On quantization of weakly nonlinear lattices. Envelope solitons

We study linear transmission and nonlinear soliton transport through quasi-periodic structures, which profiles are described by multiple modulation frequencies. We show that resonant scattering at mixed-frequency resonances limits transmission efficiency of localized wave packets, leading to radiation and possible trapping of solitons. We obtain an explicit analytical expression for optimal quasi-periodic lattice profiles, where additional aperiodic modulations suppress mixed...

We study solitons arising in a system describing the interaction of a two-dimensional discrete hexagonal lattice with an additional electron field (or, in general, an exciton field). We assume that this interaction is electron-phonon-like. In our previous paper [4], we have studied the existence of two-dimensional solitons and have found that these solitons exist only if the electron-phonon coupling constant is sufficiently large. In this paper, we report the results of our i...

We show that when anharmonicity is added to the electron-phonon interaction it facilitates electron pairing in a localized state. Such localized state appears as singlet state of two electrons bound with the traveling local lattice soliton distortion which survives when Coulomb repulsion is included.

The discovery of a new type of solitons occuring in periodic systems without photonic bandgaps is reported. Solitons are nonlinear self-trapped wave packets. They have been extensively studied in many branches of physics. Solitons in periodic systems, which have become the mainstream of soliton research in the past decade, are localized states supported by photonic bandgaps. In this Letter, we report the discovery of a new type of solitons located at the Dirac point beyond ph...

We study the relations between solitons of nonlinear Schr\"{o}dinger equation described systems and eigen-states of linear Schr\"{o}dinger equation with some quantum wells. Many different non-degenerated solitons are re-derived from the eigen-states in the quantum wells. We show that the vector solitons for coupled system with attractive interactions correspond to the identical eigen-states with the ones of coupled systems with repulsive interactions. The energy eigenvalues o...

We consider the three-dimensional (3D) mean-field model for the Bose-Einstein condensate (BEC), with a 1D nonlinear lattice (NL), which periodically changes the sign of the nonlinearity along the axial direction, and the harmonic-oscillator trapping potential applied in the transverse plane. The lattice can be created as an optical or magnetic one, by means of available experimental techniques. The objective is to identify stable 3D solitons supported by the setting. Two meth...

We study quantum squeezing and entanglement of gap solitons in a Bose-Einstein condensate loaded into a one-dimensional optical lattice. By employing a linearized quantum theory we find that quantum noise squeezing of gap solitons, produced during their evolution, is enhanced compared with the atomic solitons in a lattice-free case due to intra-soliton structure of quantum correlations induced by the Bragg scattering in the periodic potential. We also show that nonlinear inte...

We present a thorough analysis of soliton solutions to the quasi-one-dimensional nonlinear Dirac equation (NLDE) for a Bose-Einstein condensate in a honeycomb lattice with armchair geometry. Our NLDE corresponds to a quasi-one-dimensional reduction of the honeycomb lattice along the zigzag direction, in direct analogy to graphene nanoribbons. Excitations in the remaining large direction of the lattice correspond to the linear subbands in the armchair nanoribbon spectrum. Anal...

We study a quasi-one-dimensional attractive Bose gas confined in an optical lattice with a superimposed harmonic potential by analyzing the effective one-dimensional Bose-Hubbard Hamiltonian of the system. In order to have a reliable description of the ground-state, that we call quantum bright soliton, we use the Density-Matrix-Renormalization-Group (DMRG) technique. By comparing DMRG results with mean-field (MF) ones we find that beyond-mean-field effects become relevant by ...

We study quantum dynamics of a dark soliton in a one-dimensional Bose gas in an optical lattice within the truncated Wigner approximation. A previous work has revealed that in the absence of quantum fluctuations, dynamical stability of the dark soliton significantly depends on whether its phase kink is located at a lattice site or a link of two neighboring sites. It has also shown that the dark soliton is unstable in a regime of strong quantum fluctuations regardless of the p...