compare with rotating frame (RF) method. The formation of vortices are calculated, considering effects of the rotational frequency, dipole strength, tilting angle and trap ratio. The results we found are that in SMF, the formation of steady state vortices is much slower than that in RF, and it is more difficult to add large angular momentum to the condensates than to do so in RF.     

Solitary Vortex Evolution in Two-Dimensional Harmonically Trapped Bose-Einstein Condensates

We investigate solitary vortex evolution in two-dimensional Bose-Einstein condensates based on the GrossPitaevskii equation model. Through the variational method, together with the novel Gaussian ansatz incorporating asymmetric perturbation effects, we arrive at the analytical solitary vortex solution with two typical forms: a symmetric quasi-stable solution under certain parametric settings and a diverging propagation case arising from an initial asymmetric perturbation. The derived pictorial evolutionary patterns of the solitary vortices are compared with those from a pure numerical analysis, and by identifying the key qualitative features, we show the applicability of the theoretical treatment presented here.     

Solitary Vortex Evolution in Two-Dimensional Harmonically Trapped Bose-Einstein Condensates

We investigate solitary vortex evolution in two-dimensional Bose-Einstein condensates based on the Gross-Pitaevskii equation model. Through the variational method, together with the novel Gaussian ansatz incorporating asymmetric perturbation effects, we arrive at the analytical solitary vortex solution with two typical forms:a symmetric quasi-stable solution under certain parametric settings and a diverging propagation case arising from an initial asymmetric perturbation. The derived pictorial evolutionary patterns of the solitary vortices are compared with those from a pure numerical analysis, and by identifying the key qualitative features, we show the applicability of the theoretical treatment presented here.     

环形势阱中旋转玻色爱因斯坦凝聚体的基态

应用托马斯-费米近似和虚时演化数值方法研究环形势阱中旋转玻色爱因斯坦凝聚体的基态密度分布.当增加其旋转角频率,或者增加环形势阱的宽度及相应的中心高度,凝聚体基态密度分布均从涡旋晶格相转变为巨涡旋相.当旋转角频率为零时,增加环形势阱的宽度及相应的中心高度,凝聚体基态密度分布从一个圆盘变为圆环.解析结果与数值结果相互吻合.     

Effects of Higher Order Interaction on Vortex Formation in Bose-Einstein Condensates

We consider theoretically the formation of vortex in rotating Bose-Einstein condensates (BECs) with higher order interaction (HOI). Our results are obtained from the twodimensional Gross-Pitaevskii equation. As the first step, for the certain number vortices, we discuss the ground state properties and show that the critical rotation frequency for HOI is smaller than those without HOI. As the increasing of HOI strength, the critical rotation frequency decreases. In addition, we verify that the Feynman rule is meet well. Moreover, we study the vortex dynamics.Numerical results indicate that the angular momentum remains almost unchanged irrespective of the HOI strength. The time taken for the nucleation of vortices pays less for strong HOI. These results suggest that the HOI is favorable to rotate the condensate, and this mechanism is useful to control the vortex number in BECs.

     

Ground State and Single Vortex for Bose-Einstein Condensates in Anisotropic Traps

For Bose-Einstein condensation of neutral atoms in anisotropic traps at zero temperature, we present simple analytical methods for computing the properties of ground state and single vortex of Bose-Einstein condensates, and compare those results to extensive numerical simulations. The critical angular velocity for production of vortices is calculated for both positive and negative scattering lengths a, and find an analytical expression for the large-N limit of the vortex critical angular velocity for a 〉0, and the critical number for condensate population approaches the point of collapse for a 〈 0, by using approximate variational method.     

Condensates and Bose-Einstein correlations

We discuss the conditions under which Bose-Einstein correlation can be used to determine the presence of condensates. One starts from the fact that any condensate is a coherent state and uses then the formalism of quantum optics. The case of final state interactions is considered explicitly in a Landau-Ginzburg type approach as used in laser physics. By applying a mean field Hartree approximation for the many mode problem we find that the second order correlation function for identical bosons $\text{C}{}_2\text{(}\text{p}{}_1\text{?}\text{p}{}_2\text{=0)}$ does effectively not depend on the phenomenological coupling constant g and thus C₂(0) can be used to determine the amount of coherence and hence the existence of condensates. On the other hand $\text{C}{}_2\text{(}\text{p}{}_1\text{?}\text{p}{}_2\text{≠0)}$ does depend on g and therefore its measurement provides information about g. The implications of these findings for the determination of the size and lifetime of the source á la Hanbury-Brown-Twiss are discussed. Our conclusions apply both to condensates in nuclear (pion condensates, alpha and deuteron condensates) and hadronic matter.     

