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Add the weak coupling criteria of rotating wave approximation. |
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-\hbar\Omega^*e^{i\omega_Lt}|\text{g}\rangle\langle\text{e}|.
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Another critira for rotating wave approximation is the weak coupling condition, that is , the Rabi frequency should be much less than the transition frequency.
At this point the rotating wave approximation is complete. A common first step beyond this is to remove the remaining time dependence in the Hamiltonian via another unitary transformation.
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