Chaos‐related Localization in Modulated Lattice Array

Li, Liping; Wang, Bo; Lü, Xin-You; Wu, Ying

doi:10.1002/andp.201700218

Cited by 4 publications

(2 citation statements)

References 40 publications

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“…Thus, selectively irradiating the top waveguide with two harmonic frequencies is well within the reach of the related experimental setup. Dynamics of the system is governed by the dimensionless Hamiltonian (h = 1) [50][51][52],…”

Section: Model and Methodsmentioning

confidence: 99%

Integer and Fractional Floquet Resonances in a Driven Three-Well System

Wang

2022

Photonics

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We investigate Floquet dynamics of a particle held in a three-well system driven by a two-frequency field and identify integer and fractional photon resonances due to the dual-frequency driving. It is found that pairs of photon-assisted tunneling near the resonance originate from avoided level crossings in the Floquet spectra which, in essence, are quantum features of the hybridization between different quantum states. In particular, we establish a close connection between fractional-order resonances and Floquet mode properties under two-frequency driving conditions and illustrate their dependence on driving parameters. These results provide us a possibility to realize coherent control of quantum states with the assistance of classical external driving fields.

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Section: Model and Methodsmentioning

confidence: 99%

Integer and Fractional Floquet Resonances in a Driven Three-Well System

Wang

2022

Photonics

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“…In the presence of s-wave interactions, BECs can form dark and bright soliton [5][6][7][8][9][10][11][12] and exhibit Newton's cradle behavior [13], which are paradigmatic examples in nonlinear physics. In trap array and optical lattice settings, the self-trapping of the BEC emerges due to strong repulsive interactions [14][15][16][17][18][19][20][21][22][23], where the BEC is localized within a single site. This is in contrast to the homogeneous, superfluid state, which form the ground state of an infinite lattice when the interaction is weak [24][25][26].…”

Section: Introductionmentioning

confidence: 99%

Hyperchaos in a Bose-Hubbard Chain with Rydberg-Dressed Interactions

McCormack

Nath

2021

Photonics

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We study the chaos and hyperchaos of Rydberg-dressed Bose–Einstein condensates (BECs) in a one-dimensional optical lattice. Due to the long-range, soft-core interaction between the dressed atoms, the dynamics of the BECs are described by the extended Bose-Hubbard model. In the mean-field regime, we analyze the dynamical stability of the BEC by focusing on the ground state and localized state configurations. Lyapunov exponents of the two configurations are calculated by varying the soft-core interaction strength, potential bias, and length of the lattice. Both configurations can have multiple positive Lyapunov exponents, exhibiting hyperchaotic dynamics. We show the dependence of the number of the positive Lyapunov exponents and the largest Lyapunov exponent on the length of the optical lattice. The largest Lyapunov exponent is directly proportional to areas of phase space encompassed by the associated Poincaré sections. We demonstrate that linear and hysteresis quenches of the lattice potential and the dressed interaction lead to distinct dynamics due to the chaos and hyperchaos. Our work is relevant to current research on chaos as well as collective and emergent nonlinear dynamics of BECs with long-range interactions.

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