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arXiv:1909.09786 · Journal of the Optical Society of America B

Gaussian-like and flat-top solitons of atoms with spatially modulated repulsive interactions

Liangwei Zeng, Jianhua Zeng

Published Jul 26, 2019• 24 citations
arXivHTMLPDF

Abstract

Solitons, nonlinear particle-like excitations with inalterable properties (amplitude, shape, and velocity) as they propagate, are omnipresent in many branches of science—and in physics in particular. Flat-top solitons are a novel type of bright solitons that have not been well explored in pure nonlinear media. Here, a model of nonlinear Kerr (cubic) media of ultracold atoms with spatially modulated repulsive interactions is proposed and shown to support a vast variety of stable flat-top matter-wave solitons, including one-dimensional flat-top fundamental and multipole solitons, and two-dimensional flat-top fundamental and vortex solitons. We demonstrate that by varying the relevant physical parameters (nonlinearity coefficient and chemical potential), the ordinary bright (Gaussian) solitons can transform into the novel flat-top solitons. The (in)stability domains of the flat-top soliton families are checked by means of linear stability analysis and reconfirmed by direct numerical simulations. This model is generic in the contexts of nonlinear optics and Bose–Einstein condensates, which provides direct experimental access to observe the predicted solutions.

DOI
10.1364/josab.36.002278

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Solitons, nonlinear particle-like excitations with inalterable properties (amplitude, shape, and velocity) as they propagate, are omnipresent in many branches of science—and in physics in particular. Flat-top solitons are a novel type of bright solitons that have not been well explored in pure nonlinear media. Here, a model of nonlinear Kerr (cubic) media of ultracold atoms with spatially modulated repulsive interactions is proposed and shown to support a vast variety of stable flat-top matter-wave solitons, including one-dimensional flat-top fundamental and multipole solitons, and two-dimensional flat-top fundamental and vortex solitons. We demonstrate that by varying the relevant physical parameters (nonlinearity coefficient and chemical potential), the ordinary bright (Gaussian) solitons can transform into the novel flat-top solitons. The (in)stability domains of the flat-top soliton families are checked by means of linear stability analysis and reconfirmed by direct numerical simulations. This model is generic in the contexts of nonlinear optics and Bose–Einstein condensates, which provides direct experimental access to observe the predicted solutions.
We theoretically investigate the transmission dynamics of coherent matter wave pulses across finite optical lattices in both the linear and the nonlinear regimes. The shape and the intensity of the transmitted pulse are found to strongly depend on the parameters of the incident pulse, in particular its velocity and density: a clear physical picture of the main features observed in the numerical simulations is given in terms of the atomic band dispersion in the periodic potential of the optical lattice. Signatures of nonlinear effects due to the atom-atom interaction are discussed in detail, such as atom-optical limiting and atom-optical bistability. For positive scattering lengths, matter waves propagating close to the top of the valence band are shown to be subject to modulational instability. A scheme for the experimental generation of narrow bright gap solitons from a wide Bose-Einstein condensate is proposed: the modulational instability is seeded starting from the strongly modulated density profile of a standing matter wave and the solitonic nature of the generated pulses is checked from their shape and their collisional properties.
Static and dynamic properties of matter-wave solitons in dense Bose–Einstein condensates, where three-body interactions play a significant role, have been studied by a variational approximation (VA) and numerical simulations. For experimentally relevant parameters, matter-wave solitons may acquire a flat-top shape, which suggests employing a super-Gaussian trial function for VA. Comparison of the soliton profiles, predicted by VA and those found from numerical solution of the governing Gross–Pitaevskii equation shows good agreement, thereby validating the proposed approach.
We investigate the properties of modulational instability in the Salerno equation in quasi-one dimension in Bose-Einstein condensate (BEC). We analyzed the regions of modulational instability of nonlinear plane waves and determine the conditions of its existence in BEC. The existence and stability of strongly localized modes in discrete media is investigated with the framework of the Salerno model by using a linear analysis method. The regions of stability and instability are determined. Also the existence of localized modes for different values of parameters is shown numerically by homoclinic orbits intersection method. The response of Bose–Einstein condensates is studied with strong dipole–dipole atomic interactions to periodically varying perturbation. The dynamics is governed by the Gross–Pitaevskii equation with an additional nonlinear term, corresponding to nonlocal dipolar interactions. A mathematical model, based on the variational approximation, has been developed and applied to study parametric excitation of the condensates due to coefficient of nonlocal nonlinearity varying periodically. The