Generation of optical and matter-wave solitons in binary systems with a periodically modulated coupling

Abstract

We present a systematic study of the generation of the array of optical or matter-wave kinks (dark solitons) in the ground state (GS) of binary systems. We consider quasi-one-dimensional systems described by a pair of nonlinear Schrödinger (NLSE's) or Gross-Pitaevskii equations (GPE's), which are coupled by the linear mixing, with local strength , and by nonlinear interactions. We assume the self-repulsive nonlinearity in both components, and include the effects of a harmonic trapping potential, while the nonlinear interaction between the components may be both repulsive and attractive. The model may be realized in terms of periodically modulated slab waveguides in nonlinear optics and also in Bose-Einstein condensates. Depending on the sign and strengths of the linear and nonlinear couplings between the components, the ground states in such binary systems may be symmetric, antisymmetric, or asymmetric. In this work, we introduce a periodic spatial modulation of the linear coupling, making an odd or even function of the coordinate (x). The sign flips of (x) strongly modify the structure of the GS in the binary system, as the relative sign of its components tends to lock to the local sign of . Using a systematic numerical analysis and an analytic approximation, we demonstrate that the GS of the trapped system contains one or several kinks (dark solitons) in one component, while the other component does not change its sign. The final results are presented in the form of maps showing the number of kinks in the GS as a function of the system's parameters, with the odd (even) modulation function giving rise to the odd (even) number of the kinks. The modulation of (x) also produces a strong effect on the transition between states with nearly equal and strongly unequal amplitudes of the two components.

Enhancement in the performance of a quantum battery by ordered and disordered interactions

“…Moreover, we observe that the Gaussian-distributed random interaction strengths, both in the xy-plane and in the z-direction of the XY Z model, enhance the quenched-averaged power compared to that of the ordered case. Such counterintuitive phenomena were already demonstrated in physical quantities like magnetization, correlation length, entanglement computed in the static scenario i.e., in the ground or in the thermal states of the disordered models [73][74][75][76][77][78][79][80][81][82][83][84][85][86][87][88][89][90][91][92]. Our results indicate that such advantages can also be found in closed dynamics of the systems with defects.…”

Classical spin models with broken symmetry: Random-field-induced order and persistence of spontaneous magnetization in the presence of a random field

“…It is also worth mentioning that there exists an analog of random-field-induced order in temporally and spatially disordered/modulated fields (for the works on generation of solitons and patterns in nonlinear wave equations, see [24,25]). Last, but not least, the effect was also mentioned in the general context of transport in disordered ultracold quantum gases [26] (see also [27]), localization of Bogoliubov modes [28], and disorder-induced trapping and Anderson localization in expanding Bose condensates [29].…”

“…Disorder-induced order persists also in 1D quantum spin chains [22]; the corresponding quantum phase transition is related to the one occurring for ferromagnetic chains in the staggered magnetic field (for recent studies, including effects in spin dynamics, see [23]). It is also worth mentioning that there exists an analog of random field induced order in temporally and spatially disordered/modulated fields (for the works on generation of solitons and patterns in non-linear wave equations, see [24,25]). Last, but not least, the effect was also mentioned in the general context of transport in disordered ultracold quantum gases [26], localization of Bogoliubov modes [27], and disorder-induced trapping and Anderson localization in expanding Bose condensates [28].…”

Domain walls and their interactions in a two-component Bose–Einstein condensate*

“…Based on the most of previous studies on vector solitons in two-component BEC, we can know that kink-type excitation can not be obtained with identical interspecies and intra-species interaction strengths. [19][20][21] Therefore we try to find kink and anti-kink excitations in some in-tegrable cases with different inter-species and intra-species interaction strengths. The integrability could enable us to discuss the interactions between DWs more clearly and conveniently.…”