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Register a new userMatter-Wave Bright Solitons with a Finite Background in Spinor Bose-Einstein Condensates
موجات المادة الشديدة المنفردة مع خلفية محدودة في المجففات البوزي الإيثن سبينور
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نحن نقوم بتحقيق خصائص ديناميكية للسوليتون الساطعين مع خلفية محدودة في الإحياء البوزي-إيجنشتاين (BEC) بفرق F = 1، بناءً على نموذج سبينور قابل للحل الذي يساوي تفاضل الشبه الخطية الذي يحتوي على عدد غير محدود من الأعداد الصحيحة مع عدد صحيح واحد. نطبق طريقة الاستشعار العكسي المنصوصة للشروط الحدودية الغير محدودة. يمكن تصنيف الحلول السوليتون الناتجة كتطبيق عام لذلك الذي تحت الشروط الحدودية الصفرية. تم تحديد الحلول السوليتون الواحدة بشكل واضح. وفقا لسلوكها في الأبدية، فإنها تم تصنيفها إلى نوعين، نوع جدار النطاق (DW) ونوع تحويل الطور (PS). يدل DW-type على الحالة الفيرومغناطيسية مع حظوظ إجمالي ثابت و PS-type يدل على الحالة البولار، حيث يساوي حظوظ الإجمالي صفر. كما نناقش التصادمات السوليتون المزدوجة. وبالخصوص، يتم تأكيد ظاهرة خلط الإبراز في تصادم يشمل DW-type. يتوافق النتائج مع تلك التي تم الحصول عليها في الدراسات السابقة للسوليتون الساطعين تحت الشروط الحدودية الصفرية والسوليتون المظلمة. كنتيجة، نضمن ثبات وفعالية السوليتون المتعددة للإحياء البوزي-إيجنشتاين.
We investigate dynamical properties of bright solitons with a finite background in the F=1 spinor Bose-Einstein condensate (BEC), based on an integrable spinor model which is equivalent to the matrix nonlinear Schr{o}dinger equation with a self-focusing nonlineality. We apply the inverse scattering method formulated for nonvanishing boundary conditions. The resulting soliton solutions can be regarded as a generalization of those under vanishing boundary conditions. One-soliton solutions are derived in an explicit manner. According to the behaviors at the infinity, they are classified into two kinds, domain-wall (DW) type and phase-shift (PS) type. The DW-type implies the ferromagnetic state with nonzero total spin and the PS-type implies the polar state, where the total spin amounts to zero. We also discuss two-soliton collisions. In particular, the spin-mixing phenomenon is confirmed in a collision involving the DW-type. The results are consistent with those of the previous studies for bright solitons under vanishing boundary conditions and dark solitons. As a result, we establish the robustness and the usefulness of the multiple matter-wave solitons in the spinor BECs.
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We characterize the soliton solutions and their interactions for a system of coupled evolution equations of nonlinear Schrodinger (NLS) type that models the dynamics in one-dimensional repulsive Bose-Einstein condensates with spin one, taking advantage of the representation of such model as a special reduction of a 2 x 2 matrix NLS system. Specifically, we study in detail the case in which solutions tend to a non-zero background at space infinities. First we derive a compact representation for the multi-soliton solutions in the system using the Inverse Scattering Transform (IST). We introduce the notion of canonical form of a solution, corresponding to the case when the background is proportional to the identity. We show that solutions for which the asymptotic behavior at infinity is not proportional to the identity, referred to as being in non-canonical form, can be reduced to canonical form by unitary transformations that preserve the symmetric nature of the solution (physically corresponding to complex rotations of the quantization axes). Then we give a complete characterization of the two families of one-soliton solutions arising in this problem, corresponding to ferromagnetic and to polar states of the system, and we discuss how the physical parameters of the solitons for each family are related to the spectral data in the IST. We also show that any ferromagnetic one-soliton solution in canonical form can be reduced to a single dark soliton of the scalar NLS equation, and any polar one-soliton solution in canonical form is unitarily equivalent to a pair of oppositely polarized displaced scalar dark solitons up to a rotation of the quantization axes. Finally, we discuss two-soliton interactions and we present a complete classification of the possible scenarios that can arise depending on whether either soliton is of ferromagnetic or polar type.
Elongated Bose-Einstein condensates (BECs) exhibit strong spatial phase fluctuations even well below the BEC transition temperature. We demonstrate that atom interferometers using such condensates are robust against phase fluctuations, i.e. the relative phase of the split condensate is reproducible despite axial phase fluctuations. However, larger phase fluctuations limit the coherence time, especially in the presence of some asymmetries in the two wells of the interferometer.
Solitons are among the most distinguishing fundamental excitations in a wide range of non-linear systems such as water in narrow channels, high speed optical communication, molecular biology and astrophysics. Stabilized by a balance between spreading and focusing, solitons are wavepackets, which share some exceptional generic features like form-stability and particle-like properties. Ultra-cold quantum gases represent very pure and well-controlled non-linear systems, therefore offering unique possibilities to study soliton dynamics. Here we report on the first observation of long-lived dark and dark-bright solitons with lifetimes of up to several seconds as well as their dynamics in highly stable optically trapped $^{87}$Rb Bose-Einstein condensates. In particular, our detailed studies of dark and dark-bright soliton oscillations reveal the particle-like nature of these collective excitations for the first time. In addition, we discuss the collision between these two types of solitary excitations in Bose-Einstein condensates.
Extended Gross-Pitaevskii equations for the rotating F=2 condensate in a harmonic trap are solved both numerically and variationally using trial functions for each component of the wave function. Axially-symmetric vortex solutions are analyzed and energies of polar and cyclic states are calculated. The equilibrium transitions between different phases with changing of the magnetization are studied. We show that at high magnetization the ground state of the system is determined by interaction in density channel, and at low magnetization spin interactions play a dominant role. Although there are five hyperfine states, all the particles are always condensed in one, two or three states. Two novel types of vortex structures are also discussed.
We observe interlaced square vortex lattices in rotating two-component dilute-gas Bose-Einstein condensates (BEC). After preparing a hexagonal vortex lattice in a single-component BEC in an internal state $|1>$ of $^{87}$Rb atoms, we coherently transfer a fraction of the superfluid to a different internal state $|2>$. The subsequent evolution of this pseudo-spin-1/2 superfluid towards a state of offset square lattices involves an intriguing interplay of phase-separation and -mixing dynamics, both macroscopically and on the length scale of the vortex cores, and a stage of vortex turbulence. Stability of the square lattice structure is confirmed via the application of shear perturbations, after which the structure relaxes back to the square configuration. We use an interference technique to show the spatial offset between the two vortex lattices. Vortex cores in either component are filled by fluid of the other component, such that the spin-1/2 order parameter forms a Skyrmion lattice.
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