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Register a new userSymmetry breaking of quantum droplets in a dual-core trap
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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.
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We introduce a dual-core system with double symmetry, one between the cores, and one along each core, imposed by the spatial modulation of local nonlinearity in the form of two tightly localized spots, which may be approximated by a pair of ideal delta-functions. The analysis aims to investigate effects of spontaneous symmetry breaking in such systems. Stationary one-dimensional modes are constructed in an implicit analytical form. These solutions include symmetric ones, as well as modes with spontaneously broken inter-core and along-the-cores symmetries. Solutions featuring the simultaneous (double) breaking of both symmetries are produced too. In the model with the ideal delta-functions, all species of the asymmetric modes are found to be unstable. However, numerical consideration of a two dimensional extension of the system, which includes symmetric cores with a nonzero transverse thickness, and the nonlinearity-localization spots of a small finite size, produces stable asymmetric modes of all the types, realizing the separate breaking of each symmetry, and states featuring simultaneous (double) breaking of both symmetries.
It was recently demonstrated that two-dimensional Townes solitons (TSs) in two-component systems with cubic self-focusing, which are normally made unstable by the critical collapse, can be stabilized by linear spin-orbit coupling (SOC), in Bose-Einstein condensates and optics alike. We demonstrate that one-dimensional TSs, realized as optical spatial solitons in a planar dual-core waveguide with dominant quintic self-focusing, may be stabilized by SOC-like terms emulated by obliquity of the coupling between cores of the waveguide. Thus, SOC offers a universal mechanism for the stabilization of the TSs. A combination of systematic numerical considerations and analytical approximations identifies a vast stability area for skew-symmetric solitons in the systems main (semi-infinite) and annex (finite) bandgaps. Tilted (moving) solitons are unstable, spontaneously evolving into robust breathers. For broad solitons, diffraction, represented by second derivatives in the system, may be neglected, leading to a simplified model with a finite bandgap. It is populated by skew-antisymmetric gap solitons, which are nearly stable close to the gaps bottom.
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.
Quantum adiabatic evolution, an important fundamental concept inphysics, describes the dynamical evolution arbitrarily close to the instantaneous eigenstate of a slowly driven Hamiltonian. In most systems undergoing spontaneous symmetry-breaking transitions, their two lowest eigenstates change from non-degenerate to degenerate. Therefore, due to the corresponding energy-gap vanishes, the conventional adiabatic condition becomes invalid. Here we explore the existence of quantum adiabatic evolutions in spontaneous symmetry-breaking transitions and derive a symmetry-dependent adiabatic condition. Because the driven Hamiltonian conserves the symmetry in the whole process, the transition between different instantaneous eigenstates with different symmetries is forbidden. Therefore, even if the minimum energy-gap vanishes, symmetry-protected quantum adiabatic evolutioncan still appear when the driven system varies according to the symmetry-dependent adiabatic condition. This study not only advances our understandings of quantum adiabatic evolution and spontaneous symmetry-breaking transitions, but also provides extensive applications ranging from quantum state engineering, topological Thouless pumping to quantum computing.
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.
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