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Second-neighbor hopping effects on the dynamics of breathers in 2D quantum ultracold atoms loaded in optical lattices

Zacharie Isidore Djoufack, Jean Pierre Nguenang, A. Kenfack-Jiotsa

Published Nov 6, 2024• 0 citations
Publisher

Abstract

Abstract We explore analytically and numerically the dual role played bythe second-neighbor hopping on the modulation instability and onthe dynamics of breathers in 2D quantum ultracold atoms loaded inoptical lattices. Via the linear stability analysis, it is shownthat the dispersion relation formed exhibits intriguing forms. Itis found that, the existence conditions of appearance of themodulational intability (MI) regions and the growth rate may besignificantly affected by the second neighbor hopping couplingstrength. To support the analytical studies, direct numericalsimulations of MI is carried out to show the generation of a trainof short waves exhibiting periodic W-shaped and V-shaped solitonswith decreasing amplitude as time evolves. The emergence ofbreathers in the regions where the MI manifests is predicted to beinfluenced by the second neighbor hopping coupling strength. Bymaking use of Rayleigh-Ritz variational method and in agreementwith the MI analysis, the analytical results reveal the existenceof the radial symmetric modes called the dynamics of breathers.The accuracy of the outcomes is checked by numerical calculationswhich show a good agreement with the theoretical analysis.

