We consider the dynamical model of a binary bosonic gas trapped in a symmetric dual-core cigarshaped potential. The setting is modeled by a system of linearly-coupled one-dimensional Gross-Pitaevskii equations with cubic self-repulsive terms and quadratic attractive ones,which represent the Lee-Huang-Yang corrections to the mean-field theory in this geometry. The main subject is spontaneous symmetry breaking (SSB) of quantum droplets (QDs), followed by restoration of the symmetry, with respect to the identical parallel-coupled trapping cores, following the increase of the QD's total norm. The SSB transition and inverse symmetry-restoring one form a bifurcation loop, whose shape in concave at small values of the inter-core coupling constant, κ, and convex at larger κ. The loop does not exist above a critical value of κ. At very large values of the norm, QDs do not break their symmetry, featuring a flat-top shape. Some results are obtained in an analytical form, including an exact front solution connecting asymptotically constant zero and finite values of the wave function. Collisions between moving QDs are considered too, demonstrating a trend to merger into breathers.
We elaborate a method for the creation of two-and one-dimensional (2D and 1D) self-trapped modes in binary spin-orbit (SO)-coupled Bose-Einstein condensates (BECs) with the contact repulsive interaction, whose local strength grows fast enough from the center to periphery. In particular, an exact semi-vortex (SV) solution is found for the anti-Gaussian radial-modulation profile. The exact modes are included in the numerically produced family of SV solitons. Other families, in the form of mixed modes (MMs), as well as excited state of SVs and MMs, are produced too. While the excited states are unstable in all previously studied models, they are partially stable in the present one. In the 1D version of the system, exact solutions for the counterpart of the SVs, namely, semi-dipole solitons, are found too. Families of semi-dipoles, as well as the 1D version of MMs, are produced numerically.
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.
We numerically and analytically investigate the formations and features of two-dimensional discrete Bose–Einstein condensate solitons, which are constructed by quadrupole–quadrupole interactional particles trapped in the tunable anisotropic discrete optical lattices. The square optical lattices in the model can be formed by two pairs of interfering plane waves with different intensities. Two hopping rates of the particles in the orthogonal directions are different, which gives rise to a linear anisotropic system. We find that if all of the pairs of dipole and anti-dipole are perpendicular to the lattice panel and the line connecting the dipole and anti-dipole which compose the quadrupole is parallel to horizontal direction, both the linear anisotropy and the nonlocal nonlinear one can strongly influence the formations of the solitons. There exist three patterns of stable solitons, namely horizontal elongation quasi-one-dimensional discrete solitons, disk-shape isotropic pattern solitons and vertical elongation quasi-continuous solitons. We systematically demonstrate the relationships of chemical potential, size and shape of the soliton with its total norm and vertical hopping rate and analytically reveal the linear dispersion relation for quasi-one-dimensional discrete solitons.
§ These two authors contributed equally to the workWe consider possibilities to grasp and drag one-dimensional solitons in two-component Bose-Einstein condensates (BECs), under the action of gravity, by tweezers induced by spatially confined spin-orbit (SO) coupling applied to the BEC, with the help of focused laser illumination. Solitons of two types are considered, semi-dipoles and mixed modes. We find critical values of the gravity force, up to which the solitons may be held or transferred by the tweezers. The dependence of the critical force on the magnitude and spatial extension of the localized SO interaction, as well as on the soliton's norm and speed (in the transfer regime), are systematically studied by means of numerical methods, and analytically with the help of a quasi-particle approximation for the soliton. In particular, a noteworthy finding is that the critical gravity force increases with the increase of the transfer speed (i.e., moving solitons are more robust than quiescent ones). Nonstationary regimes are addressed too, by considering abrupt application of gravity to solitons created in the weightless setting. In that case, solitons feature damped shuttle motion, provided that the gravity force does not exceed a dynamical critical value, which is smaller than its static counterpart. The results may help to design gravimeters based on ultracold atoms. * Electronic address: hhzhong115@163.com
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