共查询到20条相似文献,搜索用时 31 毫秒
1.
We investigate the structure of trapped Bose-Einstein condensates (BECs) with long-range anisotropic dipolar interactions. We find that a small perturbation in the trapping potential can lead to dramatic changes in the condensate's density profile for sufficiently large dipolar interaction strengths and trap aspect ratios. By employing perturbation theory, we relate these oscillations to a previously identified "rotonlike" mode in dipolar BECs. The same physics is responsible for radial density oscillations in vortex states of dipolar BECs that have been predicted previously. 相似文献
2.
New efficient and accurate numerical methods are proposed to compute ground states and dynamics of dipolar Bose–Einstein condensates (BECs) described by a three-dimensional (3D) Gross–Pitaevskii equation (GPE) with a dipolar interaction potential. Due to the high singularity in the dipolar interaction potential, it brings significant difficulties in mathematical analysis and numerical simulations of dipolar BECs. In this paper, by decoupling the two-body dipolar interaction potential into short-range (or local) and long-range interactions (or repulsive and attractive interactions), the GPE for dipolar BECs is reformulated as a Gross–Pitaevskii–Poisson type system. Based on this new mathematical formulation, we prove rigorously existence and uniqueness as well as nonexistence of the ground states, and discuss the existence of global weak solution and finite time blow-up of the dynamics in different parameter regimes of dipolar BECs. In addition, a backward Euler sine pseudospectral method is presented for computing the ground states and a time-splitting sine pseudospectral method is proposed for computing the dynamics of dipolar BECs. Due to the adoption of new mathematical formulation, our new numerical methods avoid evaluating integrals with high singularity and thus they are more efficient and accurate than those numerical methods currently used in the literatures for solving the problem. Extensive numerical examples in 3D are reported to demonstrate the efficiency and accuracy of our new numerical methods for computing the ground states and dynamics of dipolar BECs. 相似文献
3.
The ground states and pseudospin textures of rotating two-component Bose–Einstein condensates trapped in harmonic plus quartic potential 下载免费PDF全文
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. 相似文献
4.
R.?Fedele D.?Jovanovi? B.?Eliasson S.?De Nicola P. K.?Shukla 《The European Physical Journal B - Condensed Matter and Complex Systems》2010,74(1):97-116
On the basis of recent investigations, a newly developed analytical procedure is used for constructing a wide class of localized
solutions of the controlled three-dimensional (3D) Gross-Pitaevskii equation (GPE) that governs the dynamics of Bose-Einstein
condensates (BECs) in the presence of a spatio-temporally varying external potential. The controlled 3D GPE is decomposed
into a two-dimensional (2D) linear Schr?dinger equation (called the `transverse equation’) and a one-dimensional (1D) nonlinear
Schr?dinger equation (called the
`longitudinal equation’), constrained by a variational condition for
the controlling potential. The latter corresponds to the requirement
for the minimization of the control operation in the transverse
plane. Then, the above class of localized solutions are constructed as
the product of the solutions of the transverse and longitudinal equations.
A consistency condition between the transverse and longitudinal solutions
yields a relationship between the transverse and longitudinal restoring
forces produced by the external trapping potential well through a
`controlling parameter’ (i.e. the average, with respect to the transverse
profile, of the nonlinear inter-atomic interaction term of the GPE).
It is found that the longitudinal profile supports localized solutions in
the form of bright, dark or grey solitons with time-dependent
amplitudes, widths and centroids. The related longitudinal phase is
varying in space and time with time-dependent curvature radius and wavenumber.
In turn, all the above parameters (i.e. amplitudes, widths, centroids,
curvature radius and wavenumbers) can be easily expressed in terms of
the controlling parameter. It is also found that the transverse profile
has the form of Hermite-Gauss functions (depending on the transverse coordinates),
and the explicit spatio-temporal dependence of the controlling potential is
self-consistently determined. On the basis of these exact 3D analytical
solutions, a stability analysis is carried out, focusing our attention on
the physical conditions for having collapsing or non-collapsing solutions. 相似文献
5.
6.
CHEN Hai-Jun LI Hao-Cai XUE Ju-Kui 《理论物理通讯》2008,49(6):1519-1526
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. 相似文献
7.
