Stable and mobile two-dimensional dipolar ring-dark-in-bright Bose–Einstein condensate soliton

Adhikari, Sadhan K.

doi:10.1088/1612-2011/13/3/035502

Cited by 6 publications

(2 citation statements)

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“…The main purpose of this work is to present a systematic study of a prototypical soliton among the relevant coherent structures, namely the ring dark soliton (RDS) but in the present setting as a genuinely 3D structure. The RDS has been intensively studied in 2D in both one-and two-component condensates [13][14][15][16][17]. In 2D, the soliton has a ring density node with a phase difference of π across the ring.…”

Section: Introductionmentioning

confidence: 99%

Ring dark solitons in three-dimensional Bose-Einstein condensates

2019

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In this work we present a systematic study of the three-dimensional extension of the ring dark soliton examining its existence, stability, and dynamics in isotropic harmonically trapped Bose-Einstein condensates. Detuning the chemical potential from the linear limit, the ring dark soliton becomes unstable immediately, but can be fully stabilized by an external cylindrical potential. The ring has a large number of unstable modes which are analyzed through spectral stability analysis. Furthermore, a few typical destabilization dynamical scenarios are revealed with a number of interesting vortical structures emerging such as the two or four coaxial parallel vortex rings. In the process of considering the stability of the structure, we also develop a modified version of the degenerate perturbation theory method for characterizing the spectra of the coherent structure. This semianalytical method can be reliably applied to any soliton with a linear limit to explore its spectral properties near this limit. The good agreement of the resulting spectrum is illustrated via a comparison with the full numerical Bogolyubov-de Gennes spectrum. The application of the method to the two-component ring dark-bright soliton is also discussed. * Electronic address: wenlongcmp@gmail.com † Electronic address: kevrekid@math.umass.edu FIG. 1: Density contour and phase profile of a stationary ring dark soliton in a spherical harmonic trap of frequency ω = 1 at chemical potential µ = 16 (Eq. (1)). There is a ring of vanishing density separating two segments with phase difference of π shown as two different colours (red and green). Note the ring is not vertically straight, but bends. The state is generated from numerical computation. the incongruence between the cylindrical symmetry of the 2D pattern and the closer to spherical (or more accurately: ellipsoidal) nature of the 3D condensate. A cross section perpendicular to the axis is a 2D ring, and the radius is larger at the edges and smaller at the center. See Fig. 1 for a density and phase profile of the RDS.Despite its extensive analysis in the 2D case, including the recent corroboration of its modes of vibration and even its multi-component extension [18], the RDS has not been studied in detail in three dimensions. Instead, other structures, such as the planar dark soliton (PDS) [19,20] and the spherical dark soliton (SDS) [20,21] have been considered due to their symmetry. The latter have been dynamically recognized as generating spontaneously structures such as vortex rings and multi-ring generalizations thereof [19,22,23]. In that arXiv:1910.02272v1 [cond-mat.quant-gas]

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Section: Introductionmentioning

confidence: 99%

Ring dark solitons in three-dimensional Bose-Einstein condensates

2019

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“…The recent observation of dipolar BECs of 52 Cr [8], 164 Dy [9] and 168 Er [10] atoms have started a great deal of activity in this area [11,12,13,14,15,16,17,18,19,20] including new investigation of BEC solitons in a different scenario. Apart from quasi-1D bright dipolar BEC solitons [21], asymmetric quasi-2D bright [22,23,24,25,26,27,28] and vortex [29,30] solitons have been predicted. Also, in a dipolar BEC, unlike in a nondipolar BEC, these solitons can be realized for a repulsive contact interaction.…”

Section: Introductionmentioning

confidence: 99%

Two-dimensional bright and dark-in-bright dipolar Bose–Einstein condensate solitons on a one-dimensional optical lattice

Adhikari¹

2016

Laser Phys. Lett.

