Previously I asked some questions on quantum coherence on physics stackexchange(PSE) (https://physics.stackexchange.com/questions/424578/what-is-quantum-coherence-what-does-it-really-signify-and-what-does-it-tell-us) and the answer helped me to clear the concept. I did some more literature review to understand the basic facts in relation to density matrix. But I have some more questions which I posted on PSE but no one seems to answer them. I am asking these question in the context of Nuclear Magnetic Resonance(NMR), Electron Paramagnetic Resonance(EPR) or Quantum Optics.

1. Taking Basis states as $|S_z^+\rangle = \begin{bmatrix}1\\ 0 \end{bmatrix}$ and $|S_z^-\rangle = \begin{bmatrix}0\\ 1 \end{bmatrix}$, I construct a superposition state $|S_x^+\rangle=\frac{|S_z^+\rangle+|S_z^-\rangle}{\sqrt{2}}$ for which the density matrix is given as $\rho_{S_x^+}=\frac{1}{2}\begin{bmatrix}1&1\\ 1&1\end{bmatrix}$. So the pure superposition state $|S_x^+\rangle$ is clearly coherent and it can be inferred that system coherently oscillates between the states $|S_z^+\rangle$ and $|S_z^-\rangle$ if measurement is done repeatedly with each time system being prepared in state $|S_x^+\rangle$. The question here is of terminology, should I say that states $|S_z^+\rangle$ and $|S_z^-\rangle$ are coherent or should I say that state $|S_x^+\rangle$ is coherent.

2. For an ensemble of identical atoms in a superposition state $|\phi\rangle=\alpha|S_z^+\rangle+\beta|S_z^-\rangle$ where $|\alpha|^2$ and $|\beta|^2$ are not equal(although $|\alpha|^2 + |\beta|^2 = 1$) and gives the populations of $|S_z^+\rangle$ and $|S_z^-\rangle$ respectively, we can drive a transition between the two basis states and we call this phenomenon as *population transfer* (please correct me if I am wrong). Mathematically, the field induced transitions changes the values of $|\alpha|^2$ & $|\beta|^2$.

However there can be one more phenomenon going on here called **polarization transfer** which is distinct from population transfer because polarization really counts the total spin magnetization of a state in context of NMR and EPR and may be Quantum Optics too.

Now the third phenomenon i.e. **coherence transfer **(no classical analogue) can't occur between two states but needs three level system say $|1\rangle$, $|2\rangle$ and $|3\rangle$ and the field driven transitions between states $|1\rangle$ & $|2\rangle$ and states $|1\rangle$ & $|3\rangle$ somehow creates transition of states $|2\rangle$ & $|3\rangle$ even though there is no driving field of frequency corresponding to $|2\rangle$ & $|3\rangle$ transition.

The last two phenomenon written in bolds are what I do not understand. Any insight into them will be very helpful and mathematics over them will be highly appreciated. http://140.117.34.2/faculty/phy/sw_ding/teaching/nmri01_underg/nmri01_underg_lecture04.ppt also tries to explain the difference between population transfer, polarization transfer and coherence transfer through density matrices but I cannot see much physical explanation over the phenomenons.