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     

光晶格中双组分玻色-爱因斯坦凝聚系统的调制不稳定性

利用线性稳定分析的方法,在不满足原子流相等的条件下,对光晶格中双组分玻色-爱因斯坦凝聚原子(BEC)系统的调制不稳定性区域与不同BEC组分的波长和不同的调制波长,以及两组分BEC间相互作用大小之间的关系进行了研究.结果显示,光晶格中双组分BEC系统的调制稳定性的区域在不满足原子流相等的条件下,随不同的波长,不同的调制和相互作用之间的大小会出现了较大的变化.相应结果可为实际应用中如何操控双组分BEC提供有用的信息.     

Modulational instability for a self-attractive two-component Bose--Einstein condensate

By means of the multiple-scale expansion method, the coupled nonlinear Schr?dinger equations without an explicit external potential are obtained in two-dimensional geometry for a self-attractive Bose-Einstein condensate composed of different hyperfine states. The modulational instability of two-component condensate is investigated by using a simple technique. Based on the discussion about two typical cases, the explicit expression of the growth rate for a purely growing modulational instability and the optimum stable conditions are given and analysed analytically. The results show that the modulational instability of this two-dimensional system is quite different from that in a one-dimensional system.     

A variational approach to the modulational-oscillatory instability of Bose–Einstein condensates in an optical potential

We use the time-dependent variational approach to demonstrate how the modulational and oscillatory instabilities can be generated in Bose–Einstein condensates (BECs) trapped in a periodic optical lattice with weak driving harmonic potential. We derive and analyze the ordinary differential equations for the time evolution of the amplitude and phase of the modulational perturbation, and obtain the instability condition of the condensates through the effective potential. The effect of the optical potential on the dynamics of the BECs is shown. We perform direct numerical simulations to support our theoretical findings, and good agreement is found.     

Effects of three-body interactions in the parametric and modulational instabilities of Bose-Einstein condensates

The parametric modulational instability for a discrete nonlinear Schrödinger equation with a cubic-quintic nonlinearity is analyzed. This model describes the dynamics of BECs, with both two- and three-body interatomic interactions trapped in an optical lattice. We identify and discuss the salient features of the three-body interaction in the parametric modulational instability. It is shown that the three-body interaction term can both, shift as well as narrow the window of parametric instability, and also change the behavior of a modulationally stable and parametrically unstable BEC with attractive two-body interaction. We explore this instability through the multiple-scale analysis and identify it numerically. The effect of the three body losses have also been investigated.     

Stability of Two-Component Bose-Einstein Condensates in Bessel Optical Lattices

The stability of the ground state of two-component Bose-Einstein condensates （BEGs） loaded into the central well of an axially symmetric Bessel lattices （BLs） potential with attractive or repulsive atoms interactions is studied using the time-dependent Gross-Pitaevskii equation （GPE）. By using the variational method, we find that stable ground state of two-component BEGs can exist in BLs. The BLs＇s depth and the intra-species atom interaction play an important role in the stability of ground state. The collapse of two-component BEGs in BLs is also studied and a collapse condition for trapped two-component BEGs is obtained. It is shown that the two-component BEGs exhibit rich collapse dynamics. That is, the two-component BEGs can collapse in the system with both intra- and inter-attractive, or with intra-attractive and inter-repulsive, or with intra-repulsive and inter-attractive atom interactions. Furthermore, the control of the collapse of the two-component BEGs in BLs is discussed in detail. The stability diagram of the ground state in parameter space is obtained. The results show that the collapse of two-component BEGs can be controlled by temporal modulation of the atom interaction.     

The ground states and pseudospin textures of rotating two-component Bose–Einstein condensates trapped in harmonic plus quartic potential

The ground states of two-component miscible Bose–Einstein condensates(BECs) confined in a rotating annular trap are obtained by using the Thomas–Fermi(TF) approximation method.The ground state density distribution of the condensates experiences a transition from a disc shape to an annulus shape either when the angular frequency increases and the width and the center height of the trap are fixed,or when the width and the center height of the trap increase and the angular frequency is fixed.Meantime the numerical solutions of the ground states of the trapped two-component miscible BECs with the same condition are obtained by using imaginary-time propagation method.They are in good agreement with the solutions obtained by the TF approximation method.The ground states of the trapped two-component immiscible BECs are also given by using the imaginary-time propagation method.Furthermore,by introducing a normalized complex-valued spinor,three kinds of pseudospin textures of the BECs,i.e.,giant skyrmion,coaxial double-annulus skyrmion,and coaxial three-annulus skyrmion,are found.     

