We numerically and analytically investigate the formations and features of two-dimensional discrete Bose–Einstein condensate solitons, which are constructed by quadrupole–quadrupole interactional particles trapped in the tunable anisotropic discrete optical lattices. The square optical lattices in the model can be formed by two pairs of interfering plane waves with different intensities. Two hopping rates of the particles in the orthogonal directions are different, which gives rise to a linear anisotropic system. We find that if all of the pairs of dipole and anti-dipole are perpendicular to the lattice panel and the line connecting the dipole and anti-dipole which compose the quadrupole is parallel to horizontal direction, both the linear anisotropy and the nonlocal nonlinear one can strongly influence the formations of the solitons. There exist three patterns of stable solitons, namely horizontal elongation quasi-one-dimensional discrete solitons, disk-shape isotropic pattern solitons and vertical elongation quasi-continuous solitons. We systematically demonstrate the relationships of chemical potential, size and shape of the soliton with its total norm and vertical hopping rate and analytically reveal the linear dispersion relation for quasi-one-dimensional discrete solitons.
We demonstrate the nonreciprocal dynamics of discrete solitons (DSs) induced by a uniform synthetic gauge phase (SGP) in one-dimensional waveguide array. The SGP is embedded into the coupling constant between the waveguides, which provides a directional momentum to the propagating fields and creates a nonreciprocal for the system. When a kicked Gaussian wave packet propagates through the waveguide arrays, diode effects are formed. Dependence between the diode effect and the SGP is studied. We found that the threshold of the reverse breakdown of this optical diode exhibits a perfect linear dependence against the SGP, and an extremely high diode quality can be achieved when the initial phase tilt exactly compensates the initial momentum provided by the SGP. Moreover, the direction of the diode can be switched by the direction of the SGP, which brings additional freedom to control the one-way propagation of the DSs. Our finding may have potential application to realizing new devices in high-speed all-optical communications.
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