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| Main Authors: | , , |
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| Format: | Preprint |
| Published: |
2024
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2402.17545 |
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| _version_ | 1866914889277112320 |
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| author | Sakhel, Asaad R. Ragan, Robert J. Mullin, William J. |
| author_facet | Sakhel, Asaad R. Ragan, Robert J. Mullin, William J. |
| contents | The Gross-Pitaevskii equation (GPE) in a double well potential produces solutions that break the symmetry of the underlying non-interacting Hamiltonian, i.e., asymmetric solutions. The GPE is derived from the more general second-quantized Fock Schroedinger equation (FSE). We investigate whether such solutions appear in the more general case or are artifacts of the GPE. We use two-mode analyses for a variational treatment of the GPE and to treat the Fock equation. An exact diagonalization of the FSE in dual-condensates yields degenerate ground states that are very accurately fitted by phase-state representations of the degenerate asymmetric states found in the GPE. The superposition of degenerate asymmetrical states forms a cat state. An alternative form of cat state results from a change of the two-mode basis set. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2402_17545 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Accuracy of the Gross-Pitaevskii Equation in a Double-Well Potential Sakhel, Asaad R. Ragan, Robert J. Mullin, William J. Quantum Physics Quantum Gases The Gross-Pitaevskii equation (GPE) in a double well potential produces solutions that break the symmetry of the underlying non-interacting Hamiltonian, i.e., asymmetric solutions. The GPE is derived from the more general second-quantized Fock Schroedinger equation (FSE). We investigate whether such solutions appear in the more general case or are artifacts of the GPE. We use two-mode analyses for a variational treatment of the GPE and to treat the Fock equation. An exact diagonalization of the FSE in dual-condensates yields degenerate ground states that are very accurately fitted by phase-state representations of the degenerate asymmetric states found in the GPE. The superposition of degenerate asymmetrical states forms a cat state. An alternative form of cat state results from a change of the two-mode basis set. |
| title | Accuracy of the Gross-Pitaevskii Equation in a Double-Well Potential |
| topic | Quantum Physics Quantum Gases |
| url | https://arxiv.org/abs/2402.17545 |