Symmetric and asymmetric solitons trapped in<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mi mathvariant="sans-serif">H</mml:mi></mml:math>-shaped potentials

Hung, Nguyen Viet; Trippenbach, Marek; Malomed, Boris A.

doi:10.1103/physreva.84.053618

Cited by 17 publications

(17 citation statements)

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“…Nonlinear Schrödinger (NLS) equations on quantum graphs have been recently studied in many physical and mathematical aspects [18]. In the physical literature, mostly in the context of Bose-Einstein condensation, various types of graphs have been modeled to show formation and trapping of standing waves [6,14,25,26,30]. In the mathematical literature, existence, variational properties, stability, and scattering have been studied on star graphs, including the Y -shaped graphs [2,3,4].…”

Section: Introductionmentioning

confidence: 99%

Ground State on the Dumbbell Graph

Marzuola

Pelinovsky

2016

Appl Math Res Express

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We consider standing waves in the focusing nonlinear Schrödinger (NLS) equation on a dumbbell graph (two rings attached to a central line segment subject to the Kirchhoff boundary conditions at the junctions). In the limit of small L 2 norm, the ground state (the orbitally stable standing wave of the smallest energy at a fixed L 2 norm) is represented by a constant solution. However, when the L 2 norm is increased, this constant solution undertakes two bifurcations, where the first is the pitchfork (symmetry breaking) bifurcation and the second one is the symmetry preserving bifurcation. As a result of the first symmetry breaking bifurcation, the standing wave becomes more localized in one of the two rings. As a result of the second symmetry preserving bifurcation, the standing wave becomes localized in the central line segment. In the limit of large norm solutions, both standing waves are represented by a truncated solitary wave localized in either the ring or the central line segment. Both waves are stable local constrained minimizers of the energy for the fixed L 2 norm but the asymmetric wave supported in the ring has a smaller energy. The analytical results are confirmed by numerical approximations of the ground state on the dumbbell graph.

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Section: Introductionmentioning

confidence: 99%

Ground State on the Dumbbell Graph

Marzuola

Pelinovsky

2016

Appl Math Res Express

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“…By solving Eqs. (6) and (14) with m = 0, 1 we find the boundaries t(v) separating the various regions for the ground state in δ, as shown in Fig. 6.…”

Section: B Eigenfunctionsmentioning

confidence: 72%

“…In order to compute the energy spectra E(t, v) for g = 0 and fix the parameters m and x 0 in the eigenfunctions we need to solve Eqs. (6) and (14). For this we use the Newton and quasi-Newton methods integrated in Wolfram Mathematica, which require an initial guess close enough to the solution.…”

Section: A Energy Spectramentioning

confidence: 99%

Stationary Real Solutions of the Nonlinear Schrödinger Equation on a Ring with a Defect

Pérez-Obiol

Cheon

2019

J. Phys. Soc. Jpn.

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We analyze the 1D cubic nonlinear stationary Schrödinger equation on a ring with a defect for both focusing and defocusing nonlinearity. All possible δ and δ boundary conditions are considered at the defect, computing for each of them the real eigenfunctions, written as Jacobi elliptic functions, and eigenvalues for the ground state and first few excited energy levels. All six independent Jacobi elliptic functions are found to be solutions of some boundary condition.We also provide a way to map all eigenfunctions satisfying δ/δ conditions to any other general boundary condition or point-like potential.

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“…The concept of SSB in nonlinear systems was introduced by J. C. Eilbeck [72]. Its manifestations can be found in a variety of settings, including classical and quantum mechanics, dual-core optical waveguides and Bragg gratings, nonlinear discrete systems, nonlinear optics and other physical systems [72][73][74][75]. In particular, SSB effects were studied in detail in BECs [76][77][78][79][80][81][82][83][84].…”

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confidence: 99%

Symmetry breaking of a matter-wave soliton in a double-well potential formed by spatially confined spin-orbit coupling

Chen

Zheng

et al. 2020

Chaos, Solitons & Fractals

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We consider the symmetry breaking of a matter-wave soliton formed by spinor Bose-Einstein condensates (BECs) illuminated by a two-spot laser beam. This laser beam introduces spin-orbit (SO) coupling in the BECs such that the SO coupling produces an effect similar to a linear doublewell potential (DWP). It is well known that symmetry breaking in a DWP is an important effect and has been discussed in many kinds of systems. However, it has not yet been discussed in a DWP formed by SO coupling. The objective of this work is to study the symmetry breaking of spinor BECs trapped by a DWP formed by SO coupling. We find that two kinds of symmetry breaking, displacement symmetry breaking and bimodal symmetry breaking, can be obtained in this model. The influence of the symmetry transition is systematically discussed by controlling the interaction strength of the BECs and the distance between the center of the two spots. Moreover, because SO coupling violates Galilean invariance, the influence of symmetry breaking in the moving system is also addressed in this paper. PACS numbers: 03.75.Lm, 05.45.Yv I. INTRODUCTIONMatter-wave solitons have become an interesting subject of research due to their potential applications in various fields, such as atomic interferometry, quantum information processing, and atomic lasers [1]. Experimental research on a self-trapping soliton in Bose-Einstein condensates (BECs) began with the creation of a dark soliton, followed by bright soliton and bright soliton trains [2][3][4][5]. Many studies have shown that a cold-atom BEC is an excellent system for studying solitons [6][7][8][9][10]. In particular, a stable bright soliton has already been shown to improve the performance of a Mach-Zehnder interferometer compared to regular BECs [11]. Thus, the creation of stable soliton has become a fascinating area of research.Recently, the Gross-Pitaevskii equation (GPE) with the LHY correction term has been proven to be a good mechanism to generate stable quantum droplets , and the GP equation with long-range dipole-dipole interactions can also create stable matter-wave solitons in BECs [35][36][37][38][39]. With the help of spin-orbit (SO) coupling, absolutely stable (ground-state) and metastable matter-wave solitons in 2D and 3D free space have been reported [40][41][42][43][44][45][46][47][48][49]. Moreover, stable excited state solitons [50-54], gap solitons [55,56], and solitons with novel vortices [57][58][59][60][61][62] have been reported to be created by SO coupling [63,64], and similar configurations have also been realized in an optical system [65][66][67][68][69]. However, previous studies on 2D and 3D solitons in BECs with SO coupling tacitly assumed that the SO couplings were a homogeneous effect in the entire space. Recently, by using an external laser beam of a finite width, it was shown that one can implement spatially confined SO coupling, i.e., an SO coupling defect, in spinor BECs in 1D [70] and 2D [71] space. It is interesting to find that solitons are trapped and caught by the SO co...

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Symmetric and asymmetric solitons trapped inH-shaped potentials

Cited by 17 publications

References 64 publications

Ground State on the Dumbbell Graph

Ground State on the Dumbbell Graph

Stationary Real Solutions of the Nonlinear Schrödinger Equation on a Ring with a Defect

Symmetry breaking of a matter-wave soliton in a double-well potential formed by spatially confined spin-orbit coupling

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