Modulational instability of nematic phase

We numerically observe the effect of homogeneous magnetic field on the modulationally stable case of polar phase in F = 2 spinor Bose-Einstein condensates (BECs). Also we investigate the modulational instability of uniaxial and biaxial (BN) states of polar phase. Our observations show that the magnetic field triggers the modulational instability and demonstrate that irrespective of the magnetic field effect the uniaxial and biaxial nematic phases show modulational instability.     

Modulational instability of dust acoustic waves in a dusty plasma with nonthermal electrons and ions

Effects of nonadiabaticity of variable dust charge, dust fluid temperature, trapped electrons as well as nonisothermality of ions on the amplitude modulation of dust acoustic waves in an unmagnetized dusty plasma are investigated. A modified nonlinear Schr?dinger equation (NLSE) is obtained by the standard reductive perturbation technique and is solved numerically by the split-step Fourier method. The modulational instability and the envelope solitary wave structure are found to be modified somewhat by the effects of nonthermally distributed ions and trapped electrons.     

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.     

Bessel型光晶格中双组分玻色-爱因斯坦凝聚体的基态解

研究了平面Bessel型光晶格(BL)中双组分玻色-爱因斯坦凝聚(BECs)体系的基态解.从描述三维(3D)BECs体系的动力学方程Gross-Pitaevskii方程(GPE)出发,当垂直方向囚禁频率远大于平面上囚禁频率时,得到了描述2D-BECs体系的动力学方程.利用双组分BECs体系中原子之间相互作用与BL强度相互平衡的条件,得到了平面BL光晶格中2D-GPE的一组基态精确解,给出了基态的原子数分布,总原子数和能量与原子之间相互作用强度及BL势的关系.相对于单组分BEC体系,由于不同组分原子相互作用的存在,使得BL光晶格中双组分BECs基态具有更丰富的结构.当不存在不同组分原子之间的相互作用时,模型简化到单组分体系,并给出了相应的基态解,原子数分布和能量. 关键词： Bessel型光晶格 基态解 双组分玻色-爱因斯坦凝聚     

Emergence of unstable modes in an expanding domain for energy-conserving wave equations

Motivated by recent work on instabilities in expanding domains in reaction-diffusion settings, we propose an analog of such mechanisms in energy-conserving wave equations. In particular, we consider a nonlinear Schrödinger equation in a finite domain and show how the expansion or contraction of the domain, under appropriate conditions, can destabilize its originally stable solutions through the modulational instability mechanism. Using both real and Fourier space diagnostics, we monitor and control the crossing of the instability threshold and, hence, the activation of the instability. We also consider how the manifestation of this mechanism is modified in a spatially inhomogeneous setting, namely in the presence of an external parabolic potential, which is relevant to trapped Bose-Einstein condensates.     

Modulational instability,quantum breathers and two-breathers in a frustrated ferromagnetic spin lattice under an external magnetic field

The modulational instability, quantum breathers and two-breathers in a frustrated easy-axis ferromagnetic zig-zag chain under an external magnetic field are investigated within the Hartree approximation. By means of a linear stability analysis, we analytically study the discrete modulational instability and analyze the effect of the frustration strength on the discrete modulational instability region. Using the results from the discrete modulational instability analysis, the presence conditions of those stationary bright type localized solutions are presented. On the other hand, we obtain the analytical expressions for the stationary bright localized solutions and analyze the effect of the frustration on their emergence conditions. By taking advantage of these bright type single-magnon bound wave functions obtained, quantum breather states in the present frustrated ferromagnetic zig-zag lattice are constructed. What is more, the analytical forms for quantum two-breather states are also obtained. In particular, the energy level formulas of quantum breathers and two-breathers are derived.     

