Is there a difference between "two photon absorption" and "double quantum transitions"? Wikipedia has articles on two photon absorption. And a lot of NMR literature refers to double quantum transitions. But is there a difference? 
As far as I can tell, a double quantum transition is has an intermediate step. $m = 1 \rightarrow m=2 \rightarrow m=3$. But two photon absorption just absorbs two photons and skips the $m = 2$ state. 
 A: AS I see 

"double quantum transition. [¦dəb·əl ′kwänt·əm tran′sish·ən] (atomic physics) A radiative transition between atomic or molecular states in which two or more photons are simultaneously emitted or absorbed."

See the source here:
http://www.spectroscopynow.com/userfiles/sepspec/file/specNOW/Tutorials/UnderstandingNMR_Keeler_ch2.pdf
Two photon absorption frequently happens and is frequently the cause of phosphorescence. But as you see from the source, phosphorescence is only one way of the "deactivation processes", this is the process where the electron goes back to ground state.
See the source here:
http://chem.libretexts.org/Core/Physical_and_Theoretical_Chemistry/Spectroscopy/Electronic_Spectroscopy/Electronic_Spectroscopy%3A_Theory
As you refer to, "double quantum transitions" is not so much different from Two photon absorption, here are the differences and similarities:


*

*They both are mainly about electron spin and the differences between singlet and triplet states. 

*But in the NMR articles about double quantum transitions, they are using frequencies to differentiate between energy levels, whereas for Two photon absorption, they usually go over absorption and emission rates, and their timescale.

*In the case of two photon absorption, they are mainly trying to explain the different ways of "deactivation processes".

*In both cases they try to talk about and explain the transition process of the electron going back to ground state. 
So as you see the two phrases are mainly the same thing, but in the two photon absorption article they are trying to explain the different deactivation processes, and the timescales, whereas in the NMS article they are trying to explain the different frequency/energy levels.
