Coupled Nonlinear Schrödinger Equations with a Gauge Potential: Existence and Blowup

Dias, João Paulo; Figueira, Mário

doi:10.1111/sapm.12102

Cited by 12 publications

(6 citation statements)

References 25 publications

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“…1(b) is non-monotonous. Also, in contrast to the solitons supported by the full SOC [21,22,25], but similar to 1D states maintained by SOC with the Zeeman lattice [24], the present 2D solitons exist above a threshold value of the norm,…”

Section: D System With 1d Spin-orbit Couplingmentioning

confidence: 57%

“…[20][21][22] it was shown that SOC may change the situation at cr U U  , creating stable 2D solitons, which represent the otherwise missing ground state in the system. In 3D, the supercritical collapse (which in the presence of SOC was studied in [25]) does not let SOC create the ground state, although 3D soliton solutions stable against small perturbations have been predicted [26].…”

Section: Introduction and Modelmentioning

confidence: 99%

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Multidimensional hybrid Bose-Einstein condensates stabilized by lower-dimensional spin-orbit coupling

Kartashov

Torner

Modugno

et al. 2020

Phys. Rev. Research

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We show that attractive spinor Bose-Einstein condensates under the action of spin-orbit coupling (SOC) and Zeeman splitting form self-sustained stable two-and three-dimensional (2D and 3D) states in free space, even when SOC acts in a lower-dimensional form. We find that two-dimensional states are stabilized by one-dimensional (1D) SOC in a broad range of chemical potentials, for atom numbers ( or norm of the spinor wavefunction) exceeding a threshold value, which strongly depends on the SOC strength and vanishes at a critical point. The zero-threshold point is a boundary between single-peaked and striped states, realizing hybrids combining 2D and 1D structural features. In a vicinity of such point, an asymptotic equation describing the bifurcation of the solitons from the linear spectrum is derived and investigated analytically. We show that striped 3D solitary states are as well stabilized by 2D SOC, albeit in a limited range of chemical potentials and norms.PhySH Subject Headings: Solitons; Superfluids; Mixtures of atomic and/or molecular quantum gases

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Section: D System With 1d Spin-orbit Couplingmentioning

confidence: 57%

Section: Introduction and Modelmentioning

confidence: 99%

Multidimensional hybrid Bose-Einstein condensates stabilized by lower-dimensional spin-orbit coupling

Kartashov

Torner

Modugno

et al. 2020

Phys. Rev. Research

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“…In the setting considered in Ref. [23], the SO coupling can protect 2D solitons against collapsing, creating a ground state [34], which is otherwise missing in 2D GPEs with the cubic self-attraction [35]- [38]. The collapse remains possible in the presence of SO coupling, starting with the norm of the input which exceeds the threshold value for the onset of the 2D collapse.…”

Section: Introductionmentioning

confidence: 97%

Two-dimensional composite solitons in Bose-Einstein condensates with spatially confined spin-orbit coupling

Zhang

Zhong

et al. 2019

Communications in Nonlinear Science and Numerical Simulation

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It was recently found that the spin-orbit (SO) coupling can help to create stable matter-wave solitons in spinor Bose-Einstein condensates in the two-dimensional (2D) free space. Being induced by external laser illumination, the effective SO coupling can be applied too in a spatially confined area. Using numerical methods and the variational approximation (VA), we build families of 2D solitons of the semi-vortex (SV) and mixed-mode (MM) types, and explore their stability, assuming that the SO-coupling strength is confined in the radial direction as a Gaussian. The most essential result is identification, by means of the VA and numerical methods, of the minimum size of the spatial confinement for which the 2D system maintains stable solitons of the SV and MM types.

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“…A fundamental problem which impedes the creation of 2D and 3D solitons in BEC, nonlinear optics, and other nonlinear settings, is that the ubiquitous cubic self-attraction, which usually gives rise to solitons, simultaneously drives the critical and supercritical collapse (catastrophic self-compression) in the 2D and 3D cases, respectively [19,20]. Although SOC modifies the conditions of the existence of solutions and of the blow up, it does not arrest the collapse completely [21]. The collapse destabilizes formally existing solitons, which makes stabilization of 2D and 3D solitons a well-known challenging problem [22,23].…”

Section: Introductionmentioning

confidence: 99%

Solitons in Bose-Einstein Condensates with Helicoidal Spin-Orbit Coupling

2017

Self Cite

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We report on the existence and stability of freely moving solitons in a spatially inhomogeneous Bose-Einstein condensate with helicoidal spin-orbit (SO) coupling. In spite of the periodically varying parameters, the system allows for existence of stable propagating solitons. Such states are found in the rotating frame, where the helicoidal SO coupling is reduced to a homogeneous one. In the absence of the Zeeman splitting the coupled Gross-Pitaevskii equations describing localized states feature many properties of the integrable systems. In particular, four-parametric families of solitons can be obtained in the exact form. Such solitons interact elastically. Zeeman splitting still allows for the existence of two families of moving solitons, but makes collisions of solitons inelastic. PACS numbers:When parameters of a continuous medium vary periodically the translational invariance is broken and nonlinear localized excitations cannot propagate freely. This is at variance with the linear systems, where the Bloch theory allows for quantum particles or waves to move without backscattering. The well-known examples are electrons in solids, atoms in optical latices, electromagnetic waves in photonic crystals, and many others. Physical understanding of the interplay between the nonlinearity and periodicity is simple. Since the nonlinear excitations are localized, in the presence of a periodic potential their energy depends on the spatial location of the wavepacket. Respectively, a steady forward motion is impossible because of the potential barriers causing radiative losses of moving localized wavepackets.. These facts are well documented, both theoretically and experimentally, in the physics of Bose-Einstein condensates (BECs) [1] and in nonlinear optics [2]. Several approaches to obtaining moving solitons in periodic media were suggested. Radiation is reduced for sufficiently wide and small-amplitude solitons in linear lattices (described using envelope function approach in photonics [3] or effective mass approximation in the meanfield theory [4]), as well as in nonlinear lattices [5]. Mobility of strongly localized solitons can be enhanced in lattices with saturable, quadratic or nonlocal nonlinearities, as well as in materials with competing linear and nonlinear lattices (see [6] for a review). However, in all these models radiation is not arrested completely: it becomes detectable at large propagation distances.In this Letter we show that freely moving nonlinear waves can exist if a system obeys special symmetries. In contrast to all previous studies, the solitons reported here do not radiate and propagate over infinitely long distances for any peak amplitude or any ratio of soliton width to system period. As the case example we consider a spin-orbit (SO) coupled BEC which is well accessible in laboratories [7,8] and represents a versatile tool for study of the nonlinear physics of synthetic fields [9] and gauge potentials [10,11]. We consider a SO-BEC described by the Hamiltonian, whose linear part reads2 /2 + ∆σ ...

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Coupled Nonlinear Schrödinger Equations with a Gauge Potential: Existence and Blowup

Cited by 12 publications

References 25 publications

Multidimensional hybrid Bose-Einstein condensates stabilized by lower-dimensional spin-orbit coupling

Multidimensional hybrid Bose-Einstein condensates stabilized by lower-dimensional spin-orbit coupling

Two-dimensional composite solitons in Bose-Einstein condensates with spatially confined spin-orbit coupling

Solitons in Bose-Einstein Condensates with Helicoidal Spin-Orbit Coupling

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