Semiclassical dynamics of quasi-one-dimensional, attractive Bose-Einstein condensates

The strongly interacting regime for attractive Bose-Einstein condensates (BECs) tightly confined in an extended cylindrical trap is studied. For appropriately prepared, non-collapsing BECs, the ensuing dynamics are found to be governed by the one-dimensional focusing Nonlinear Schrödinger equation (NLS) in the semiclassical (small dispersion) regime. In spite of the modulational instability of this regime, some mathematically rigorous results on the strong asymptotics of the semiclassical limiting solutions were obtained recently. Using these results, “implosion-like” and “explosion-like” events are predicted whereby an initial hump focuses into a sharp spike which then expands into rapid oscillations. Seemingly related behavior has been observed in three-dimensional experiments and models, where a BEC with a sufficient number of atoms undergoes collapse. The dynamical regimes studied here, however, are not predicted to undergo collapse. Instead, distinct, ordered structures, appearing after the “implosion”, yield interesting new observables that may be experimentally accessible.     

Modulation of dust acoustic waves with non-adiabatic dust charge fluctuations

The modulational instability of dust acoustic waves in a dusty plasma with non-adiabatic dust charge fluctuation is studied. Using the perturbation method, a modified nonlinear Schrödinger equation containing a damping term that comes from the effect of dust charge variation is derived. It is found that the modulational instability of the wave packet and the propagation characters of the envelope solitary waves are modified significantly by the non-adiabatic dust charge fluctuation.     

One-dimensional modulational instability of broad optical beams in biased centrosymmetric photorefractive crystals

We study the one-dimensional modulational instability of broad optical beams in biased centrosymmetric photorefractive crystals under steady-state conditions. The one-dimensional modulational instability growth rates are obtained by globally and locally treating the space-charge field, which depend on the external bias field and the ratio of the intensity of optical beam to that of the dark irradiance. Our analysis indicates that the modulational instability growth rate in local effects can be determined from that in nonlocal effects.     

Analytical studies of two-component Bose-Einstein condensates in two-dimensional optical lattices

The two-component Bose-Einstein condensates (BECs) trapped in 2D optical lattice potential is studied analytically. A new family of stationary exact solutions of the coupled Gross-Pitaevskii (GP) equations with 2D periodic potential are obtained. In particular, the phase diagram of the system in the trigonometric limit is determined analytically according to the nontrivial phase macroscopic wave functions of the condensates.     

Stationary States and Modulational Instability of Coupled Two-Component Bose-Einstein Condensates in a Ring Trap

We investigate modulational instability (MI) of a coupled two-component Bose-Einstein condensates in a rotating ring trap. The excitation spectrum and the MI condition of the system are presented analytically. We find that the coupling between the two components strongly modifies the MI condition, and the MI condition is phase-dependent. Furthermore, we discuss the effect of MI on both density excitation and spin excitation. If the inter- and intra-component interaction strengths are all equal, the MI causes density excitation but not spin excitation, and if the inter- and intra-component interaction strengths are different, the MI causes both density excitation and spin excitation. Our results provide a promising approach for controlling the stability and excitation of a rotating two-component Bose-Einstein condensates by modulating its coupling strength and interaction strength.     

Dynamical superfluid-insulator transition in a chain of weakly coupled bose-Einstein condensates

We predict a dynamical classical superfluid-insulator transition in a Bose-Einstein condensate trapped in an optical and a magnetic potential. In the tight-binding limit, this system realizes an array of weakly coupled condensates driven by an external harmonic field. For small displacements of the parabolic trap about the equilibrium position, the condensates coherently oscillate in the array. For large displacements, the condensates remain localized on the side of the harmonic trap with a randomization of the relative phases. The superfluid-insulator transition is due to a discrete modulational instability, occurring when the condensate center of mass velocity is larger than a critical value.     

Nonlinear distribution function for a plasma obeying Vlasov-Maxwell system of equations

The nonlinear distribution function of Allis, generalised to include the transverse electromagnetic waves in a plasma, is used to set up the coupled wave equations for the longitudinal and the transverse modes. These are solved, keeping terms up to the cubic order of nonlinearity, by using the method of multiple scales. The equations of wave modulation are derived, which are solved to discuss the nature of the modulational instability and solitary wave propagation. It is found that the solutions so obtained satisfy conditions which are very similar to the well known Lighthill criterion for stability, appropriately modified due to the coupling of the two modes. The role of the average constant current due to any flow of the resonant and trapped electrons in determining the stability, is also discussed.