# What is the difference between population transfer, polarization transfer and coherence transfer in a quantum system?

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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.

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