https://doi.org/10.1140/epjd/s10053-023-00599-4
Regular Article – Atomic Physics
Dominant Lyapunov mapping in phase and parameters spaces corresponding to the thermodynamic limit of the two-mode Bose–Hubbard model applied to the control of collapses of Josephson oscillations
1
Programa de Pós-Graduação em Modelagem Matemática e Computacional, Av. Amazonas, 7675, CEP 30510-000, Belo Horizonte, Brazil
2
Departamento de Matemática, Centro Federal de Educação Tecnológica de Minas Gerais (CEFET-MG), Av. Amazonas, 7675, CEP 30510-000, Belo Horizonte, Brazil
Received:
16
June
2022
Accepted:
13
January
2023
Published online:
25
January
2023
In this work, we propose the mapping of the phase space and parameters space of a classical counterpart of a system of spinless interacting bosonic particles trapped in a double-well potential submitted to a temporal modulation of on-site atom–atom interaction. To do this, we present a mapping of the dominant Lyapunov exponent of the equations of motion governed by the classical Hamiltonian corresponding to the thermodynamic limit of the two-mode Bose–Hubbard model. Such a proposal can be used to determine parameter ranges and regions of atomic coherent states that are amenable to undergo the control of collapses of Josephson oscillations. Our findings suggest that states and parameters associated with regular regime in the classical domain are amenable to this control be applied, whereas states settled in chaotic regions are not eligible.
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