DOI
10.21203/rs.3.rs-5321036/v1

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Abstract We explore analytically and numerically the dual role played bythe second-neighbor hopping on the modulation instability and onthe dynamics of breathers in 2D quantum ultracold atoms loaded inoptical lattices. Via the linear stability analysis, it is shownthat the dispersion relation formed exhibits intriguing forms. Itis found that, the existence conditions of appearance of themodulational intability (MI) regions and the growth rate may besignificantly affected by the second neighbor hopping couplingstrength. To support the analytical studies, direct numericalsimulations of MI is carried out to show the generation of a trainof short waves exhibiting periodic W-shaped and V-shaped solitonswith decreasing amplitude as time evolves. The emergence ofbreathers in the regions where the MI manifests is predicted to beinfluenced by the second neighbor hopping coupling strength. Bymaking use of Rayleigh-Ritz variational method and in agreementwith the MI analysis, the analytical results reveal the existenceof the radial symmetric modes called the dynamics of breathers.The accuracy of the outcomes is checked by numerical calculationswhich show a good agreement with the theoretical analysis.
In this paper, we employ the auxiliary equation method (AEM) to show the leverage of the nearest neighbors hopping and the boson–boson interaction in a zig zag optical lattice on the stressed optical solitons (os) and the Modulation Instability (MI) gain of cold bosonic atoms. The pedestal of the work is set on the continuum approximation of a cold bosonic atoms in a zig zag optical lattice which has demonstrated in detailed in refs. [Tala-Tebue E, Rezazadeh H, Djoufack ZI, et al. Optical solutions of cold bosonic atoms in a zig–zag optical lattice. Opt Quant Electron 53(2021):44; Djoufack ZI, TalaTebue E, FotsaNgafo F, et al. Quantum breathers associated with modulational instability in 1D ultracold boson in optical lattices involving nextnearest neighbor interactions. Optik 164(2018):575–589]. The results collected have enclosed bright, dark optical solitons and the combined bright-dark and bright-bright optical solitons. Compared the acquired results with Tala-Tebue et al. [Optical solutions of cold bosonic atoms in a zig–zag optical lattice. Opt Quant Electron 53(2021):44], further the os including U-shaped and W-shaped profile have been drop in and the powerful of the nearest neighbors hopping and the boson–boson interaction has been exposed across the spatiotemporal and plot evolution of the bright and dark os. Therewith, the MI bands have been stressed and it is observed some new attitude of the MI gain spectra under the induction of the model parameters. The collected results are new in literature in our knowledge and will improve the previous results acquired in refs. [Tala-Tebue E, Rezazadeh H, Djoufack ZI, et al. Optical solutions of cold bosonic atoms in a zig–zag optical lattice. Opt Quant Electron 53(2021):44; Djoufack ZI, TalaTebue E, FotsaNgafo F, et al. Quantum breathers associated with modulational instability in 1D ultracold boson in optical lattices involving nextnearest neighbor interactions. Optik 164(2018):575–589; Zhao XH, Tian B, Liu DY, et al. Dark solitons interaction for a (2+1)-dimensional nonlinear Schrödinger equation in the Heisenberg ferromagnetic spin chain. Superlattices Microstruct 100(2016):587–595; Uddin MF, Hafez MG, Hammouch Z, et al. Periodic and rogue waves for Heisenberg models of ferromagnetic spin chains with fractional beta derivative evolution and obliqueness. Waves Random Complex Media 2020. https://doi.org/10.1080/17455030.2020.1722331; Inc M, Aliyu AI, Yusuf A. Optical solitons to the nonlinear Shrdingers equation with spatio-temporal dispersion using complex amplitude ansatz. J Mod Opt 2017;64(21):2273–2280].
We investigate the properties of discrete breathers in a Bose-Einstein condensate with two- and three-body interactions in optical lattice. In the tight-binding approximation the Gross-Pitaevskii equation with periodic potential for the condensate wavefunction is reduced to the cubic-quintic discrete nonlinear Schrödinger equation. We analyze the regions of modulational instabilities of nonlinear plane waves. This result is important to obtain the conditions for generation of discrete solitons(breathers) in optical lattice. Also using the Page approach, we derive the conditions for the existence and stability for bright discrete breather solutions. It is shown that the quintic nonlinearity brings qualitatively new conditions for stability of strongly localized modes. The numerical simulations conform with the analytical predictions.
We investigate the dynamical instabilities of a one-dimensional ultracold Bose-Bose mixture with long-range dipole-dipole interactions, trapped in deep optical lattices and subject to periodically varying contact interaction. The effect of beyond-mean-field corrections due to quantum fluctuations is considered. In the tight-binding regime, we employ Wannier functions to derive a discrete nonlinear Schrödinger equation that captures the dynamics of the system. Using linear stability analysis coupled to multiple scale expansion, we systematically study the modulational and parametric instabilities of the system in the miscible regime, identifying the conditions under which these instabilities emerge. The corresponding instability domains are found and examined. The roles of long-range interactions and quantum fluctuations are highlighted, demonstrating their significant impact on the stability and dynamics of the lattice system. Our analytical predictions are validated through direct numerical simulations, which confirm the instability diagrams through the effective onset of instabilities and reveal the intricate interplay between interaction strength, quantum fluctuation, and the long-range nature of the dipole-dipole forces. This work provides insights into the control and manipulation of ultracold quantum gases in optical lattices, which have potential applications in quantum simulation and condensed-matter physics.
We study the properties of modulational instability and discrete breathers arising in a quasi-one-dimensional discrete Gross-Pitaevskii equation with Lee-Huang-Yang corrections. Conditions for modulation instability and instability regions of nonlinear plane waves are determined in parameter space. We analytically investigate the existence of different quantum droplet solutions, including intersite, onsite, front-like, flat-top, and dark localized modes, using the Page method and variational approach. Their stability is checked using linear stability analyses and numerical simulations. The analytical predictions corroborated with the numerical simulations.
Abstract Through a semiquantal procedure, we study the perturbed modulation of amplitude and phase of Gross-Piteavskii equation describing trapped Bose–Einstein condensates in an optical lattice potential. By introducing quantum correctional parameters, the problem is quantized and leads to the derivation of a novel dynamical instability criterion. Additional degrees of freedom carrying quantum properties play a central role on the refine of the instability bandwidth, and, combined to the strength of optical lattice potential, entail unstable modes into full stability. A set of computational tools exhibited various features that bear instability characteristics, to confirm analytically predicted results. The quantum fluctuations thus have a stabilizing effect on the dynamics of harmonically trapped Bose–Einstein condensates in an optical lattice potential.