Content deleted Content added
Changed the Hamiltonian after approximation to include H_0. If this is not correct, that is the original energies of ground state g and excited state e get shifted up by hbar omega_0/2 then the text should reflect upon that. The way the approximation is stated now however, it seems that we only need to exclude the exponential terms in H_1 - therefore H_0 remains unchanged. |
Changed the final Hamiltonian in the Derivation in order to coincide with the recently changed Hamiltonian in the paragraph just above. |
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The atomic Hamiltonian was unaffected by the approximation, so the total Hamiltonian in the Schrödinger picture under the rotating wave approximation is
:
H^\text{RWA}=H_0+H_1^{\text{RWA}} = \frac{\hbar\omega_0}{2}|\text{e}\rangle\langle\text{e}|-
\frac{\hbar\omega_0}{2}|\text{g}\rangle\langle\text{g}|
-\hbar\Omega e^{-i\omega_Lt}|\text{e}\rangle\langle\text{g}|
-\hbar\Omega^*e^{i\omega_Lt}|\text{g}\rangle\langle\text{e}|.
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