《Physics letters. A》2006,358(1):74-79
The evolution of Bose–Einstein condensates (BECs) loaded into a periodic ring optical lattices (OL) trap is studied. By means of the variational method and direct numerical simulations of the Gross–Pitaevskii (GP) equation, the ground state properties and the vortex stabilities of the condensates for both repulsive and attractive cases are investigated. The results show that the bound states exist for determinate OL strength and interatomic interaction. However, the ground states of BECs undergo delocalizing–localizing transition for both attractive and repulsive cases as the strength of the OL or the interatomic interaction is decreased below the critical value. The ring OL can suppress the delocalizing transition efficiently. 相似文献
8.
Interaction between two coupled Bose-Einstein condensates (BECs) is investigated by the variational approach in two finite traps, and the effects of the spacing between the two traps on dynamics of the two BECs are analyzed. The spacing determines the stable condition of stationary states, affects the existence condition of each BEC, and changes the switching and self-trapping effects on the two BECs. The dynamic mechanism is demonstrated by performing a coordinate of classical particle moving in an effective potential field, and confirmed by the evolution of the atom population transferring ratio. 相似文献
9.
S. De Nicola R. Fedele D. Jovanovic B. Malomed M. A. Man'ko V. I. Man'ko P. K. Shukla 《The European Physical Journal B - Condensed Matter and Complex Systems》2006,54(1):113-119
We present one-dimensional (1D) stability analysis of a recently
proposed method to filter and control localized states of the
Bose–Einstein condensate (BEC), based on novel trapping
techniques that allow one to conceive methods to select a
particular BEC shape by controlling and manipulating the external
potential well in the three-dimensional (3D)
Gross–Pitaevskii equation (GPE). Within the framework of this
method, under suitable conditions, the GPE can be exactly
decomposed into a pair of coupled equations: a transverse
two-dimensional (2D) linear Schr?dinger equation and a
one-dimensional (1D) longitudinal nonlinear Schr?dinger
equation (NLSE) with, in a general case, a time-dependent
nonlinear coupling coefficient. We review the general idea how
to filter and control localized solutions of the GPE. Then,
the 1D longitudinal NLSE is numerically solved
with suitable non-ideal controlling potentials that differ from
the ideal one so as to introduce relatively small errors
in the designed spatial profile. It is shown that a BEC with an
asymmetric initial position in the confining potential exhibits
breather-like oscillations in the longitudinal direction but,
nevertheless, the BEC state remains confined within the potential
well for a long time. In particular, while the condensate remains
essentially stable, preserving its longitudinal soliton-like
shape, only a small part is lost into “radiation”. 相似文献
10.
《Physics letters. A》2019,383(25):3175-3179
Two different kinds of spin-orbit (SO) coupling are often investigated theoretically and experimentally in atomic Bose-Einstein condensates (BECs), namely, Rashba and Dresselhaus SO couplings. We show that ground states for these two SO-coupled BECs share lots of similarities and it is impossible to distinguish them from the observation of ground states. We find that an Ioffe-Pritchard magnetic field can be utilized as a tool to distinguish them. In the presence of the Ioffe-Pritchard magnetic field, ground states manifest distinctively for the Rashba and Dresselhaus SO-coupled BECs. 相似文献
11.
An overview of the physics of spinor and dipolar Bose–Einstein condensates (BECs) is given. Mean-field ground states, Bogoliubov spectra, and many-body ground and excited states of spinor BECs are discussed. Properties of spin-polarized dipolar BECs and those of spinor–dipolar BECs are reviewed. Some of the unique features of the vortices in spinor BECs such as fractional vortices and non-Abelian vortices are delineated. The symmetry of the order parameter is classified using group theory, and various topological excitations are investigated based on homotopy theory. Some of the more recent developments in a spinor BEC are discussed. 相似文献
12.
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. 相似文献
13.
We report observations of vortex formation by merging and interfering multiple (87)Rb Bose-Einstein condensates (BECs) in a confining potential. In this experiment, a single harmonic potential well is partitioned into three sections by a barrier, enabling the simultaneous formation of three independent, uncorrelated BECs. The BECs may either automatically merge together during their growth, or for high-energy barriers, the BECs can be merged together by barrier removal after their formation. Either process may instigate vortex formation in the resulting BEC, depending on the initially indeterminate relative phases of the condensates and the merging rate. 相似文献
14.