model predicts the waveform of solitons in dipolar condensates and describes their small amplitude dynamics quite accurately. Theoretical predictions are verified by numerical simulations of the nonlocal Gross–Pitaevskii equation and a good agreement between them is found. The results can lead to better understanding of the properties of ultra-cold quantum gases, such as 52Cr, 164Dy and 168Er, where the long-range dipolar atomic interactions dominate the usual contact interactions. Dynamics of a matter wave soliton bouncing on the reflecting surface (atomic mirror) under the effect of gravity has been studied by analytical and numerical means. The iv analytical description is based on the variational approach. Resonant oscillations of the soliton's center of mass and width, induced by appropriate modulation of the atomic scattering length and the slope of the linear potential are analyzed. In numerical experiments, we observe the Fermi type acceleration of the soliton when the vertical position of the reflecting surface is periodically varied in time. Analytical predictions are compared with the results of numerical simulations of the Gross-Pitaevskii equation and a qualitative agreement between them is found.
The novel phenomena arising from Bose-Einstein condensates with spatially and spatiotemporally modulated nonlinearities in external potential is reviewed from a theoretical viewpoint. We first present theoretical analysis and numerical studies of the localized nonlinear matter waves in one-dimensional single and two-component BECs with spatially and spatiotemporally modulated nonlinearities, respectively. It is shown that the spatially or spatiotemporally modulated nonlinearity can support stable novel localized nonlinear matter waves such as the breathing solitons and moving solitons. Then the quasi-two-dimensional BEC with spatially modulated nonlinearity is investigated and we show that all of the BECs, similar to the linear harmonic oscillator, can have an arbitrary number of localized nonlinear matter waves with discrete energies. Their properties are determined by the principal quantum number and secondary quantum number. Moreover, we investigate the quantized vortices in a rotating BEC with spatiotemporally modulated interaction in harmonic and anharmonic potentials, respectively. The exact quantized vortex and giant vortex solutions are constructed explicitly by similarity transformation. Their stability behavior is examined by numerical simulation, which shows that a new series of stable vortex states which are defined by radial and angular quantum numbers, can be supported by the spatiotemporally modulated interaction in this system. We find that there exist stable quantized vortices with large topological charges in repulsive condensates with spatiotemporally modulated interaction.
Optical lattices have been used as a versatile toolbox to control Bose-Einstein condensates (BECs) in recent years, and a wealth of emergent nonlinear phenomena have been found, including bright gap solitons and dark ones, among which the former has been realized in experiments. The latter, however, has only theoretical results and its fundamental properties are still not well understood. Here we theoretically and numerically explore an open issue of creating stable matter-wave dark gap solitons in a one-dimensional optical lattice, onto which the BECs with self-defocusing quintic nonlinearity are loaded. Using linear-stability analysis and direct simulations, the formation, structures, and properties of dark gap solitons in quintic nonlinearity have been compared to those upheld by cubic Kerr nonlinearity. In particular, we uncover that the dark gap solitons and soliton clusters are robustly stable in the first finite band gap of the underlying linear spectrum, and are hard to be stabilized in the second gap. The predicted dark gap solitons are observable in current experiments on dense ultracold atoms, using an optical lattice technique, and in the optics domain for nonlinear light propagation in periodic optical media with quintic nonlinearity.
We present a theoretical analysis of three-dimensional (3D) matter-wave solitons and their stability properties in coupled atomic and molecular Bose-Einstein condensates (BECs). The soliton solutions to the mean-field equations are obtained in an approximate analytical form by means of a variational approach. We investigate soliton stability within the parameter space described by the atom-molecule conversion coupling, the atom-atom sss-wave scattering, and the bare formation energy of the molecular species. In terms of ordinary optics, this is analogous to the process of sub- or second-harmonic generation in a quadratic nonlinear medium modified by a cubic nonlinearity, together with a phase mismatch term between the fields. While the possibility of formation of multidimensional spatiotemporal solitons in pure quadratic media has been theoretically demonstrated previously, here we extend this prediction to matter-wave interactions in BEC systems where higher-order nonlinear processes due to interparticle collisions are unavoidable and may not be neglected. The stability of the solitons predicted for repulsive atom-atom interactions is investigated by direct numerical simulations of the equations of motion in a full 3D lattice. Our analysis also leads to a possible technique for demonstrating the ground state of the Schr\"odinger-Newton and related equations that describe Bose-Einstein condensates with nonlocal interparticle forces.