Hyperchaos in a Bose-Hubbard Chain with Rydberg-Dressed Interactions
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...
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MDPI AG
2021-12-01
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| Series: | Photonics |
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| Online Access: | https://www.mdpi.com/2304-6732/8/12/554 |
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| author | Gary McCormack Rejish Nath Weibin Li |
| author_facet | Gary McCormack Rejish Nath Weibin Li |
| author_sort | Gary McCormack |
| collection | DOAJ |
| description | 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. |
| first_indexed | 2024-03-10T03:18:16Z |
| format | Article |
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| issn | 2304-6732 |
| language | English |
| last_indexed | 2024-03-10T03:18:16Z |
| publishDate | 2021-12-01 |
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| series | Photonics |
| spelling | doaj.art-3c74f3f14bb04d68b882a854b6e98df12023-11-23T10:08:47ZengMDPI AGPhotonics2304-67322021-12-0181255410.3390/photonics8120554Hyperchaos in a Bose-Hubbard Chain with Rydberg-Dressed InteractionsGary McCormack0Rejish Nath1Weibin Li2School of Physics and Astronomy, Centre for the Mathematics and Theoretical Physics of Quantum Non-Equilibrium Systems, University of Nottingham, Nottingham NG7 2RD, UKDepartment of Physics, Indian Institute of Science Education and Research, Pune 411 008, IndiaSchool of Physics and Astronomy, Centre for the Mathematics and Theoretical Physics of Quantum Non-Equilibrium Systems, University of Nottingham, Nottingham NG7 2RD, UKWe 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.https://www.mdpi.com/2304-6732/8/12/554hyperchaosBose–Einstein condensationRydberg dressingLyapunov exponentsdynamical stability |
| spellingShingle | Gary McCormack Rejish Nath Weibin Li Hyperchaos in a Bose-Hubbard Chain with Rydberg-Dressed Interactions Photonics hyperchaos Bose–Einstein condensation Rydberg dressing Lyapunov exponents dynamical stability |
| title | Hyperchaos in a Bose-Hubbard Chain with Rydberg-Dressed Interactions |
| title_full | Hyperchaos in a Bose-Hubbard Chain with Rydberg-Dressed Interactions |
| title_fullStr | Hyperchaos in a Bose-Hubbard Chain with Rydberg-Dressed Interactions |
| title_full_unstemmed | Hyperchaos in a Bose-Hubbard Chain with Rydberg-Dressed Interactions |
| title_short | Hyperchaos in a Bose-Hubbard Chain with Rydberg-Dressed Interactions |
| title_sort | hyperchaos in a bose hubbard chain with rydberg dressed interactions |
| topic | hyperchaos Bose–Einstein condensation Rydberg dressing Lyapunov exponents dynamical stability |
| url | https://www.mdpi.com/2304-6732/8/12/554 |
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