Modulational Instability and Quantum Discrete Breather States of Cold Bosonic Atoms in a Zig-Zag Optical Lattice

Xu, Chunju; Xie, Jiayu; Wu, Tianle; Tang, Bing

doi:10.1007/s10773-018-3747-x

Cited by 7 publications

(1 citation statement)

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“…Exact solutions were found via the exp function method and the hyperbolic function methods [15]. In [16], a theoretical study on modulation instability and quantum discrete breather states in a system of cold bosonic atoms in zigzag optical lattices was presented. A density-dependent gauge field may induce density-induced geometric frustration.…”

Section: Introductionmentioning

confidence: 99%

On continuum model analog to zig-zag optical lattice in quantum optics

Tantawy

Abdel‐Gawad

2021

Appl. Phys. B

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A discrete model governing a system of cold bosonic atoms in zig-zag optical lattices in quantum optics was proposed in the literature. In an analog to this model, a continuum model is, here constructed. The resulting equation is a nonlinear Schrodinger equation NLSE with drift force and linear growth. Exact solutions of this equation are obtained. To this issue, a new transformation that allows to inspect the optical lattice due to soliton-periodic wave collision is introduced. Here, the colliding dynamics are inspected. A class of polynomial and rational solutions of the model equation constructed are obtained by using the unified and generalized unified methods. The solutions found reveal the propagation of local zigzagshaped pulses in optical lattices. Mixed smooth-sharp (shock-like) optical pulses are also observed. This leads to the issue that the collision is locally elastic (or inelastic). Furthermore, self-modulation zigzag-shaped pulses with compression, are remarked. We mention that the zigzag-shaped pulses, in an optical lattice, was not found in the literature. Thus, the results found in this work are original. It is found that the polarization of zig-zag optical lattice is self-focusing.

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Section: Introductionmentioning

confidence: 99%

On continuum model analog to zig-zag optical lattice in quantum optics

Tantawy

Abdel‐Gawad

2021

Appl. Phys. B

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Analytical insights into cold bosonic atoms in a zigzag optical lattice: Invariant analysis, exact solutions, and bifurcation analysis using phase portraits

Yadav,

Kumar Gupta

2024

Math Methods in App Sciences

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This work delves into the behavior of cold bosonic atoms within a zigzag optical lattice which offers a rich platform for studying quantum many‐body physics and has potential applications in various fields including quantum simulation, quantum computing, and precision measurement. The study aims to derive exact solutions and explore qualitative properties through dynamical analysis. Exact solutions of the nonlinear differential equation model can provide insights into the behavior of bosonic atoms in complex optical lattice configurations, allowing researchers to simulate and study phenomena such as quantum phase transitions, many‐body localization, and exotic states of matter. The invariant analysis has been performed for the first time on the specified equation, yielding a reduced system of equations with forms that are easier to handle. Novel techniques are applied to extract solutions from the reduced system of equations obtained via invariant analysis. The results reveal a rich set of solutions, including various traveling wave solutions and doubly periodic functions in the form of Jacobian elliptic functions. Bifurcation analysis, conducted through phase portraits, provides insights into the system's long‐term behavior under different parameter values. This work contributes to a deeper understanding of the dynamics of cold bosonic atoms in optical lattices via 2D and 3D plots of obtained solutions depicting the change in the behavior of soliton solutions with fractional derivative parameter.

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