The atom interacts with an electromagnetic wave, and the interaction is approximately the coupling between the dipole moment \(\hat{\mathbf{d}}\) associated with the \(|g\rangle \leftrightarrow|e\rang...The atom interacts with an electromagnetic wave, and the interaction is approximately the coupling between the dipole moment \(\hat{\mathbf{d}}\) associated with the \(|g\rangle \leftrightarrow|e\rangle\) transition and the electric field E, leading to the interaction Hamiltonian \[H_{\mathrm{int}}=g|e\rangle\langle g|\left(\hat{a} e^{-i \omega t}+\hat{a}^{\dagger} e^{i \omega t}\right)+g^{*}| g\rangle\langle e|\left(\hat{a} e^{-i \omega t}+\hat{a}^{\dagger} e^{i \omega t}\right).\tag{9.45}\]