Conditions for Time-Independence of N-level Systems under the Rotating Wave Approximation (RWA) and Dipole Selection Rules
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arXiv
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| Format: | Preprint |
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2025
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| _version_ | 1866918163033096192 |
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| author | Paing, Phoenix M. M. James, Daniel F. V. |
| author_facet | Paing, Phoenix M. M. James, Daniel F. V. |
| contents | We analyze the time-dependence of N-level systems under the Rotating Wave Approximation and dipole selection rules. Such systems can be solved straightforwardly if the Hamiltonian can be transformed into a time-independent form. The conditions under which a unitary transformation can be used to render time-dependent Hamiltonians into a time-independent form, thereby making the solution, are examined. After case-by-case analysis of different four and five-level systems, we conclude that systems having only one odd or even parity level achieve time-independence. In contrast, the others must satisfy a condition of laser detuning to achieve time-independence. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2503_21689 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Conditions for Time-Independence of N-level Systems under the Rotating Wave Approximation (RWA) and Dipole Selection Rules Paing, Phoenix M. M. James, Daniel F. V. Quantum Physics We analyze the time-dependence of N-level systems under the Rotating Wave Approximation and dipole selection rules. Such systems can be solved straightforwardly if the Hamiltonian can be transformed into a time-independent form. The conditions under which a unitary transformation can be used to render time-dependent Hamiltonians into a time-independent form, thereby making the solution, are examined. After case-by-case analysis of different four and five-level systems, we conclude that systems having only one odd or even parity level achieve time-independence. In contrast, the others must satisfy a condition of laser detuning to achieve time-independence. |
| title | Conditions for Time-Independence of N-level Systems under the Rotating Wave Approximation (RWA) and Dipole Selection Rules |
| topic | Quantum Physics |
| url | https://arxiv.org/abs/2503.21689 |