# Double photon emission, half photon absorption

Is it possible for atom with two electons to absorb one photon in this manner,

$$|gg\rangle|n\rangle \to |ee\rangle|n-1\rangle$$

or for one electron to emit two photons like this

$$|e\rangle|n\rangle \to |g\rangle|n+2\rangle$$

or maybe two different frequencies like this

$$|e\rangle|n\rangle_{f_1}|m\rangle_{f_2} \to |g\rangle|n+1\rangle_{f_1}|m+1\rangle_{f_2}$$

The third process is just sequential de-excitation via some intermediate state. One example would be the production of electronic excited molecular hydrogen in a discharge so that singlet and triplet Rydberg states of H$_2$ are populated. The singlet states will decay by a single photon to the ground state, but the triplet states will first decay to the lowest excited triplet state that is metastable and subsequently decay to the singlet ground state via spin-orbit interaction.