Conditions for Time-Independence of N-level Systems under the Rotating Wave Approximation (RWA) and Dipole Selection Rules

2025/03/27 by Phoenix M. M. Paing, Daniel F. V. James, Paing, Phoenix M. M. +1 · 1 citation
Engineering · Physics and Astronomy · #FOS: Physical sciences #Magnetic confinement fusion research #Particle accelerators and beam dynamics #Quantum Physics (quant-ph) #Quantum chaos and dynamical systems

paper · pdf · doi:10.48550/arxiv.2503.21689

openalex publication_date 2025/03/27 · openalex created_date 2025/10/11 · openalex updated_date 2026/07/31

Abstract

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.

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