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In quantum optics, when we talk about atom field interaction with a classical field and quantized atom, we say that the Hamiltonian has an interaction part of the form [itex]\hat{d}.\vec{E}[/itex] where d is the dipole operator.

For a two level atom, the dipole operator has only off diagonal elements and these are of the form [itex]\langle g\mid\hat{d}\mid e\rangle[/itex]. Now, this expectation value still has a direction because we take its dot product with the polarization direction of the electric field. But, in any atom, both g and e are spherically symmetrical states so what "direction" is being talked about here?

Thank you :)