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We study the statics and dynamics of anisotropic, stable, bright and dark-inbright dipolar quasi-two-dimensional Bose-Einstein condensate (BEC) solitons on a one-dimensional (1D) optical-lattice (OL) potential. These solitons mobile in a plane perpendicular to the 1D OL trap can have both repulsive and attractive contact interactions. The dark-in-bright solitons are the excited states of the bright solitons. The solitons, when subject to a small perturbation, exhibit sustained breathing oscillation. The dark-in-bright solitons can be created by phase imprinting a bright soliton. At medium velocities the collision between two solitons is found to be quasi elastic. The results are demonstrated by a numerical simulation of the three-dimensional mean-field Gross-Pitaevskii equation in three spatial dimensions employing realistic interaction parameters for a dipolar 164 Dy BEC.

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OpenMP GNU and Intel Fortran programs for solving the time-dependent Gross–Pitaevskii equation

Young-S.

Muruganandam

Adhikari

et al. 2017

Computer Physics Communications

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We present Open Multi-Processing (OpenMP) version of Fortran 90 programs for solving the Gross-Pitaevskii (GP) equation for a Bose-Einstein condensate in one, two, and three spatial dimensions, optimized for use with GNU and Intel compilers. We use the split-step Crank-Nicolson algorithm for imaginary-and real-time propagation, which enables efficient calculation of stationary and non-stationary solutions, respectively. The present OpenMP programs are designed for computers with multi-core processors and optimized for compiling with both commercially-licensed Intel Fortran and popular free open-source GNU Fortran compiler. The programs are easy to use and are elaborated with helpful comments for the users. All input parameters are listed at the beginning of each program. Different output files provide physical quantities such as energy, chemical potential, root-mean-square sizes, densities, etc. We also present speedup test results for new versions of the programs. New version program summaryProgram title: BEC-GP-OMP-FOR software package, consisting of: (i) imag1d-th, (ii) imag2d-th, (iii) imag3d-th, (iv) imagaxi-th, (v) imagcir-th, (vi) imagsph-th, (vii) real1d-th, (viii) real2d-th, (ix) real3d-th, (x) realaxi-th, (xi) realcir-th, (xii) realsph-th. . Now virtually all computers have multi-core processors and some have motherboards with more than one physical computer processing unit (CPU), which may increase the number of available CPU cores on a single computer to several tens. The C programs have been adopted to be very fast on such multi-core modern computers using general-purpose graphic processing units (GPGPU) with Nvidia CUDA and computer clusters using Message Passing Interface (MPI) [6]. Nevertheless, previously developed Fortran programs are also commonly used for scientific computation and most of them use a single CPU core at a time in modern multi-core laptops, desktops, and workstations. Unless the Fortran programs are made aware and capable of making efficient use of the available CPU cores, the solution of even a realistic dynamical 1d problem, not to mention the more complicated 2d and 3d problems, could be time consuming using the Fortran programs. Previously, we published auto-parallel Fortran programs [2] suitable for Intel (but not GNU) compiler for solving the GP equation. Hence, a need for the full OpenMP version of the Fortran programs to reduce the execution time cannot be overemphasized. To address this issue, we provide here such OpenMP Fortran programs, optimized for both Intel and GNU Fortran compilers and capable of using all available CPU cores, which can significantly reduce the execution time. Summary of revisions: Previous Fortran programs [1]for solving the time-dependent GP equation in 1d, 2d, and 3d with different trap symmetries have been parallelized using the OpenMP interface to reduce the execution time on multi-core processors.There are six different trap symmetries considered, resulting in six programs for imaginary-time propagation and six for real-time propa...

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Stable and mobile two-dimensional dipolar ring-dark-in-bright Bose–Einstein condensate soliton

Cited by 6 publications

References 54 publications

Ring dark solitons in three-dimensional Bose-Einstein condensates

Ring dark solitons in three-dimensional Bose-Einstein condensates

Two-dimensional bright and dark-in-bright dipolar Bose–Einstein condensate solitons on a one-dimensional optical lattice

OpenMP GNU and Intel Fortran programs for solving the time-dependent Gross–Pitaevskii equation

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