I Understanding the diagonal elements of the transition dipole moment

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How am I supposed to interpret the diagonal elements of the transition dipole matrix. We learned that the matrix elements ##\neq 0## tells us that a certain transition is possible but what if that matrix element is on the diagonal of my matrix. A transition from ##|2\rangle## to ##|2\rangle## for example doesn't make much sense to me.
Hey guys, I just numerically calculated the matrix elements for a superconducting qubit and I'm having some trouble to interpret the result.
I will include a plot of the matrix I got below:

Unbenannt.JPG

I basically have "large" non zero elements on the main diagonal of this matrix. In previous courses I was told that for example the matrix element ##\langle 2|d|3\rangle## would indicate me that transitions for this quantum system from ##2## to ##3## and vice versa are allowed. Therefore I have a little bit of a hard time understanding the non zero values on the main diagonal.

One interpretation I have is that the system can therefore be polarized but I'm not quite sure about that.

Would be really awesome if someone could share his opinion on this, thank you!
 
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The transition matrix can always have non-zero diagonal elements. There is some probability that no transition occurs, and that's reflected by the diagonal elements.
 
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