A. Gubeskys | Searcharxiv

arXiv2006

Mismatch management for optical and matter-wave quadratic solitons

We propose a way to control solitons in $χ^{(2)}$ (quadratically-nonlinear) systems by means of periodic modulation imposed on the phase-mismatch parameter ("mismatch management", MM). It may be realized in the co-transmission of fundamental-frequency (FF) and second-harmonic (SH) waves in a planar optical waveguide via a long-period modulation of the usual quasi-phase-matching pattern of ferroelectric domains. The MM may also be implemented by dint of the Feshbach resonance in a harmonically-modulated magnetic field in a hybrid atomic-molecular Bose-Einstein condensate (BEC), with the atomic and molecular mean fields (MFs) playing the roles of the FF and SH, respectively. The problem is analyzed by two methods. First, we identify stability regions for spatial solitons in the MM system, in terms of the MM amplitude and period, using the MF equations for spatially-inhomogeneous configurations. In particular, an instability enclave is found inside the stability area.The robustness of the solitons is also tested against variation of the shape of the input pulse, and a threshold for the formation of stable solitons is found in terms of its power. Interactions between solitons are virtually unaffected by the MM. The second method (\textit{parametric approximation}), going beyond the MF description, is developed for spatially-homogeneous states. It demonstrates that the MF description is valid for large modulation periods, while at smaller periods the non-MF component acquires gain, which implies destruction of MF under the action of the high-frequency MM.

physics.optics↗

arXiv2005

Two-component gap solitons in two- and one-dimensional Bose-Einstein condensates

We introduce 2D and 1D models of a binary Bose-Einstein condensate in a periodic potential, with repulsive interactions. We chiefly consider the most fundamental case of the inter-species repulsion with zero intra-species interactions. Existence and stability regions for gap solitons (GSs) supported by the interplay of the inter-species repulsion and periodic potential are identified. Two-component GSs are constructed by means of the variational approximation (VA) and in a numerical form. The VA provides accurate description for the GS which is a bound state of two tightly-bound components, each essentially trapped in one cell of the periodic potential. GSs of this type dominate in the case of intra-gap solitons, with both components belonging to the first finite bandgap of the linear spectrum. Inter-gap solitons, with one component residing in the second bandgap, and intra-gap solitons which have both components in the second gap, are possible in a deeper periodic potential, with the strength essentially exceeding the recoil energy of the atoms. Inter-gap solitons are, typically, bound states of one tightly- and one loosely-bound components. In this case, results are obtained in a numerical form. For 2D solitons, the stability is identified in direct simulations, while in the 1D case it is done via eigenfrequencies of small perturbations, and then verified by simulations. In the latter case, if the intra-gap soliton in the first bandgap is weakly unstable, it evolves into a stable breather, while unstable solitons of other types get completely destroyed. The intra-gap 2D solitons in the first bandgap are less robust, and in some cases they are completely destroyed by the instability. Addition of intra-species repulsion to the repulsion between the components leads to further stabilization of the GSs.

cond-mat.other↗