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We consider a binary bosonic condensate with weak mean-field (MF) residual repulsion, loaded in an array of nearly one-dimensional traps coupled by transverse hopping. With the MF force balanced by the effectively one-dimensional attraction, induced in each trap by the Lee-Hung-Yang correction (produced by quantum fluctuations around the MF state), stable onsite-centered and intersite-centered semi-discrete quantum droplets (QDs) emerge in the array, as fundamental ones and self-trapped vortices, with winding numbers, at least, up to 5, in both tightly-bound and quasi-continuum forms. The application of a relatively strong trapping potential leads to squeezing transitions, which increase the number of sites in fundamental QDs, and eventually replace vortex modes by fundamental or dipole ones. The results provide the first realization of stable semi-discrete vortex QDs, including ones with multiple vorticity.
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We consider the dynamical model of a binary bosonic gas trapped in a symmetric dual-core cigar-shaped potential. The setting is modeled by a system of linearly-coupled one-dimensional Gross-Pitaevskii equations with the 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 symmetric parallel-coupled trapping cores, following the increase of the QDs 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, $kappa$, and convex at larger $kappa $. The loop does not exist above a critical value of $kappa $. 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 constant zero and finite values of the wave function. Collisions between moving QDs are considered too, demonstrating a trend to merger into breathers.
We demonstrate a possibility of the creation of stable optical solitons combining one continuous and one discrete coordinate, with embedded vorticity, in an array of planar waveguides with intrinsic cubic-quintic nonlinearity. The same system may be realized in terms of the spatiotemporal light propagation in an array of tunnel-coupled optical fibers with the cubic-quintic nonlinearity. In contrast with zero-vorticity states, semidiscrete vortex solitons do not exist without the quintic term in the nonlinearity. Two types of the solitons, emph{viz.}, intersite- and onsite-centered ones (IC and OC, respectively), with even and odd numbers $N$ of actually excited sites in the discrete direction, are identified. We consider the modes carrying the embedded vorticity $S=1$ and $2$. In accordance with their symmetry, the vortex solitons of the OC type exhibit an intrinsic core, while the IC solitons with a small $N$ may have a coreless structure. Facilitating their creation in the experiment, the modes reported in the present work may be much more compact states than their counterparts considered in other systems, and they feature strong anisotropy. They can be set in motion in the discrete direction, provided that the coupling constant exceeds a certain minimum value. Collisions between moving vortex solitons are considered too.
The article produces a brief review of some recent results which predict stable propagation of solitons and solitary vortices in models based on the nonlinear Schroedinger equation including fractional one- or two-dimensional diffraction and cubic or cubic-quintic nonlinear terms, as well as linear potentials. The fractional diffraction is represented by fractional-order spatial derivatives of the Riesz type, defined in terms of the direct and inverse Fourier transform. In this form, it can be realized by spatial-domain light propagation in optical setups with a specially devised combination of mirrors, lenses, and phase masks. The results presented in the article were chiefly obtained in a numerical form. Some analytical findings are included too -- in particular, for fast moving solitons, and results produced by the variational approximation. Also briefly considered are dissipative solitons which are governed by the fractional complex Ginzburg-Landau equation.
We consider the existence, stability and dynamics of the nodeless state and fundamental nonlinear excitations, such as vortices, for a quasi-two-dimensional polariton condensate in the presence of pumping and nonlinear damping. We find a series of interesting features that can be directly contrastedto the case of the typically energy-conserving ultracold alkali-atom Bose-Einstein condensates (BECs). For sizeable parameter ranges, in line with earlier findings, the nodeless state becomes unstable towards the formation of {em stable} nonlinear single or multi-vortex excitations. The potential instability of the single vortex is also examined and is found to possess similar characteristics to those of the nodeless cloud. We also report that, contrary to what is known, e.g., for the atomic BEC case, {it stable} stationary gray rings (that can be thought of as radial forms of a Nozaki-Bekki hole) can be found for polariton condensates in suitable parametric regimes. In other regimes, however, these may also suffer symmetry breaking instabilities. The dynamical, pattern-forming implications of the above instabilities are explored through direct numerical simulations and, in turn, give rise to waveforms with triangular or quadrupolar symmetry.
The rotation of a quantum liquid induces vortices to carry angular momentum. When the system is composed of multiple components that are distinguishable from each other, vortex cores in one component may be filled by particles of the other component, and coreless vortices form. Based on evidence from computational methods, here we show that the formation of coreless vortices occurs very similarly for repulsively interacting bosons and fermions, largely independent of the form of the particle interactions. We further address the connection to the Halperin wave functions of non-polarized quantum Hall states.
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