S. K. Adhikari 《The European Physical Journal D - Atomic, Molecular, Optical and Plasma Physics》2007,42(2):279-286
Using variational and numerical solutions we show that
stationary
negative-energy localized (normalizable) bound states can appear in the
three-dimensional nonlinear Schr?dinger equation with a finite
square-well potential for a range of nonlinearity parameters. Below a
critical attractive nonlinearity, the system becomes unstable and
experiences collapse. Above a limiting repulsive nonlinearity, the
system becomes highly repulsive and cannot be bound. The system also
allows nonnormalizable states of infinite norm at positive energies in
the continuum. The normalizable negative-energy bound states could be
created in BECs and studied in the laboratory with present knowhow. 相似文献
15.
We investigate the phenomena of symmetry breaking and phase transition
in the ground state of Bose-Einstein condensates (BECs) trapped in
a double square well and in an optical lattice well, respectively.
By using standing-wave expansion method, we present symmetric and
asymmetric ground state solutions of nonlinear Schrödinger
equation (NLSE) with a symmetric double square well potential for
attractive nonlinearity. In particular, we study the ground state
wave function's properties by changing the depth of potential
and atomic interactions (here we restrict ourselves to the attractive
regime). By using the Fourier grid Hamiltonian method, we also
reveal a phase transition of BECs trapped in one-dimensional
optical lattice potential. 相似文献
16.
This brief review summarizes recent theoretical and experimental results which predict and establish the existence of quantum droplets (QDs), i.e., robust two- and three-dimensional (2D and 3D) selftrapped states in Bose–Einstein condensates (BECs), which are stabilized by effective self-repulsion induced by quantum fluctuations around the mean-field (MF) states [alias the Lee–Huang–Yang (LHY) effect]. The basic models are presented, taking special care of the dimension crossover, 2D→3D. Recently reported experimental results, which exhibit stable 3D and quasi-2D QDs in binary BECs, with the inter-component attraction slightly exceeding the MF self-repulsion in each component, and in single-component condensates of atoms carrying permanent magnetic moments, are presented in some detail. The summary of theoretical results is focused, chiefly, on 3D and quasi-2D QDs with embedded vorticity, as the possibility to stabilize such states is a remarkable prediction. Stable vortex states are presented both for QDs in free space, and for singular but physically relevant 2D modes pulled to the center by the inverse-square potential, with the quantum collapse suppressed by the LHY effect. 相似文献
17.
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. 相似文献
18.
Matter-wave solutions of Bose—Einstein condensates with three-body interaction in linear magnetic and time-dependent laser fields 下载免费PDF全文
We construct, through a further extension of the tanh-function method, the matter-wave solutions of Bose-Einstein condensates (BECs) with a three-body interaction. The BECs are trapped in a potential comprising the linear magnetic and the time-dependent laser fields. The exact solutions obtained include soliton solutions, such as kink and antikink as well as bright, dark, multisolitonic modulated waves. We realize that the motion and the shape of the solitary wave can be manipulated by controlling the strengths of the fields. 相似文献
19.
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 相似文献
20.
Chen Jiao Jun-Cheng Liang Zi-Fa Yu Yan Chen Ai-Xia Zhang Ju-Kui Xue 《Frontiers of Physics》2022,17(6):61503
We study the ground-state phases, the stability phase diagram and collapse dynamics of Bose−Einstein condensates (BECs) with tunable spin−orbit (SO) coupling in the two-dimensional harmonic potential by variational analysis and numerical simulation. Here we propose the theory that the collapse stability and collapse dynamics of BECs in the external trapping potential can be manipulated by the periodic driving of Raman coupling (RC), which can be realized experimentally. Through the high-frequency approximation, an effective time-independent Floquet Hamiltonian with two-body interaction in the harmonic potential is obtained, which results in a tunable SO coupling and a new effective two-body interaction that can be manipulated by the periodic driving strength. Using the variational method, the phase transition boundary and collapse boundary of the system are obtained analytically, where the phase transition between the spin-nonpolarized phase with zero momentum (zero momentum phase) and spin-polarized phase with non-zero momentum (plane wave phase) can be manipulated by the external driving and sensitive to the strong external trapping potential. Particularly, it is revealed that the collapsed BECs can be stabilized by periodic driving of RC, and the mechanism of collapse stability manipulated by periodic driving of RC is clearly revealed. In addition, we find that the collapse velocity and collapse time of the system can be manipulated by periodic driving strength, which also depends on the RC, SO coupling strength and external trapping potential. Finally, the variational approximation is confirmed by numerical simulation of Gross−Pitaevskii equation. Our results show that the periodic driving of RC provides a platform for manipulating the ground-state phases, collapse stability and collapse dynamics of the SO coupled BECs in an external harmonic potential, which can be realized easily in current experiments. 相似文献