Condensed Vortex Ground States of Rotating Bose-Einstein Condensate in Harmonic Atomic Trap

We study a system of N Bose atoms trapped by a symmetric harmonic potential, interacting via weak central forces. Considering the ground state of the rotating system as a function of the two conserved quantities, the total angular momentum, and its collective component, we develop an algebraic approach to derive exact wave functions and energies of these ground states. We describe a broad class of the interactions for which these results are valid. This universality class is defined by simple integral condition on the potential. Most of the potentials of practical interest which have pronounced repulsive component belong to this universality class.     

Soliton Solutions in Three-Component Bose-Einstein Condensates

We obtain soliton and plane wave solutions for the coupled nonlinear Schrotinger equations, which describe the dynamics of the three-component Bose-Einstein condensates by using the Hirota method. Meanwhile we find that the system which has attractive atomic interaction will only possess a shape changing （inelastic） collision property due to intensity redistribution in the absence of the spin-exchange interaction. As a discussed example, we investigate the one-soliton, two-soliton solutions and collisional effects between bright two-soliotn solution, which lead to the intensity redistribu tion.     

The Transition to a Giant Vortex Phase in a Fast Rotating Bose-Einstein Condensate

We study the Gross-Pitaevskii (GP) energy functional for a fast rotating Bose-Einstein condensate on the unit disc in two dimensions. Writing the coupling parameter as 1/ε ² we consider the asymptotic regime ε → 0 with the angular velocity Ω proportional to (ε ²|log ε|)⁻¹. We prove that if Ω = Ω₀(ε ²|log ε|)⁻¹ and Ω₀ > 2(3π)⁻¹ then a minimizer of the GP energy functional has no zeros in an annulus at the boundary of the disc that contains the bulk of the mass. The vorticity resides in a complementary ‘hole’ around the center where the density is vanishingly small. Moreover, we prove a lower bound to the ground state energy that matches, up to small errors, the upper bound obtained from an optimal giant vortex trial function, and also that the winding number of a GP minimizer around the disc is in accord with the phase of this trial function.     

Quantum Effects of Bose-Einstein Condensates

In this paper, we study quadrature squeezings of two Bose-Einstein condensates with collision and nonclassical properties of pair entanglement in four wave mixing in Bose-Einstein condensates. With the aid of a numerical method, we find that the two modes (pair entanglement modes) a₁ and a₂ may exhibit quadrature squeezing, in which they are affected by the initial phase. It is shown that the two pump modes exhibit the same super-Poissonian distribution. The analysis for the mode-mode correlation shows that there always exists a violation of the Cauchy-Schwartz inequality, which means that correlation between the two pump modes is nonclassical.     

The Weak-Coupling of Bose-Einstein Condensates

The coherent characteristics of four trapped Bose-Einstein condensates (BEC) conjunct one by one in aring shape which is divided by two far off-resonant lasers, are studied. Four coupled Gross-Pitaevskii equations are usedto describe the dynamics of the system. Two kinds of self-trapping effects are discussed in the coupled BECs, and thephase diagrams for different initial conditions and different coupling strengths are discussed. This study can be used todetermine interaction parameters between atoms in BEC.     

Hyperbolic Bending of Vortex Lines with Finite Number and Length in Rotating Trapped Bose-Einstein Condensates

The minimal energy configurations of hyperbolic bending vortex lines in the rotating trapped Bose-Einstein condensates are investigated by using a variational ansatz and numerical simulation. The theoretical calculation of the energy of the vortex lines as a function of the rotation frequency gives self-consistently vortex number, curvature and configuration. The numerical results show that bending is more stable than straight vortex line along the z-axis, and the vortex configuration in the xy-plane has a little expansion by increasing z.     

Collective Excitations in Spin-2 Bose-Einstein Condensates

The Green‘s functions and the correlation functions in spin-2 Bose-Einstein condensates at finite temperature are defined and the generalized Dyson-Beliaev equations are introduced. We discuss the spin conservation in z direction and decouple thre Green‘s functions and the generalized Dyson-Beliaev equations according to different spin conservations in z direction. The anomalous vertex functions are introduced and the self-energies are separated into the proper self-energies and the improper self-energies. The generalized Dyson-Beliaev equations are decoupled according to separation of the self-energies. We calculate the Green‘s functions step by step in the Bogoliubov approximation and discuss the collective excitations in spin-2 Bose-Einstein condensates in the polar, ferromagnetic, and cyclic cases,respectively.     

Entanglement in Bose-Einstein Condensates with One-Body Losses

We investigate quantum entanglement in two mutually non-interacting and spatially non-overlapping Bose-Einstein condensates in two harmonic potentials with one-body losses. One-body losses play an important role in the dynamical process of generating quantum entanglement. The stronger one-body losses induce more entanglement and maintain in a longer time interval.